diff --git a/anomaly/gmm-change-detection/CMakeLists.txt b/anomaly/gmm-change-detection/CMakeLists.txt
new file mode 100644
index 00000000..012e5d71
--- /dev/null
+++ b/anomaly/gmm-change-detection/CMakeLists.txt
@@ -0,0 +1,30 @@
+# Copyright (c) 2021, United States Government, as represented by the
+# Administrator of the National Aeronautics and Space Administration.
+#
+# All rights reserved.
+#
+# The "ISAAC - Integrated System for Autonomous and Adaptive Caretaking
+# platform" software is licensed under the Apache License, Version 2.0
+# (the "License"); you may not use this file except in compliance with the
+# License. You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
+# WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
+# License for the specific language governing permissions and limitations
+# under the License.
+
+cmake_minimum_required(VERSION 3.0 FATAL_ERROR)
+project(gmm)
+
+## Compile as C++14, supported in ROS Kinetic and newer
+add_compile_options(-std=c++14)
+
+
+## Find catkin macros and libraries
+find_package(catkin REQUIRED COMPONENTS)
+
+catkin_package()
+
diff --git a/anomaly/gmm-change-detection/README.md b/anomaly/gmm-change-detection/README.md
new file mode 100644
index 00000000..b05a4cba
--- /dev/null
+++ b/anomaly/gmm-change-detection/README.md
@@ -0,0 +1,15 @@
+\page gmm GMM Change Detection
+
+# Overview
+
+This implementation of a GMM-based anomaly detection algorithm was created by Jamie Santos, for the purposes of a [Master thesis]().
+This algorithm is able to detect changes on environments such as the ISS using 3D point depth cloud data.
+
+# Requirements
+[To-Do]
+
+## Usage
+
+ rosrun gmm gmm_change_detection.py
+
+
diff --git a/anomaly/gmm-change-detection/package.xml b/anomaly/gmm-change-detection/package.xml
new file mode 100644
index 00000000..c49a2e9f
--- /dev/null
+++ b/anomaly/gmm-change-detection/package.xml
@@ -0,0 +1,21 @@
+
+
+ gmm
+ 0.0.0
+ GMM Change Detection package
+
+ Apache License, Version 2.0
+
+
+ ISAAC Flight Software
+
+
+ ISAAC Flight Software
+
+
+ catkin
+ roscpp
+ cv_bridge
+ roscpp
+ roscpp
+
diff --git a/anomaly/gmm-change-detection/scripts/__init__.py b/anomaly/gmm-change-detection/scripts/__init__.py
new file mode 100644
index 00000000..cb0030c1
--- /dev/null
+++ b/anomaly/gmm-change-detection/scripts/__init__.py
@@ -0,0 +1 @@
+from .gmm_mml import GmmMml
diff --git a/anomaly/gmm-change-detection/scripts/artificial_data.py b/anomaly/gmm-change-detection/scripts/artificial_data.py
new file mode 100644
index 00000000..bce24197
--- /dev/null
+++ b/anomaly/gmm-change-detection/scripts/artificial_data.py
@@ -0,0 +1,122 @@
+#!/usr/bin/env python
+# Copyright (c) 2017, United States Government, as represented by the
+# Administrator of the National Aeronautics and Space Administration.
+#
+# All rights reserved.
+#
+# The Astrobee platform is licensed under the Apache License, Version 2.0
+# (the "License"); you may not use this file except in compliance with the
+# License. You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
+# WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
+# License for the specific language governing permissions and limitations
+# under the License.
+
+import copy
+
+import numpy as np
+
+
+def generate_data(n_start, n_disappearances, n_appearances):
+ N = 1000 # N points in each cluster
+ point_set_1 = []
+ point_set_2 = []
+
+ # Define first set of points
+ means_1 = np.random.uniform(-2, 2, (n_start, 3)).round(2)
+ covs_1 = np.zeros(shape=(n_start, 3, 3))
+ for i in range(n_start):
+ covs_1[i] = np.diag(np.random.uniform(-0.1, 0.1, (1, 3))[0].round(2))
+
+ # Remove old clusters in second set of points
+ means_2 = copy.deepcopy(means_1)
+ covs_2 = copy.deepcopy(covs_1)
+
+ for i in range(n_disappearances):
+ means_2 = np.delete(means_2, 0, 0)
+ covs_2 = np.delete(covs_2, 0, 0)
+
+ # Add new clusters in second set of points
+ means_appearances = np.random.uniform(-2, 2, (n_appearances, 3)).round(2)
+ covs_appearances = np.zeros(shape=(n_appearances, 3, 3))
+ for i in range(n_appearances):
+ covs_appearances[i] = np.diag(np.random.uniform(-0.1, 0.1, (1, 3))[0].round(2))
+ means_2 = np.vstack((means_2, means_appearances))
+ covs_2 = np.vstack((covs_2, covs_appearances))
+
+ # Concatenate clusters into point clouds
+ for i in range(len(means_1)):
+ x = np.random.multivariate_normal(means_1[i], covs_1[i], N)
+ point_set_1.append(x)
+ points_1 = np.concatenate(point_set_1)
+
+ for i in range(len(means_2)):
+ x = np.random.multivariate_normal(means_2[i], covs_2[i], N)
+ point_set_2.append(x)
+ points_2 = np.concatenate(point_set_2)
+
+ return points_1, points_2
+
+
+if __name__ == "__main__":
+ points_1, points_2 = generate_data(5, 3, 9)
+ print(points_1.shape, points_2.shape)
+
+# if fake_data:
+# # Generate 3D data with 4 clusters
+# # set Gaussian centers and covariances in 3D
+# means = np.array([[1, 0.0, 0.0],
+# [0.0, 0.0, 0.0],
+# [-0.5, -0.5, -0.5],
+# [-0.8, 0.3, 0.4]])
+# covs = np.array([np.diag([0.01, 0.01, 0.03]),
+# np.diag([0.08, 0.01, 0.01]),
+# np.diag([0.01, 0.05, 0.01]),
+# np.diag([0.03, 0.07, 0.01])])
+#
+# N = 1000 #Number of points to be generated for each cluster.
+# points_a = []
+# points_b = []
+#
+# for i in range(len(means)):
+# x = np.random.multivariate_normal(means[i], covs[i], N )
+# points_a.append(x)
+# points_b.append(x)
+#
+# points1 = np.concatenate(points_a)
+#
+# if appearance:
+# # Add an extra Gaussian
+# means2 = np.array([[1.5, 1.5, 1.5],
+# [0.2, 0.2, 0.2],
+# [0.8, -.03, -0.4]])
+# covs2 = np.array([np.diag([0.01, 0.01, 0.01]),
+# np.diag([0.02, 0.01, 0.03]),
+# np.diag([0.03, 0.02, 0.01])])
+#
+# for i in range(len(means2)):
+# x = np.random.multivariate_normal(means2[i], covs2[i], N )
+# points_b.append(x)
+#
+# points2 = np.concatenate(points_b)
+#
+# else:
+# # Remove an extra Gaussian
+# means2 = np.array([[1, 0.0, 0.0],
+# [0.0, 0.0, 0.0],
+# [-0.5, -0.5, -0.5]])
+# covs2 = np.array([np.diag([0.01, 0.01, 0.03]),
+# np.diag([0.08, 0.01, 0.01]),
+# np.diag([0.01, 0.05, 0.01])])
+# points_b = []
+#
+# for i in range(len(means2)):
+# x2 = np.random.multivariate_normal(means2[i], covs2[i], N )
+# points_b.append(x2)
+#
+# points2 = np.concatenate(points_b)
+#
diff --git a/anomaly/gmm-change-detection/scripts/emd_gmm.py b/anomaly/gmm-change-detection/scripts/emd_gmm.py
new file mode 100644
index 00000000..611112b7
--- /dev/null
+++ b/anomaly/gmm-change-detection/scripts/emd_gmm.py
@@ -0,0 +1,84 @@
+# https://towardsdatascience.com/linear-programming-using-python-priyansh-22b5ee888fe0
+import numpy as np
+from pulp import *
+
+
+class EMDGMM:
+ def __init__(self, gmm1_weights, gmm2_weights):
+ self.warehouse_supply = gmm1_weights # Supply Matrix
+ self.cust_demands = gmm2_weights # Demand Matrix
+ self.n_warehouses = gmm1_weights.size
+ self.n_customers = gmm2_weights.size
+ self.weight_sum1 = np.sum(self.warehouse_supply)
+ self.weight_sum2 = np.sum(self.cust_demands)
+ self.distances = None
+ self.emd = None
+
+ def get_distance(self, means1, means2):
+ """Given two GMMs, generate a distance matrix between all cluster
+ representatives (means) of GMM1 and GMM2. Output: K1 x K2 matrix"""
+
+ distances = np.zeros((means1.shape[0], means2.shape[0]))
+ for i, row1 in enumerate(means1):
+ for j, row2 in enumerate(means2):
+ distances[i][j] = np.linalg.norm(row1 - row2)
+ self.distances = distances
+
+ def calculate_emd(self):
+ """Optimize the cost-distance (weight-distance) flow between the
+ two GMMs and use the optimized distance as the EMD distance metric."""
+
+ # Cost Matrix
+ cost_matrix = self.distances
+
+ # Initialize Model
+ model = LpProblem("Supply-Demand-Problem", LpMinimize)
+
+ # Define Variable Names
+ variable_names = [
+ str(i) + "_" + str(j)
+ for j in range(1, self.n_customers + 1)
+ for i in range(1, self.n_warehouses + 1)
+ ]
+ variable_names.sort()
+
+ # Decision Variables
+ DV_variables = LpVariable.matrix(
+ "X", variable_names, cat="Continuous", lowBound=0
+ )
+ allocation = np.array(DV_variables).reshape(self.n_warehouses, self.n_customers)
+
+ # Objective Function
+ obj_func = lpSum(allocation * cost_matrix)
+ model += obj_func
+
+ # Constraints
+ for i in range(self.n_warehouses):
+ # print(lpSum(allocation[i][j] for j in range(self.n_customers)) <= warehouse_supply[i])
+ model += lpSum(
+ allocation[i][j] for j in range(self.n_customers)
+ ) <= self.warehouse_supply[i], "Supply Constraints " + str(i)
+
+ for j in range(self.n_customers):
+ # print(lpSum(allocation[i][j] for i in range(self.n_warehouses)) >= cust_demands[j])
+ model += lpSum(
+ allocation[i][j] for i in range(self.n_warehouses)
+ ) >= self.cust_demands[j], "Demand Constraints " + str(j)
+
+ model.solve(GLPK_CMD(msg=0))
+ status = LpStatus[model.status]
+ # print(status)
+
+ # print("Total Cost:", model.objective.value())
+ # for v in model.variables():
+ # try:
+ # print(v.name, "=", v.value())
+ # except:
+ # print("error couldn't find value")
+
+ # for i in range(self.n_warehouses):
+ # print("Warehouse ", str(i+1))
+ # print(lpSum(allocation[i][j].value() for j in range(self.n_customers)))
+
+ total_flow = min(self.weight_sum1, self.weight_sum2)
+ self.emd = model.objective.value() / total_flow
diff --git a/anomaly/gmm-change-detection/scripts/example_code/emd/emd_gmm.py b/anomaly/gmm-change-detection/scripts/example_code/emd/emd_gmm.py
new file mode 100644
index 00000000..79576e58
--- /dev/null
+++ b/anomaly/gmm-change-detection/scripts/example_code/emd/emd_gmm.py
@@ -0,0 +1,46 @@
+import numpy as np
+
+
+def earth_movers_distance(m1, m2):
+ """Compute the Earth Movers Distance between two Gaussian mixture models.
+
+ Parameters
+ ----------
+ m1 : np.ndarray
+ Array of means and covariances of the first Gaussian mixture model.
+ m2 : np.ndarray
+ Array of means and covariances of the second Gaussian mixture model.
+
+ Returns
+ -------
+ np.ndarray
+ Earth Movers Distance between the two Gaussian mixture models.
+ """
+ # Compute the mean and covariance of the combined Gaussian mixture model.
+ mean_combined = (m1.mean() + m2.mean()) / 2
+ covariance_combined = (m1.covariance() + m2.covariance()) / 2
+
+ # Compute the Earth Movers Distance between the two Gaussian mixture models.
+ earth_movers_distance = np.linalg.norm(mean_combined - m1.mean()) + np.linalg.norm(
+ mean_combined - m2.mean()
+ )
+
+ return earth_movers_distance
+
+
+def main():
+ m1 = np.random.multivariate_normal(mean=[0, 0, 0], covariance=np.eye(3))
+ m2 = np.random.multivariate_normal(mean=[1, 2, 3], covariance=np.eye(3))
+
+ # Compute the Earth Movers Distance between the two Gaussian mixture models.
+ earth_movers_distance = earth_movers_distance(m1, m2)
+
+ # Print the Earth Movers Distance.
+ print(
+ "The Earth Movers Distance between the two Gaussian mixture models is "
+ + earth_movers_distance
+ )
+
+
+if __name__ == "__main__":
+ main()
diff --git a/anomaly/gmm-change-detection/scripts/example_code/emd/emd_numpy.py b/anomaly/gmm-change-detection/scripts/example_code/emd/emd_numpy.py
new file mode 100644
index 00000000..3310f515
--- /dev/null
+++ b/anomaly/gmm-change-detection/scripts/example_code/emd/emd_numpy.py
@@ -0,0 +1,45 @@
+import numpy as np
+
+
+def earth_movers_distance(m1, m2):
+ """Compute the Earth Movers Distance between two Gaussian mixture models.
+
+ Parameters
+ ----------
+ m1 : np.ndarray
+ Array of means and covariances of the first Gaussian mixture model.
+ m2 : np.ndarray
+ Array of means and covariances of the second Gaussian mixture model.
+
+ Returns
+ -------
+ np.ndarray
+ Earth Movers Distance between the two Gaussian mixture models.
+ """
+ # Compute the mean and covariance of the combined Gaussian mixture model.
+ mean_combined = (m1.mean() + m2.mean()) / 2
+ covariance_combined = (np.cov(m1) + np.cov(m2)) / 2
+
+ # Compute the Earth Movers Distance between the two Gaussian mixture models.
+ earth_movers_distance = np.linalg.norm(mean_combined - m1.mean()) + np.linalg.norm(
+ mean_combined - m2.mean()
+ )
+
+ return earth_movers_distance
+
+
+def main():
+ m1 = np.random.multivariate_normal((0, 0, 0), np.eye(3))
+ m2 = np.random.multivariate_normal((1, 2, 3), np.eye(3))
+ print(m1.shape)
+ print(m1)
+
+ # Compute the Earth Movers Distance between the two Gaussian mixture models.
+ emd = earth_movers_distance(m1, m2)
+
+ # Print the Earth Movers Distance.
+ print(emd)
+
+
+if __name__ == "__main__":
+ main()
diff --git a/anomaly/gmm-change-detection/scripts/example_code/emd/emd_numpy_was.py b/anomaly/gmm-change-detection/scripts/example_code/emd/emd_numpy_was.py
new file mode 100644
index 00000000..6b485d70
--- /dev/null
+++ b/anomaly/gmm-change-detection/scripts/example_code/emd/emd_numpy_was.py
@@ -0,0 +1,49 @@
+import matplotlib.pyplot as plt
+import numpy as np
+
+
+def emd(m1, m2):
+ """Computes the Earth Movers Distance between two 3D Gaussian mixture models.
+
+ Args:
+ m1 (numpy.ndarray): The first 3D Gaussian mixture model.
+ m2 (numpy.ndarray): The second 3D Gaussian mixture model.
+
+ Returns:
+ numpy.ndarray: The Earth Movers Distance between the two models.
+ """
+ # Compute the ground distance matrix.
+ d = np.linalg.norm(m1 - m2, axis=2)
+
+ # Compute the Earth Movers Distance.
+ EMD = np.sum(np.min(d, d.T))
+
+ return EMD
+
+
+def wasserstein(m1, m2):
+ """Computes the Wasserstein Distance between two 3D Gaussian mixture models.
+
+ Args:
+ m1 (numpy.ndarray): The first 3D Gaussian mixture model.
+ m2 (numpy.ndarray): The second 3D Gaussian mixture model.
+
+ Returns:
+ numpy.ndarray: The Wasserstein Distance between the two models.
+ """
+ # Compute the optimal transport matrix.
+ T = np.argmin(np.sum(m1**2) + np.sum(m2**2) - 2 * np.dot(m1, m2))
+
+ # Compute the Wasserstein Distance.
+ Wasserstein = np.sum(np.dot(m1, T) * d)
+
+ return Wasserstein
+
+
+# Generate two 3D Gaussian mixture models.
+m1 = np.random.multivariate_normal(mean=np.array([0, 0, 0]), cov=np.eye(3), size=100)
+m2 = np.random.multivariate_normal(mean=np.array([1, 1, 1]), cov=np.eye(3), size=100)
+
+# Compute the Earth Movers Distance and Wasserstein Distance.
+# EMD = emd(m1, m2)
+Wasserstein = wasserstein(m1, m2)
diff --git a/anomaly/gmm-change-detection/scripts/example_code/emd/emd_test.py b/anomaly/gmm-change-detection/scripts/example_code/emd/emd_test.py
new file mode 100644
index 00000000..5f8e9655
--- /dev/null
+++ b/anomaly/gmm-change-detection/scripts/example_code/emd/emd_test.py
@@ -0,0 +1,27 @@
+import numpy as np
+from sklearn.mixture import GaussianMixture
+
+# Define the first GMM
+gmm1 = GaussianMixture(n_components=2, covariance_type="full", random_state=42)
+X1 = np.random.randn(100, 2)
+gmm1.fit(X1)
+
+# Define the second GMM
+gmm2 = GaussianMixture(n_components=3, covariance_type="full", random_state=42)
+X2 = np.random.randn(100, 2)
+gmm2.fit(X2)
+
+from scipy.stats import wasserstein_distance
+
+# Extract the means and weights from the first GMM
+means1 = gmm1.means_
+weights1 = gmm1.weights_
+
+# Extract the means and weights from the second GMM
+means2 = gmm2.means_
+weights2 = gmm2.weights_
+
+emd = wasserstein_distance(
+ weights1, weights2, np.linalg.norm(means1[:, np.newaxis] - means2, axis=-1)
+)
+print(emd)
diff --git a/anomaly/gmm-change-detection/scripts/example_code/emd/emd_test_3d.py b/anomaly/gmm-change-detection/scripts/example_code/emd/emd_test_3d.py
new file mode 100644
index 00000000..76ec964e
--- /dev/null
+++ b/anomaly/gmm-change-detection/scripts/example_code/emd/emd_test_3d.py
@@ -0,0 +1,40 @@
+import numpy as np
+from scipy.stats import wasserstein_distance
+from sklearn.mixture import GaussianMixture
+
+# Generate some data
+np.random.seed(0)
+n_samples = 1000
+X1 = np.concatenate(
+ [
+ np.random.normal(-1, 1, int(0.3 * n_samples)),
+ np.random.normal(5, 1, int(0.7 * n_samples)),
+ ]
+).reshape(-1, 1)
+X2 = np.concatenate(
+ [
+ np.random.normal(0, 2, int(0.4 * n_samples)),
+ np.random.normal(3, 1, int(0.6 * n_samples)),
+ ]
+).reshape(-1, 1)
+
+# Fit Gaussian mixture models to the data
+gm1 = GaussianMixture(n_components=2, random_state=0)
+gm1.fit(X1)
+gm2 = GaussianMixture(n_components=2, random_state=0)
+gm2.fit(X2)
+
+# Get the means and covariances of the components
+means1 = gm1.means_.ravel()
+covs1 = gm1.covariances_.ravel()
+weights1 = gm1.weights_
+
+means2 = gm2.means_.ravel()
+covs2 = gm2.covariances_.ravel()
+weights2 = gm2.weights_
+
+# Calculate the EMD between the GMMs
+emd = wasserstein_distance(
+ means1, means2, u_weights=weights1, v_weights=weights2, metric="euclidean"
+)
+print("The EMD between the two GMMs is: " + emd)
diff --git a/anomaly/gmm-change-detection/scripts/example_code/emd/emd_test_3d_pyemd.py b/anomaly/gmm-change-detection/scripts/example_code/emd/emd_test_3d_pyemd.py
new file mode 100644
index 00000000..b4c39ca1
--- /dev/null
+++ b/anomaly/gmm-change-detection/scripts/example_code/emd/emd_test_3d_pyemd.py
@@ -0,0 +1,42 @@
+import numpy as np
+import pyemd
+from sklearn.mixture import GaussianMixture
+
+# Generate some random data for two Gaussian mixture models
+np.random.seed(0)
+n_samples = 1000
+X1 = np.concatenate(
+ [
+ np.random.normal(-1, 1, int(0.3 * n_samples)),
+ np.random.normal(5, 1, int(0.7 * n_samples)),
+ ]
+).reshape(-1, 1)
+X2 = np.concatenate(
+ [
+ np.random.normal(0, 2, int(0.4 * n_samples)),
+ np.random.normal(3, 1, int(0.6 * n_samples)),
+ ]
+).reshape(-1, 1)
+
+# Fit Gaussian mixture models to the data
+gm1 = GaussianMixture(n_components=2, random_state=0)
+gm1.fit(X1)
+gm2 = GaussianMixture(n_components=2, random_state=0)
+gm2.fit(X2)
+
+# Get the means and covariances of the components
+means1 = gm1.means_.ravel()
+covs1 = gm1.covariances_.ravel()
+means2 = gm2.means_.ravel()
+covs2 = gm2.covariances_.ravel()
+
+# Create the distance matrix between the means
+D = pyemd.euclidean_distances(means1.reshape(-1, 1), means2.reshape(-1, 1))
+
+# Create the flow matrix between the components
+flow = pyemd.emd(
+ gm1.weights_, gm2.weights_, D, covs1.reshape(-1, 1), covs2.reshape(-1, 1)
+)
+
+# Print the EMD between the two Gaussian mixture models
+print("EMD between the two Gaussian mixture models: {:.2f}".format(flow))
diff --git a/anomaly/gmm-change-detection/scripts/example_code/gmm/gmm_em.py b/anomaly/gmm-change-detection/scripts/example_code/gmm/gmm_em.py
new file mode 100644
index 00000000..694464f8
--- /dev/null
+++ b/anomaly/gmm-change-detection/scripts/example_code/gmm/gmm_em.py
@@ -0,0 +1,247 @@
+# This code is taken from a tutorial from the following website:
+# https://python-course.eu/machine-learning/expectation-maximization-and-gaussian-mixture-models-gmm.php
+
+import matplotlib.pyplot as plt
+from matplotlib import style
+from mpl_toolkits import mplot3d
+
+style.use("fivethirtyeight")
+import numpy as np
+from scipy.stats import multivariate_normal
+from sklearn.datasets.samples_generator import make_blobs
+
+DEBUG = 0
+
+# 0. Create dataset
+X, Y = make_blobs(
+ cluster_std=1.5, n_features=3, random_state=20, n_samples=50, centers=3
+)
+
+# Stretch dataset to get ellipsoid data
+X = np.dot(X, np.random.RandomState(0).randn(3, 3))
+
+print(X.shape)
+
+
+class GMM:
+ def __init__(self, X, number_of_sources, iterations):
+ self.iterations = iterations
+ self.number_of_sources = number_of_sources
+ self.X = X
+ self.mu = None
+ self.pi = None
+ self.cov = None
+ self.XYZ = None
+
+ """Define a function which runs for iterations, iterations"""
+
+ def run(self):
+ self.reg_cov = 1e-6 * np.identity(len(self.X[0]))
+ x, y, z = np.meshgrid(
+ np.sort(self.X[:, 0]), np.sort(self.X[:, 1]), np.sort(self.X[:, 2])
+ )
+ self.XYZ = np.array([x.flatten(), y.flatten(), z.flatten()]).T
+
+ """ 1. Set the initial mu, covariance and pi values"""
+ self.mu = np.random.randint(
+ min(self.X[:, 0]),
+ max(self.X[:, 0]),
+ size=(self.number_of_sources, len(self.X[0])),
+ ) # This is a nxm matrix since we assume n sources (n Gaussians) where each has m dimensions
+ self.cov = np.zeros(
+ (self.number_of_sources, len(X[0]), len(X[0]))
+ ) # We need a nxmxm covariance matrix for each source since we have m features --> We create symmetric covariance matrices with ones on the digonal
+ for dim in range(len(self.cov)):
+ np.fill_diagonal(self.cov[dim], 5)
+
+ self.pi = (
+ np.ones(self.number_of_sources) / self.number_of_sources
+ ) # Are "Fractions"
+ log_likelihoods = (
+ []
+ ) # In this list we store the log likehoods per iteration and plot them in the end to check if
+ # if we have converged
+
+ if DEBUG:
+ #################################################
+ print("Debug enabled")
+ x = X[:, 0]
+ y = X[:, 1]
+ z = X[:, 2]
+
+ # Creating figures for the plot
+ fig = plt.figure(figsize=(10, 7))
+ ax = plt.axes(projection="3d")
+
+ # Creating a plot using the random datasets
+ ax.scatter3D(x, y, z, color="red")
+ plt.title("3D scatter plot")
+
+ # display the plot
+ plt.show()
+ #################################################
+
+ """Plot the initial state"""
+ fig = plt.figure(figsize=(10, 10))
+ ax0 = plt.axes(projection="3d")
+ # ax0 = fig.add_subplot(111)
+ ax0.scatter3D(self.X[:, 0], self.X[:, 1], self.X[:, 2])
+ ax0.set_title("Initial state")
+ for m, c in zip(self.mu, self.cov):
+ c += self.reg_cov
+ multi_normal = multivariate_normal(mean=m, cov=c)
+ # ax0.contour(np.sort(self.X[:,0]),np.sort(self.X[:,1]),np.sort(self.X[:,2]),multi_normal.pdf(self.XYZ).reshape(len(self.X),len(self.X),len(self.X)),colors='black',alpha=0.3)
+ # ax0.contour3D(np.sort(self.X[:,0]),np.sort(self.X[:,1]),np.sort(self.X[:,2]).reshape((len(self.X[:,0]),len(self.X[:,1]))),multi_normal.pdf(self.XYZ).reshape(len(self.X),len(self.X),len(self.X)),colors='black',alpha=0.3)
+ ax0.scatter(m[0], m[1], c="grey", zorder=10, s=100)
+
+ for i in range(self.iterations):
+
+ """E Step"""
+ r_ic = np.zeros((len(self.X), len(self.cov)))
+
+ for m, co, p, r in zip(self.mu, self.cov, self.pi, range(len(r_ic[0]))):
+ co += self.reg_cov
+ mn = multivariate_normal(mean=m, cov=co)
+ r_ic[:, r] = (
+ p
+ * mn.pdf(self.X)
+ / np.sum(
+ [
+ pi_c * multivariate_normal(mean=mu_c, cov=cov_c).pdf(X)
+ for pi_c, mu_c, cov_c in zip(
+ self.pi, self.mu, self.cov + self.reg_cov
+ )
+ ],
+ axis=0,
+ )
+ )
+
+ """
+ The above calculation of r_ic is not that obvious why I want to quickly derive what we have done above.
+ First of all the nominator:
+ We calculate for each source c which is defined by m,co and p for every instance x_i, the multivariate_normal.pdf() value.
+ For each loop this gives us a 100x1 matrix (This value divided by the denominator is then assigned to r_ic[:,r] which is in
+ the end a 100x3 matrix).
+ Second the denominator:
+ What we do here is, we calculate the multivariate_normal.pdf() for every instance x_i for every source c which is defined by
+ pi_c, mu_c, and cov_c and write this into a list. This gives us a 3x100 matrix where we have 100 entrances per source c.
+ Now the formula wants us to add up the pdf() values given by the 3 sources for each x_i. Hence we sum up this list over axis=0.
+ This gives us then a list with 100 entries.
+ What we have now is FOR EACH LOOP a list with 100 entries in the nominator and a list with 100 entries in the denominator
+ where each element is the pdf per class c for each instance x_i (nominator) respectively the summed pdf's of classes c for each
+ instance x_i. Consequently we can now divide the nominator by the denominator and have as result a list with 100 elements which we
+ can then assign to r_ic[:,r] --> One row r per source c. In the end after we have done this for all three sources (three loops)
+ and run from r==0 to r==2 we get a matrix with dimensionallity 100x3 which is exactly what we want.
+ If we check the entries of r_ic we see that there mostly one element which is much larger than the other two. This is because
+ every instance x_i is much closer to one of the three gaussians (that is, much more likely to come from this gaussian) than
+ it is to the other two. That is practically speaing, r_ic gives us the fraction of the probability that x_i belongs to class
+ c over the probability that x_i belonges to any of the classes c (Probability that x_i occurs given the 3 Gaussians).
+ """
+
+ """M Step"""
+
+ # Calculate the new mean vector and new covariance matrices, based on the probable membership of the single x_i to classes c --> r_ic
+ self.mu = []
+ self.cov = []
+ self.pi = []
+ log_likelihood = []
+
+ for c in range(len(r_ic[0])):
+ m_c = np.sum(r_ic[:, c], axis=0)
+ mu_c = (1 / m_c) * np.sum(
+ self.X * r_ic[:, c].reshape(len(self.X), 1), axis=0
+ )
+ self.mu.append(mu_c)
+
+ # Calculate the covariance matrix per source based on the new mean
+ self.cov.append(
+ (
+ (1 / m_c)
+ * np.dot(
+ (
+ np.array(r_ic[:, c]).reshape(len(self.X), 1)
+ * (self.X - mu_c)
+ ).T,
+ (self.X - mu_c),
+ )
+ )
+ + self.reg_cov
+ )
+ # Calculate pi_new which is the "fraction of points" respectively the fraction of the probability assigned to each source
+ self.pi.append(
+ m_c / np.sum(r_ic)
+ ) # Here np.sum(r_ic) gives as result the number of instances. This is logical since we know
+ # that the columns of each row of r_ic adds up to 1. Since we add up all elements, we sum up all
+ # columns per row which gives 1 and then all rows which gives then the number of instances (rows)
+ # in X --> Since pi_new contains the fractions of datapoints, assigned to the sources c,
+ # The elements in pi_new must add up to 1
+
+ """Log likelihood"""
+ log_likelihoods.append(
+ np.log(
+ np.sum(
+ [
+ k * multivariate_normal(self.mu[i], self.cov[j]).pdf(X)
+ for k, i, j in zip(
+ self.pi, range(len(self.mu)), range(len(self.cov))
+ )
+ ]
+ )
+ )
+ )
+
+ """
+ This process of E step followed by a M step is now iterated a number of n times. In the second step for instance,
+ we use the calculated pi_new, mu_new and cov_new to calculate the new r_ic which are then used in the second M step
+ to calculat the mu_new2 and cov_new2 and so on....
+ """
+
+ fig2 = plt.figure(figsize=(10, 10))
+ ax1 = fig2.add_subplot(111)
+ ax1.set_title("Log-Likelihood")
+ ax1.plot(range(0, self.iterations, 1), log_likelihoods)
+ plt.show()
+
+ """Predict the membership of an unseen, new datapoint"""
+
+ def predict(self, Y):
+ # PLot the point onto the fittet gaussians
+ fig3 = plt.figure(figsize=(10, 10))
+ # ax2 = fig3.add_subplot(111)
+ ax2 = fig3.add_subplot(projection="3d")
+ ax2.scatter(self.X[:, 0], self.X[:, 1], self.X[:, 2])
+ for m, c in zip(self.mu, self.cov):
+ multi_normal = multivariate_normal(mean=m, cov=c)
+ ax2.contour(
+ np.sort(self.X[:, 0]),
+ np.sort(self.X[:, 1]),
+ np.sort(self.X[:, 2]),
+ multi_normal.pdf(self.XY).reshape(
+ len(self.X), len(self.X), len(self.X)
+ ),
+ colors="black",
+ alpha=0.3,
+ )
+ ax2.scatter(m[0], m[1], c="grey", zorder=10, s=100)
+ ax2.set_title("Final state")
+ for y in Y:
+ ax2.scatter(y[0], y[1], c="orange", zorder=10, s=100)
+ prediction = []
+ for m, c in zip(self.mu, self.cov):
+ print(c)
+ prediction.append(
+ multivariate_normal(mean=m, cov=c).pdf(Y)
+ / np.sum(
+ [
+ multivariate_normal(mean=mean, cov=cov).pdf(Y)
+ for mean, cov in zip(self.mu, self.cov)
+ ]
+ )
+ )
+ plt.show()
+ return prediction
+
+
+GMM = GMM(X, 3, 100)
+GMM.run()
+GMM.predict([[0.5, 0.5]])
diff --git a/anomaly/gmm-change-detection/scripts/example_code/gmm/gmm_em_example.py b/anomaly/gmm-change-detection/scripts/example_code/gmm/gmm_em_example.py
new file mode 100644
index 00000000..c3101fa4
--- /dev/null
+++ b/anomaly/gmm-change-detection/scripts/example_code/gmm/gmm_em_example.py
@@ -0,0 +1,219 @@
+# This code is taken from a tutorial from the following website:
+# https://python-course.eu/machine-learning/expectation-maximization-and-gaussian-mixture-models-gmm.php
+
+import matplotlib.pyplot as plt
+from matplotlib import style
+
+style.use("fivethirtyeight")
+import numpy as np
+from scipy.stats import multivariate_normal
+from sklearn.datasets.samples_generator import make_blobs
+
+# 0. Create dataset
+X, Y = make_blobs(cluster_std=1.5, random_state=20, n_samples=500, centers=3)
+
+# Stratch dataset to get ellipsoid data
+X = np.dot(X, np.random.RandomState(0).randn(2, 2))
+
+
+class GMM:
+ def __init__(self, X, number_of_sources, iterations):
+ self.iterations = iterations
+ self.number_of_sources = number_of_sources
+ self.X = X
+ self.mu = None
+ self.pi = None
+ self.cov = None
+ self.XY = None
+
+ """Define a function which runs for iterations, iterations"""
+
+ def run(self):
+ self.reg_cov = 1e-6 * np.identity(len(self.X[0]))
+ x, y = np.meshgrid(np.sort(self.X[:, 0]), np.sort(self.X[:, 1]))
+ self.XY = np.array([x.flatten(), y.flatten()]).T
+
+ """ 1. Set the initial mu, covariance and pi values"""
+ self.mu = np.random.randint(
+ min(self.X[:, 0]),
+ max(self.X[:, 0]),
+ size=(self.number_of_sources, len(self.X[0])),
+ ) # This is a nxm matrix since we assume n sources (n Gaussians) where each has m dimensions
+ self.cov = np.zeros(
+ (self.number_of_sources, len(X[0]), len(X[0]))
+ ) # We need a nxmxm covariance matrix for each source since we have m features --> We create symmetric covariance matrices with ones on the digonal
+ for dim in range(len(self.cov)):
+ np.fill_diagonal(self.cov[dim], 5)
+
+ self.pi = (
+ np.ones(self.number_of_sources) / self.number_of_sources
+ ) # Are "Fractions"
+ log_likelihoods = (
+ []
+ ) # In this list we store the log likehoods per iteration and plot them in the end to check if
+ # if we have converged
+
+ """Plot the initial state"""
+ fig = plt.figure(figsize=(10, 10))
+ ax0 = fig.add_subplot(111)
+ ax0.scatter(self.X[:, 0], self.X[:, 1])
+ ax0.set_title("Initial state")
+ for m, c in zip(self.mu, self.cov):
+ c += self.reg_cov
+ multi_normal = multivariate_normal(mean=m, cov=c)
+ ax0.contour(
+ np.sort(self.X[:, 0]),
+ np.sort(self.X[:, 1]),
+ multi_normal.pdf(self.XY).reshape(len(self.X), len(self.X)),
+ colors="black",
+ alpha=0.3,
+ )
+ ax0.scatter(m[0], m[1], c="grey", zorder=10, s=100)
+
+ for i in range(self.iterations):
+
+ """E Step"""
+ r_ic = np.zeros((len(self.X), len(self.cov)))
+
+ for m, co, p, r in zip(self.mu, self.cov, self.pi, range(len(r_ic[0]))):
+ co += self.reg_cov
+ mn = multivariate_normal(mean=m, cov=co)
+ r_ic[:, r] = (
+ p
+ * mn.pdf(self.X)
+ / np.sum(
+ [
+ pi_c * multivariate_normal(mean=mu_c, cov=cov_c).pdf(X)
+ for pi_c, mu_c, cov_c in zip(
+ self.pi, self.mu, self.cov + self.reg_cov
+ )
+ ],
+ axis=0,
+ )
+ )
+
+ """
+ The above calculation of r_ic is not that obvious why I want to quickly derive what we have done above.
+ First of all the nominator:
+ We calculate for each source c which is defined by m,co and p for every instance x_i, the multivariate_normal.pdf() value.
+ For each loop this gives us a 100x1 matrix (This value divided by the denominator is then assigned to r_ic[:,r] which is in
+ the end a 100x3 matrix).
+ Second the denominator:
+ What we do here is, we calculate the multivariate_normal.pdf() for every instance x_i for every source c which is defined by
+ pi_c, mu_c, and cov_c and write this into a list. This gives us a 3x100 matrix where we have 100 entrances per source c.
+ Now the formula wants us to add up the pdf() values given by the 3 sources for each x_i. Hence we sum up this list over axis=0.
+ This gives us then a list with 100 entries.
+ What we have now is FOR EACH LOOP a list with 100 entries in the nominator and a list with 100 entries in the denominator
+ where each element is the pdf per class c for each instance x_i (nominator) respectively the summed pdf's of classes c for each
+ instance x_i. Consequently we can now divide the nominator by the denominator and have as result a list with 100 elements which we
+ can then assign to r_ic[:,r] --> One row r per source c. In the end after we have done this for all three sources (three loops)
+ and run from r==0 to r==2 we get a matrix with dimensionallity 100x3 which is exactly what we want.
+ If we check the entries of r_ic we see that there mostly one element which is much larger than the other two. This is because
+ every instance x_i is much closer to one of the three gaussians (that is, much more likely to come from this gaussian) than
+ it is to the other two. That is practically speaing, r_ic gives us the fraction of the probability that x_i belongs to class
+ c over the probability that x_i belonges to any of the classes c (Probability that x_i occurs given the 3 Gaussians).
+ """
+
+ """M Step"""
+
+ # Calculate the new mean vector and new covariance matrices, based on the probable membership of the single x_i to classes c --> r_ic
+ self.mu = []
+ self.cov = []
+ self.pi = []
+ log_likelihood = []
+
+ for c in range(len(r_ic[0])):
+ m_c = np.sum(r_ic[:, c], axis=0)
+ mu_c = (1 / m_c) * np.sum(
+ self.X * r_ic[:, c].reshape(len(self.X), 1), axis=0
+ )
+ self.mu.append(mu_c)
+
+ # Calculate the covariance matrix per source based on the new mean
+ self.cov.append(
+ (
+ (1 / m_c)
+ * np.dot(
+ (
+ np.array(r_ic[:, c]).reshape(len(self.X), 1)
+ * (self.X - mu_c)
+ ).T,
+ (self.X - mu_c),
+ )
+ )
+ + self.reg_cov
+ )
+ # Calculate pi_new which is the "fraction of points" respectively the fraction of the probability assigned to each source
+ self.pi.append(
+ m_c / np.sum(r_ic)
+ ) # Here np.sum(r_ic) gives as result the number of instances. This is logical since we know
+ # that the columns of each row of r_ic adds up to 1. Since we add up all elements, we sum up all
+ # columns per row which gives 1 and then all rows which gives then the number of instances (rows)
+ # in X --> Since pi_new contains the fractions of datapoints, assigned to the sources c,
+ # The elements in pi_new must add up to 1
+
+ """Log likelihood"""
+ log_likelihoods.append(
+ np.log(
+ np.sum(
+ [
+ k * multivariate_normal(self.mu[i], self.cov[j]).pdf(X)
+ for k, i, j in zip(
+ self.pi, range(len(self.mu)), range(len(self.cov))
+ )
+ ]
+ )
+ )
+ )
+
+ """
+ This process of E step followed by a M step is now iterated a number of n times. In the second step for instance,
+ we use the calculated pi_new, mu_new and cov_new to calculate the new r_ic which are then used in the second M step
+ to calculat the mu_new2 and cov_new2 and so on....
+ """
+
+ fig2 = plt.figure(figsize=(10, 10))
+ ax1 = fig2.add_subplot(111)
+ ax1.set_title("Log-Likelihood")
+ ax1.plot(range(0, self.iterations, 1), log_likelihoods)
+ plt.show()
+
+ """Predict the membership of an unseen, new datapoint"""
+
+ def predict(self, Y):
+ # PLot the point onto the fittet gaussians
+ fig3 = plt.figure(figsize=(10, 10))
+ ax2 = fig3.add_subplot(111)
+ ax2.scatter(self.X[:, 0], self.X[:, 1])
+ for m, c in zip(self.mu, self.cov):
+ multi_normal = multivariate_normal(mean=m, cov=c)
+ ax2.contour(
+ np.sort(self.X[:, 0]),
+ np.sort(self.X[:, 1]),
+ multi_normal.pdf(self.XY).reshape(len(self.X), len(self.X)),
+ colors="black",
+ alpha=0.3,
+ )
+ ax2.scatter(m[0], m[1], c="grey", zorder=10, s=100)
+ ax2.set_title("Final state")
+ for y in Y:
+ ax2.scatter(y[0], y[1], c="orange", zorder=10, s=100)
+ prediction = []
+ for m, c in zip(self.mu, self.cov):
+ print(c)
+ prediction.append(
+ multivariate_normal(mean=m, cov=c).pdf(Y)
+ / np.sum(
+ [
+ multivariate_normal(mean=mean, cov=cov).pdf(Y)
+ for mean, cov in zip(self.mu, self.cov)
+ ]
+ )
+ )
+ plt.show()
+ return prediction
+
+
+GMM = GMM(X, 3, 50)
+GMM.run()
+GMM.predict([[0.5, 0.5]])
diff --git a/anomaly/gmm-change-detection/scripts/example_code/gmm/gmm_sklearn.py b/anomaly/gmm-change-detection/scripts/example_code/gmm/gmm_sklearn.py
new file mode 100644
index 00000000..3424e9dc
--- /dev/null
+++ b/anomaly/gmm-change-detection/scripts/example_code/gmm/gmm_sklearn.py
@@ -0,0 +1,47 @@
+# This code was taken from a tutorial from the following website:
+# https://python-course.eu/machine-learning/expectation-maximization-and-gaussian-mixture-models-gmm.php
+
+import matplotlib.pyplot as plt
+from matplotlib import style
+
+style.use("fivethirtyeight")
+import numpy as np
+from mpl_toolkits import mplot3d
+from scipy.stats import multivariate_normal
+from sklearn.datasets.samples_generator import make_blobs
+from sklearn.mixture import GaussianMixture
+from visualization import visualize_3d_gmm
+
+# 0. Create dataset
+X, Y = make_blobs(
+ cluster_std=0.5, random_state=20, n_features=3, n_samples=100, centers=5
+)
+
+# Stratch dataset to get ellipsoid data
+X = np.dot(X, np.random.RandomState(0).randn(3, 3))
+
+x, y, z = np.meshgrid(np.sort(X[:, 0]), np.sort(X[:, 1]), np.sort(X[:, 2]))
+XY = np.array([x.flatten(), y.flatten(), z.flatten()]).T
+
+GMM = GaussianMixture(n_components=10).fit(X) # Instantiate and fit the model
+print("Converged:", GMM.converged_) # Check if the model has converged
+means = GMM.means_
+covariances = GMM.covariances_
+
+
+# Predict
+Y = np.array([[0.5], [0.5], [0.5]])
+prediction = GMM.predict_proba(Y.T)
+print(prediction)
+
+# Plot
+# fig = plt.figure(figsize=(10,10))
+# ax0 = plt.axes(projection="3d")
+# ax0.scatter3D(X[:,0],X[:,1],X[:,2])
+# ax0.scatter3D(Y[0,:],Y[1,:],Y[2,:],c='orange',zorder=10,s=100)
+for m, c in zip(means, covariances):
+ multi_normal = multivariate_normal(mean=m, cov=c)
+ # ax0.contour3D(np.sort(X[:,0]),np.sort(X[:,1]),np.sort(X[:,2]),multi_normal.pdf(XY).reshape(len(X),len(X),len(X)),colors='black',alpha=0.3)
+ # ax0.scatter3D(m[0],m[1],m[3],c='grey',zorder=10,s=100)
+visualize_3d_gmm(X, GMM.weights_, means.T, np.sqrt(covariances).T)
+# plt.show()
diff --git a/anomaly/gmm-change-detection/scripts/example_code/gmm/gmm_sklearn_example.py b/anomaly/gmm-change-detection/scripts/example_code/gmm/gmm_sklearn_example.py
new file mode 100644
index 00000000..80f00af7
--- /dev/null
+++ b/anomaly/gmm-change-detection/scripts/example_code/gmm/gmm_sklearn_example.py
@@ -0,0 +1,48 @@
+# This code was taken from a tutorial from the following website:
+# https://python-course.eu/machine-learning/expectation-maximization-and-gaussian-mixture-models-gmm.php
+
+import matplotlib.pyplot as plt
+from matplotlib import style
+
+style.use("fivethirtyeight")
+import numpy as np
+from scipy.stats import multivariate_normal
+from sklearn.datasets.samples_generator import make_blobs
+from sklearn.mixture import GaussianMixture
+
+# 0. Create dataset
+X, Y = make_blobs(cluster_std=0.5, random_state=20, n_samples=1000, centers=5)
+
+# Stratch dataset to get ellipsoid data
+X = np.dot(X, np.random.RandomState(0).randn(2, 2))
+
+x, y = np.meshgrid(np.sort(X[:, 0]), np.sort(X[:, 1]))
+XY = np.array([x.flatten(), y.flatten()]).T
+
+GMM = GaussianMixture(n_components=5).fit(X) # Instantiate and fit the model
+print("Converged:", GMM.converged_) # Check if the model has converged
+means = GMM.means_
+covariances = GMM.covariances_
+
+
+# Predict
+Y = np.array([[0.5], [0.5]])
+prediction = GMM.predict_proba(Y.T)
+print(prediction)
+
+# Plot
+fig = plt.figure(figsize=(10, 10))
+ax0 = fig.add_subplot(111)
+ax0.scatter(X[:, 0], X[:, 1])
+ax0.scatter(Y[0, :], Y[1, :], c="orange", zorder=10, s=100)
+for m, c in zip(means, covariances):
+ multi_normal = multivariate_normal(mean=m, cov=c)
+ ax0.contour(
+ np.sort(X[:, 0]),
+ np.sort(X[:, 1]),
+ multi_normal.pdf(XY).reshape(len(X), len(X)),
+ colors="black",
+ alpha=0.3,
+ )
+ ax0.scatter(m[0], m[1], c="grey", zorder=10, s=100)
+plt.show()
diff --git a/anomaly/gmm-change-detection/scripts/example_code/linear_programming.py b/anomaly/gmm-change-detection/scripts/example_code/linear_programming.py
new file mode 100644
index 00000000..70e87f19
--- /dev/null
+++ b/anomaly/gmm-change-detection/scripts/example_code/linear_programming.py
@@ -0,0 +1,63 @@
+# https://towardsdatascience.com/linear-programming-using-python-priyansh-22b5ee888fe0
+import numpy as np
+import pandas as pd
+from pulp import *
+
+n_warehouses = 2
+n_customers = 4
+
+# Cost Matrix
+cost_matrix = np.array([[1, 3, 0.5, 4], [2.5, 5, 1.5, 2.5]])
+
+# Demand Matrix
+cust_demands = np.array([35000, 22000, 18000, 30000])
+
+# Supply Matrix
+warehouse_supply = np.array([60000, 80000])
+
+# Initialize Model
+model = LpProblem("Supply-Demand-Problem", LpMinimize)
+
+# Define Variable Names
+variable_names = [
+ str(i) + str(j)
+ for j in range(1, n_customers + 1)
+ for i in range(1, n_warehouses + 1)
+]
+variable_names.sort()
+
+# Decision Variables
+DV_variables = LpVariable.matrix("X", variable_names, cat="Integer", lowBound=0)
+allocation = np.array(DV_variables).reshape(2, 4)
+
+# Objective Function
+obj_func = lpSum(allocation * cost_matrix)
+model += obj_func
+
+# Constraints
+for i in range(n_warehouses):
+ print(lpSum(allocation[i][j] for j in range(n_customers)) <= warehouse_supply[i])
+ model += lpSum(allocation[i][j] for j in range(n_customers)) <= warehouse_supply[
+ i
+ ], "Supply Constraints " + str(i)
+
+for j in range(n_customers):
+ print(lpSum(allocation[i][j] for i in range(n_warehouses)) >= cust_demands[j])
+ model += lpSum(allocation[i][j] for i in range(n_warehouses)) >= cust_demands[
+ j
+ ], "Demand Constraints " + str(j)
+
+model.solve(PULP_CBC_CMD())
+status = LpStatus[model.status]
+print(status)
+
+print("Total Cost:", model.objective.value())
+for v in model.variables():
+ try:
+ print(v.name, "=", v.value())
+ except:
+ print("error couldn't find value")
+
+for i in range(n_warehouses):
+ print("Warehouse ", str(i + 1))
+ print(lpSum(allocation[i][j].value() for j in range(n_customers)))
diff --git a/anomaly/gmm-change-detection/scripts/example_code/registration/icp_registration_example.py b/anomaly/gmm-change-detection/scripts/example_code/registration/icp_registration_example.py
new file mode 100644
index 00000000..b6f6def9
--- /dev/null
+++ b/anomaly/gmm-change-detection/scripts/example_code/registration/icp_registration_example.py
@@ -0,0 +1,69 @@
+import copy
+
+import numpy as np
+import open3d as o3d
+
+
+def draw_registration_result(source, target, transformation):
+ source_temp = copy.deepcopy(source)
+ target_temp = copy.deepcopy(target)
+ source_temp.paint_uniform_color([1, 0.706, 0])
+ target_temp.paint_uniform_color([0, 0.651, 0.929])
+ source_temp.transform(transformation)
+ o3d.visualization.draw_geometries([source_temp, target_temp])
+
+
+if __name__ == "__main__":
+ source = o3d.io.read_point_cloud("normal0.pcd")
+ target = o3d.io.read_point_cloud("normal1.pcd")
+ threshold = 0.02
+ trans_init = np.asarray(
+ [
+ [0.862, 0.011, -0.507, 0.5],
+ [-0.139, 0.967, -0.215, 0.7],
+ [0.487, 0.255, 0.835, -1.4],
+ [0.0, 0.0, 0.0, 1.0],
+ ]
+ )
+ draw_registration_result(source, target, trans_init)
+ print("Initial alignment")
+ evaluation = o3d.registration.evaluate_registration(
+ source, target, threshold, trans_init
+ )
+ print(evaluation)
+
+ print("Apply point-to-point ICP")
+ reg_p2p = o3d.registration.registration_icp(
+ source,
+ target,
+ threshold,
+ trans_init,
+ o3d.registration.TransformationEstimationPointToPoint(),
+ )
+ print(reg_p2p)
+ print("Transformation is:")
+ print(reg_p2p.transformation)
+ print("")
+# draw_registration_result(source, target, reg_p2p.transformation)
+
+# print("Apply point-to-plane ICP")
+# reg_p2l = o3d.registration.registration_icp(
+# source, target, threshold, trans_init,
+# o3d.registration.TransformationEstimationPointToPlane())
+# print(reg_p2l)
+# print("Transformation is:")
+# print(reg_p2l.transformation)
+# print("")
+# draw_registration_result(source, target, reg_p2l.transformation)
+
+
+for count in range(100):
+ reg_p2l = o3d.registration.registration_icp(
+ source,
+ target,
+ threshold,
+ trans_init,
+ o3d.registration.TransformationEstimationPointToPoint(),
+ )
+
+draw_registration_result(source, target, reg_p2l.transformation)
diff --git a/anomaly/gmm-change-detection/scripts/example_code/registration/inliers.pcd b/anomaly/gmm-change-detection/scripts/example_code/registration/inliers.pcd
new file mode 100644
index 00000000..9e815070
--- /dev/null
+++ b/anomaly/gmm-change-detection/scripts/example_code/registration/inliers.pcd
@@ -0,0 +1,35126 @@
+# .PCD v0.7 - Point Cloud Data file format
+VERSION 0.7
+FIELDS x y z
+SIZE 4 4 4
+TYPE F F F
+COUNT 1 1 1
+WIDTH 35115
+HEIGHT 1
+VIEWPOINT 0 0 0 1 0 0 0
+POINTS 35115
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diff --git a/anomaly/gmm-change-detection/scripts/example_code/registration/normal0.pcd b/anomaly/gmm-change-detection/scripts/example_code/registration/normal0.pcd
new file mode 100644
index 00000000..cca22397
--- /dev/null
+++ b/anomaly/gmm-change-detection/scripts/example_code/registration/normal0.pcd
@@ -0,0 +1,38315 @@
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index 00000000..d78e041f
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diff --git a/anomaly/gmm-change-detection/scripts/example_code/registration/outliers.pcd b/anomaly/gmm-change-detection/scripts/example_code/registration/outliers.pcd
new file mode 100644
index 00000000..da2fc99f
--- /dev/null
+++ b/anomaly/gmm-change-detection/scripts/example_code/registration/outliers.pcd
@@ -0,0 +1,3200 @@
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diff --git a/anomaly/gmm-change-detection/scripts/gmm.py b/anomaly/gmm-change-detection/scripts/gmm.py
new file mode 100644
index 00000000..8da10c8b
--- /dev/null
+++ b/anomaly/gmm-change-detection/scripts/gmm.py
@@ -0,0 +1,63 @@
+#!/usr/bin/env python
+# Copyright (c) 2017, United States Government, as represented by the
+# Administrator of the National Aeronautics and Space Administration.
+#
+# All rights reserved.
+#
+# The Astrobee platform is licensed under the Apache License, Version 2.0
+# (the "License"); you may not use this file except in compliance with the
+# License. You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
+# WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
+# License for the specific language governing permissions and limitations
+# under the License.
+
+
+# Small class that holds precalculated GMM and
+# allows clusters to be edited and removed
+
+import numpy as np
+
+
+class GMM:
+ def __init__(self, weights, means, covariances):
+ self.weights = weights
+ self.means = means
+ self.covariances = covariances
+ self.n_gaussians = self.weights.size
+
+ def remove_gaussian(self, index): # Index of gaussian to remove
+ # removed_gauss = GMM(self.weights[index], self.means[index,:].reshape((1,3)), self.covariances[index,:].reshape((1,3)))
+ removed_gauss = GMM(
+ self.weights[index],
+ self.means[index, :].reshape((1, 3)),
+ np.array(self.covariances[:, :, index].reshape((3, 3))),
+ )
+ new_weights = np.delete(self.weights, index, 0)
+ self.weights = new_weights / np.linalg.norm(new_weights, ord=1)
+ self.means = np.delete(self.means, index, 0)
+ self.covariances = np.delete(self.covariances, index, -1)
+ self.n_gaussians = self.weights.size
+ return removed_gauss
+
+ def add_gaussian(self, gaussian): # Gaussian in form of GMM, k=1
+ self.weights = np.append(
+ self.weights, gaussian.weights
+ ) # PLACEHOLDER (weights are now incorrect)
+ self.means = np.append(self.means, gaussian.means, axis=0)
+ print("Gauss type: " + str(type(gaussian.covariances.reshape((3, 3)))))
+ if type(self.covariances) is not np.ndarray:
+ self.covariances = gaussian.covariances.reshape((3, 3))
+ print("Pi cov initialized: " + str(self.covariances.shape))
+ else:
+ print("Curr cov size: " + str(self.covariances.shape))
+ print("Gauss cov size: " + str(gaussian.covariances.reshape((3, 3)).shape))
+ # self.covariances = np.vstack([[self.covariances], [gaussian.covariances.reshape((3,3))]])
+ self.covariances = np.concatenate(
+ [self.covariances, gaussian.covariances], axis=0
+ )
+ self.n_gaussians = self.weights.size
diff --git a/anomaly/gmm-change-detection/scripts/gmm_change_detection.py b/anomaly/gmm-change-detection/scripts/gmm_change_detection.py
new file mode 100755
index 00000000..9478c150
--- /dev/null
+++ b/anomaly/gmm-change-detection/scripts/gmm_change_detection.py
@@ -0,0 +1,396 @@
+#!/usr/bin/env python
+# Copyright (c) 2017, United States Government, as represented by the
+# Administrator of the National Aeronautics and Space Administration.
+#
+# All rights reserved.
+#
+# The Astrobee platform is licensed under the Apache License, Version 2.0
+# (the "License"); you may not use this file except in compliance with the
+# License. You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
+# WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
+# License for the specific language governing permissions and limitations
+# under the License.
+
+import copy
+import os
+import pickle
+import sys
+
+import numpy as np
+from artificial_data import generate_data
+from emd_gmm import *
+from gmm import *
+from gmm_mml import GmmMml
+from preprocess_data import *
+from visualization import *
+
+np.set_printoptions(threshold=sys.maxsize)
+np.set_printoptions(suppress=True)
+
+############
+# Settings #
+############
+
+visualize = True # Visualize GMMs
+
+fake_data = True # Generate point clouds
+n_start = 4
+n_disappearances = 0
+n_appearances = 3
+
+# Path to input data (.pk for pickled GMMs, PCL file,
+# or bag files cropped to same positions at different times)
+
+# t_0 = './data/ground_truth/ground_truth_run5.pcd'
+# t_1 = './data/ground_truth/ground_truth_run4.pcd'
+
+t_1 = "./data/single_frame_bags/20230313_1901_survey_no_bag_panorama_precut.bag"
+t_0 = "./data/single_frame_bags/20230313_1908_survey_bag_panorama_precut.bag"
+
+# t_0 = './data/single_frame_bags/run5_astrobee.bag'
+# t_1 = './data/single_frame_bags/run1_astrobee.bag'
+
+# t_0 = './data/image_reconstruction/run5.pcd'
+# t_1 = './data/image_reconstruction/run2.pcd'
+
+# t_0 = './saved_models/fake_data_t0_1.pk'
+# t_1 = './saved_models/fake_data_t1_1.pk'
+
+# t_0 = './saved_models/20230313_1901_survey_no_bag_panorama_precut_1.pk'
+# t_1 = './saved_models/20230313_1908_survey_bag_panorama_precut_1.pk'
+
+# t_0 = 'data/image_reconstruction/run5.pcd'
+# t_1 = 'data/image_reconstruction/run4.pcd'
+
+# Get file extension
+ext = os.path.splitext(os.path.basename(t_0))[1]
+
+#############################
+# Set up caching the models #
+#############################
+def get_filename(original_file):
+ """Make sure the filename is unique"""
+ counter = 1
+ filename = original_file + "_{}"
+ while os.path.isfile(".saved_models/" + filename.format(counter)):
+ counter += 1
+ filename = filename.format(counter)
+ return filename
+
+
+# Load pre-clustered GMMs if provided
+if ext == ".pk":
+ with open(t_0, "rb") as fi:
+ (
+ gmm1_init_bestk,
+ gmm1_init_bestpp,
+ gmm1_init_bestcov,
+ gmm1_init_bestmu,
+ predictions1,
+ ) = pickle.load(fi)
+ with open(t_1, "rb") as fi:
+ (
+ gmm2_init_bestk,
+ gmm2_init_bestpp,
+ gmm2_init_bestcov,
+ gmm2_init_bestmu,
+ predictions2,
+ ) = pickle.load(fi)
+else:
+ if fake_data:
+ filename_1 = get_filename("fake_data_t0")
+ filename_2 = get_filename("fake_data_t1")
+ else:
+ filename_1 = get_filename(os.path.splitext(os.path.basename(t_0))[0])
+ filename_2 = get_filename(os.path.splitext(os.path.basename(t_1))[0])
+
+ t0_save_file = (
+ os.path.dirname(os.path.realpath(__file__))
+ + "/saved_models/"
+ + filename_1
+ + ".pk"
+ )
+ t1_save_file = (
+ os.path.dirname(os.path.realpath(__file__))
+ + "/saved_models/"
+ + filename_2
+ + ".pk"
+ )
+
+ ###################
+ # Format the data #
+ ###################
+
+ if fake_data:
+ points1, points2 = generate_data(n_start, n_disappearances, n_appearances)
+
+ elif ext == ".bag": # sensor_msgs::PointCloud2 data from bagfile
+ points1 = read_pc2_msgs(t_0)
+ points2 = read_pc2_msgs(t_1)
+
+ elif ext == ".pcd": # PCL formatted file (e.g. from reconstructed map)
+ points1 = read_pcd(t_0)
+ points2 = read_pcd(t_1)
+ else:
+ sys.exit("Invalid file format")
+
+ # Plot the figures
+ fig1 = plt.figure()
+ ax1 = fig1.add_subplot(111, projection="3d")
+ ax1.scatter(points1[:, 0], points1[:, 1], points1[:, 2], s=0.7, alpha=0.07)
+ fig2 = plt.figure()
+ ax2 = fig2.add_subplot(111, projection="3d")
+ ax2.scatter(points2[:, 0], points2[:, 1], points2[:, 2], s=0.7, alpha=0.07)
+ # plt.show()
+
+ #####################################
+ # Cluster the point clouds int GMMs #
+ #####################################
+
+ # Run split-and-merge expectation-maximization algorithm
+ # described in "Unsupervised Learning of Finite Mixture Models" by Figueiredo et al.
+ print("Fitting Gamma")
+ gmm1_init = GmmMml()
+ gmm1_init = gmm1_init.fit(points1, verb=True)
+ gmm1_init_bestk = gmm1_init.bestk
+ gmm1_init_bestpp = gmm1_init.bestpp
+ gmm1_init_bestcov = gmm1_init.bestcov
+ gmm1_init_bestmu = gmm1_init.bestmu
+ predictions1 = gmm1_init.predict(points1)
+
+ print("Fitting Theta")
+ gmm2_init = GmmMml()
+ gmm2_init = gmm2_init.fit(points2, verb=True)
+ gmm2_init_bestk = gmm2_init.bestk
+ gmm2_init_bestpp = gmm2_init.bestpp
+ gmm2_init_bestcov = gmm2_init.bestcov
+ gmm2_init_bestmu = gmm2_init.bestmu
+ predictions2 = gmm2_init.predict(points2)
+
+
+print("Gamma number of Gaussians: " + str(gmm1_init_bestk))
+print("Theta number of Gaussians: " + str(gmm2_init_bestk))
+
+# Move the GMMs to a new data structure to be able to remove
+# Gaussians from GMMs for change detection
+gamma_t0 = GMM(gmm1_init_bestpp[0, :], gmm1_init_bestmu, gmm1_init_bestcov)
+theta_t1 = GMM(gmm2_init_bestpp[0, :], gmm2_init_bestmu, gmm2_init_bestcov)
+
+######################################
+# Generate GMM with Detected Changes #
+######################################
+
+
+def find_emd(gmm1, gmm2):
+ """Find the Earth Mover's Distance between two GMMs"""
+ emdgmm = EMDGMM(gmm1.weights, gmm2.weights)
+ emdgmm.get_distance(gmm1.means, gmm2.means)
+ emdgmm.calculate_emd()
+ return emdgmm.emd
+
+
+def greedy_select_gmm(gamma, theta, start_emd):
+ """Find the Gaussian in Theta that contributes the
+ highest degree of positive change (i.e., removal results
+ in the lowest EMD) and return "best" Theta GMM from which such
+ Gaussian has been removed
+ """
+
+ lowest_emd = start_emd # Metric for degree of change
+ best_theta = theta
+ best_gauss = GMM(
+ np.array([]), np.array([]).reshape((0, 3)), np.array([]).reshape((0, 3))
+ ) # GMM w/ k=1
+
+ # Remove Gaussians one at a time and track which contributes most change
+ for gauss in range(theta.n_gaussians - 1):
+ theta_temp = copy.deepcopy(theta)
+ removed_gauss = theta_temp.remove_gaussian(gauss) # Remove the next Gaussian
+ new_emd = find_emd(gamma, theta_temp)
+
+ # print("NEW EMD: " + str(new_emd) + " LOWEST: " + str(lowest_emd))
+
+ if new_emd < lowest_emd:
+ lowest_emd = new_emd
+ best_theta = theta_temp
+ best_gauss = removed_gauss
+
+ return lowest_emd, best_theta, best_gauss
+
+
+def change_detection(gamma, theta):
+ """Greedily remove Gaussians that contribute the most change
+ and place them into a tertiary "change" GMM
+ """
+
+ # Initialize empty Pi (change) GMM
+ pi = GMM(np.array([]), np.array([]).reshape((0, 3)), None)
+
+ # Iteratively remove Gaussians from "after" GMM until EMD is the same
+ dGMM_old = find_emd(gamma, theta)
+ dGMM, new_theta, best_gauss = greedy_select_gmm(gamma, theta, dGMM_old)
+
+ for i in range(new_theta.n_gaussians):
+ if best_gauss.n_gaussians == 0:
+ break
+
+ # Update Pi with new Gaussian
+ pi.add_gaussian(best_gauss)
+
+ # Obtain "best Gaussian" that produces highest degree of change
+ dGMM, new_theta, best_gauss = greedy_select_gmm(gamma, new_theta, dGMM_old)
+ if dGMM_old > dGMM:
+ dGMM_old = dGMM
+ else:
+ break
+
+ # Map the change Gaussians back to the original Theta GMM
+ theta_changes = []
+ for gauss in range(pi.n_gaussians):
+ change_gauss = np.where(np.prod(gmm2_init_bestmu == pi.means[gauss], axis=-1))
+ theta_changes.append(change_gauss)
+
+ # Readjust the Pi covariance shape back to [3,3,K]
+ if pi.n_gaussians != 0:
+ pi.covariances = pi.covariances.reshape(pi.n_gaussians, 3, 3).T
+ return pi
+
+
+pi_appearances = change_detection(gamma_t0, theta_t1)
+pi_disappearances = change_detection(theta_t1, gamma_t0)
+
+# Output change Gaussian information
+print("\nCHANGE GAUSSIANS")
+print("################################")
+print("Clusters associated with appearances: " + str(pi_appearances.n_gaussians))
+print("Clusters associated with disappearances: " + str(pi_disappearances.n_gaussians))
+
+
+def get_diag(covs, k):
+ """Get diagonal covariance from full covariance
+ matrix for plotting"""
+
+ diag_covs = []
+ for i in range(k):
+ cov = covs[:, :, i]
+ l = len(cov[0])
+ diag = [cov[j][j] for j in range(l)]
+ diag_covs.append(diag)
+ return np.array(diag_covs)
+
+
+########################
+# Visualize the Output #
+########################
+if visualize:
+ gmm1_k = gmm1_init_bestk
+ gmm2_k = gmm2_init_bestk
+
+ fig = plt.figure(figsize=(12, 4))
+ ax1 = fig.add_subplot(141, projection="3d")
+ ax1.set(xlabel="X", ylabel="Y", zlabel="Z")
+ ax1.view_init(elev=-75, azim=-90)
+ ax1.title.set_text("Gamma (Before)")
+
+ ax2 = fig.add_subplot(142, projection="3d")
+ ax2.set(xlabel="X", ylabel="Y", zlabel="Z")
+ ax2.view_init(elev=-75, azim=-90)
+ ax2.title.set_text("Theta (After)")
+
+ ax3 = fig.add_subplot(143, projection="3d")
+ ax3.set(xlabel="X", ylabel="Y", zlabel="Z")
+ ax3.view_init(elev=-75, azim=-90)
+ ax3.title.set_text("Pi (Appearances)")
+
+ ax4 = fig.add_subplot(144, projection="3d")
+ ax4.set(xlabel="X", ylabel="Y", zlabel="Z")
+ ax4.view_init(elev=-75, azim=-90)
+ ax4.title.set_text("Pi (Disappearances)")
+
+ # GMM 1 (Gamma)
+ diag_covs1 = get_diag(gmm1_init_bestcov, gmm1_init_bestk)
+ visualize_3d_gmm(
+ points1,
+ predictions1,
+ gmm1_init_bestpp[0],
+ gmm1_init_bestmu.T,
+ np.sqrt(diag_covs1).T,
+ gmm1_k,
+ ax1,
+ )
+
+ # GMM 2 (Theta)
+ diag_covs2 = get_diag(gmm2_init_bestcov, gmm2_init_bestk)
+ visualize_3d_gmm(
+ points2,
+ predictions2,
+ gmm2_init_bestpp[0],
+ gmm2_init_bestmu.T,
+ np.sqrt(diag_covs2).T,
+ gmm2_k,
+ ax2,
+ )
+
+ # Appearance GMM (Pi 1), compared to GMM2 original points
+ piagonal = get_diag(pi_appearances.covariances, pi_appearances.weights.shape[0])
+ visualize_3d_gmm(
+ points2,
+ predictions2,
+ pi_appearances.weights,
+ pi_appearances.means.T,
+ np.sqrt(piagonal).T,
+ gmm2_k,
+ ax3,
+ )
+
+ # Disappearance GMM (Pi 2), compared to GMM2 original points
+ piagonal_dis = get_diag(
+ pi_disappearances.covariances, pi_disappearances.weights.shape[0]
+ )
+ visualize_3d_gmm(
+ points2,
+ predictions2,
+ pi_disappearances.weights,
+ pi_disappearances.means.T,
+ np.sqrt(piagonal_dis).T,
+ gmm2_k,
+ ax4,
+ )
+
+ # Save model parameters for future use
+ if ext != ".pk":
+ with open(t0_save_file, "wb") as fi:
+ pickle.dump(
+ [
+ gmm1_init.bestk,
+ gmm1_init.bestpp,
+ gmm1_init.bestcov,
+ gmm1_init.bestmu,
+ predictions1,
+ points1,
+ ],
+ fi,
+ )
+ with open(t1_save_file, "wb") as fi:
+ pickle.dump(
+ [
+ gmm2_init.bestk,
+ gmm2_init.bestpp,
+ gmm2_init.bestcov,
+ gmm2_init.bestmu,
+ predictions2,
+ points2,
+ ],
+ fi,
+ )
+
+ print("Saved to: ")
+ print(" " + str(t0_save_file))
+ print(" " + str(t1_save_file))
+
+plt.show()
diff --git a/anomaly/gmm-change-detection/scripts/gmm_mml.py b/anomaly/gmm-change-detection/scripts/gmm_mml.py
new file mode 100644
index 00000000..62d3ccd2
--- /dev/null
+++ b/anomaly/gmm-change-detection/scripts/gmm_mml.py
@@ -0,0 +1,382 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Wed Jun 7 18:44:27 2017
+
+@author: abriosi
+"""
+
+import numpy as np
+from scipy.stats import multivariate_normal
+from sklearn.base import TransformerMixin
+
+
+class GmmMml(TransformerMixin):
+ def __init__(
+ self,
+ kmin=1,
+ kmax=25,
+ regularize=1e-6,
+ threshold=1e-5,
+ covoption=0,
+ max_iters=100,
+ live_2d_plot=False,
+ plots=False,
+ ):
+
+ self.kmin = kmin
+ self.kmax = kmax
+ self.regularize = regularize
+ self.th = threshold
+ self.covoption = covoption
+ self.live_2d_plot = live_2d_plot
+ self.max_iters = max_iters
+ self.check_plot = plots
+
+ def _draw_elipse(self, ax, estcov, estmu):
+ import matplotlib as mpl
+
+ v, w = np.linalg.eigh(estcov)
+ u = w[0] / np.linalg.norm(w[0])
+ angle = np.arctan2(u[1], u[0])
+ angle = 180 * angle / np.pi # convert to degrees
+ v = 2.0 * np.sqrt(2.0) * np.sqrt(v)
+
+ ell = mpl.patches.Ellipse(
+ estmu, v[0], v[1], 180 + angle, facecolor="none", edgecolor="black"
+ )
+ ell.set_clip_box(ax.bbox)
+ ell.set_alpha(1)
+ ax.add_artist(ell)
+ return ax
+
+ def _plot_graph(self, estcov, estmu, k, y, message):
+ if y.shape[1] == 2:
+ import matplotlib.pyplot as plt
+
+ ax = plt.subplot(111)
+ plt.title(message)
+ plt.scatter(y[:, 0], y[:, 1], alpha=0.2, s=10)
+ for i in range(k):
+ ax = self._draw_elipse(ax, estcov[:, :, i], estmu[i])
+ plt.show()
+ else:
+ print("only supports 2d data for plots")
+
+ def _posterior_probability(self, y, estmu, estcov, i):
+ try:
+ return multivariate_normal.pdf(
+ y, estmu[i], estcov[:, :, i], allow_singular=False
+ )
+ except Exception as inst:
+ raise Exception(
+ "Possible singular matrix detected. Try adding (more) regularization"
+ )
+
+ def fit(self, X, y=None, verb=False):
+ y = np.array(X)
+
+ dl = []
+ npoints = y.shape[0]
+ dimens = y.shape[1]
+
+ if self.covoption == 0:
+ npars = dimens + dimens * (dimens + 1) / 2
+ elif self.covoption == 1:
+ npars = 2 * dimens
+ elif self.covoption == 2:
+ npars = dimens
+ elif self.covoption == 3:
+ npars = dimens
+ else:
+ npars = dimens + dimens * (dimens + 1) / 2
+
+ nparsover2 = npars / 2
+
+ k = self.kmax
+
+ indic = np.zeros((k, npoints))
+ randindex = np.random.randint(0, npoints, npoints)
+ randindex = np.random.choice(randindex, k)
+ estmu = y[randindex]
+
+ estpp = (1 / float(k)) * np.ones((1, k))
+
+ if dimens > 1:
+ globcov = np.cov(y, rowvar=False)
+ else:
+ globcov = np.array([np.array([np.cov(y, rowvar=False)])])
+
+ estcov = np.empty(globcov.shape + (self.kmax,))
+ for i in range(k):
+ estcov[:, :, i] = np.diag(
+ (np.diag(np.ones((dimens, dimens)) * np.max(np.diag(globcov / 10))))
+ )
+
+ if self.check_plot == True:
+ self._plot_graph(estcov, estmu, k, y, "Random Guassian Initialization")
+
+ semi_indic = np.empty((k, y.shape[0]))
+ for i in range(k):
+
+ min_eig = np.min(np.real(np.linalg.eigvals(estcov[:, :, i])))
+ if min_eig < 0:
+ estcov[:, :, i] -= 10 * min_eig * np.eye(*estcov[:, :, i].shape)
+
+ semi_indic[i, :] = self._posterior_probability(y, estmu, estcov, i)
+ indic[i, :] = semi_indic[i, :] * estpp[:, i]
+
+ countf = 0
+ loglike = []
+ kappas = []
+
+ loglike.append(
+ np.sum(np.log(np.sum(np.finfo(np.float64).tiny + indic, axis=0)))
+ )
+ dlength = (
+ -loglike[countf]
+ + (nparsover2 * np.sum(np.log(estpp)))
+ + (nparsover2 + 0.5) * k * np.log(npoints)
+ )
+ dl.append(dlength)
+ kappas.append(k)
+
+ transitions1 = []
+ transitions2 = []
+
+ mindl = dl[countf]
+ self.bestmu = estmu
+ self.bestcov = estcov
+
+ k_cont = True
+
+ iteration = 0
+
+ while k_cont == True:
+
+ cont = True
+
+ while cont == True and iteration < self.max_iters:
+ # while iteration 0")
+
+ estpp[:, comp] = (
+ np.max(np.sum(normindic[comp, :]) - nparsover2, axis=0)
+ / npoints
+ )
+ estpp = estpp / np.sum(estpp)
+
+ killed = 0
+
+ if estpp[:, comp] <= 0:
+ killed = 1
+
+ transitions1.append(countf)
+
+ estmu = np.delete(estmu, comp, axis=0)
+ estcov = np.delete(estcov, comp, axis=-1)
+ estpp = np.delete(estpp, comp, axis=-1)
+ semi_indic = np.delete(semi_indic, comp, axis=0)
+
+ k = k - 1
+
+ if killed == 0:
+
+ min_eig = np.min(np.real(np.linalg.eigvals(estcov[:, :, comp])))
+ if min_eig < 0:
+ estcov[:, :, comp] -= (
+ 10 * min_eig * np.eye(*estcov[:, :, comp].shape)
+ )
+
+ semi_indic[comp, :] = self._posterior_probability(
+ y, estmu, estcov, comp
+ )
+ comp += 1
+
+ countf = countf + 1
+
+ indic = np.zeros((k, npoints))
+ semi_indic = np.empty((k, y.shape[0]))
+
+ for i in range(k):
+
+ min_eig = np.min(np.real(np.linalg.eigvals(estcov[:, :, i])))
+ if min_eig < 0:
+ estcov[:, :, i] -= 10 * min_eig * np.eye(*estcov[:, :, i].shape)
+
+ semi_indic[i, :] = self._posterior_probability(y, estmu, estcov, i)
+ indic[i, :] = semi_indic[i, :] * estpp[:, i]
+
+ if k != 1:
+ loglike.append(
+ np.sum(
+ np.log(np.finfo(np.float64).tiny + np.sum(indic, axis=0))
+ )
+ )
+ else:
+ loglike.append(np.sum(np.log(np.finfo(np.float64).tiny + indic)))
+
+ dlength = (
+ -loglike[countf]
+ + (nparsover2 * np.sum(np.log(estpp)))
+ + (nparsover2 + 0.5) * k * np.log(npoints)
+ )
+ dl.append(dlength)
+ kappas.append(k)
+
+ deltlike = loglike[countf] - loglike[countf - 1]
+
+ if verb == True:
+ toprint = np.abs(deltlike / loglike[countf - 1]) / self.th
+ print("deltaloglike/th =" + str(toprint))
+
+ if np.abs(deltlike / loglike[countf - 1]) < self.th:
+ cont = False
+
+ if self.live_2d_plot == True:
+ self._plot_graph(estcov, estmu, k, y, None)
+
+ iteration += 1
+
+ iteration = 0
+
+ if dl[countf] < mindl:
+ self.bestpp = estpp
+ self.bestmu = estmu
+ self.bestcov = estcov
+ self.bestk = k
+ mindl = dl[countf]
+
+ if k > self.kmin:
+ indminp = np.argmin(estpp)
+
+ estmu = np.delete(estmu, indminp, axis=0)
+ estcov = np.delete(estcov, indminp, axis=-1)
+ estpp = np.delete(estpp, indminp, axis=-1)
+
+ k = k - 1
+
+ estpp = estpp / np.sum(estpp)
+
+ transitions2.append(countf)
+
+ countf = countf + 1
+
+ indic = np.zeros((k, npoints))
+ semi_indic = np.empty((k, y.shape[0]))
+
+ for i in range(k):
+
+ min_eig = np.min(np.real(np.linalg.eigvals(estcov[:, :, i])))
+ if min_eig < 0:
+ estcov[:, :, i] -= 10 * min_eig * np.eye(*estcov[:, :, i].shape)
+
+ semi_indic[i, :] = self._posterior_probability(y, estmu, estcov, i)
+ indic[i, :] = semi_indic[i, :] * estpp[:, i]
+
+ if k != 1:
+ loglike.append(
+ np.sum(
+ np.log(np.finfo(np.float64).tiny + np.sum(indic, axis=0))
+ )
+ )
+ else:
+ loglike.append(np.sum(np.log(np.finfo(np.float64).tiny + indic)))
+
+ dlength = (
+ -loglike[countf]
+ + (nparsover2 * np.sum(np.log(estpp)))
+ + (nparsover2 + 0.5) * k * np.log(npoints)
+ )
+ dl.append(dlength)
+
+ # countf=countf-1
+ kappas.append(k)
+ else:
+ k_cont = False
+
+ if self.check_plot == True:
+ import matplotlib.pyplot as plt
+
+ plt.title("Evaluation of the cost function")
+ plt.plot(range(len(dl)), dl)
+ plt.show()
+
+ self._plot_graph(
+ self.bestcov,
+ self.bestmu,
+ self.bestcov.shape[-1],
+ y,
+ "Best number of components",
+ )
+
+ return self
+
+ def sample(self, sample):
+ output = []
+ select_sample = np.random.multinomial(sample, self.bestpp[0])
+ gmm = 0
+ for i in select_sample:
+ for i in range(i):
+ output.append(
+ np.random.multivariate_normal(
+ self.bestmu[gmm], np.swapaxes(self.bestcov, 0, 2)[gmm]
+ )
+ )
+ gmm += 1
+ return np.array(output)
+
+ def transform(self, X, y=None):
+ y = np.array(X)
+ semi_indic = np.empty((self.bestmu.shape[0], y.shape[0]))
+ for i in range(self.bestmu.shape[0]):
+ semi_indic[i, :] = self._posterior_probability(
+ y, self.bestmu, self.bestcov, i
+ )
+ return semi_indic.T
+
+ def fit_transform(self, X, y=None):
+ self.fit(X)
+ return self.transform(X)
+
+ def predict_proba(self, X):
+ return self.transform(X)
+
+ def predict(self, X):
+ return np.argmax(self.transform(X), axis=1)
diff --git a/anomaly/gmm-change-detection/scripts/ground_truth.py b/anomaly/gmm-change-detection/scripts/ground_truth.py
new file mode 100644
index 00000000..25817d0a
--- /dev/null
+++ b/anomaly/gmm-change-detection/scripts/ground_truth.py
@@ -0,0 +1,107 @@
+#!/usr/bin/python2
+# Copyright (c) 2017, United States Government, as represented by the
+# Administrator of the National Aeronautics and Space Administration.
+#
+# All rights reserved.
+#
+# The Astrobee platform is licensed under the Apache License, Version 2.0
+# (the "License"); you may not use this file except in compliance with the
+# License. You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
+# WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
+# License for the specific language governing permissions and limitations
+# under the License.
+
+# Python2 script to convert a series of haz_cam point clouds
+# to a single merged point cloud in the world reference frame
+
+import geometry_msgs
+import numpy as np
+import ros_numpy
+import rosbag
+import rospy
+import sensor_msgs
+import tf2_py as tf2
+import tf2_ros
+from tf import transformations as ts
+from tf2_sensor_msgs.tf2_sensor_msgs import do_transform_cloud
+
+
+# Transform the pc2 msg camera coordinates from the haz_cam to body:
+def translate_cam_frame(pc2_msg):
+ t = geometry_msgs.msg.TransformStamped()
+ t.header.stamp = pc2_msg.header.stamp
+ t.header.frame_id = "haz_cam"
+ t.child_frame_id = "body"
+
+ t.transform.translation.x = 0.036
+ t.transform.translation.y = -0.083
+ t.transform.translation.z = -0.133
+
+ # In quaternions:
+ t.transform.rotation.x = 0.500
+ t.transform.rotation.y = -0.500
+ t.transform.rotation.z = 0.500
+ t.transform.rotation.w = -0.500
+
+ body_tf = do_transform_cloud(pc2_msg, t)
+ return body_tf
+
+
+# Transform point cloud coordinates to map ground truth (from Marina and Ryan)
+def ground_truth(msg, pc2_msg):
+ # Get transformation info from hazcam pc2 message
+ t = geometry_msgs.msg.TransformStamped()
+ # t.header.stamp = rospy.Time.now()
+ t.header.stamp = msg.header.stamp
+ t.header.frame_id = "body"
+ t.child_frame_id = "world"
+
+ t.transform.translation.x = msg.pose.position.x
+ t.transform.translation.y = msg.pose.position.y
+ t.transform.translation.z = msg.pose.position.z
+
+ t.transform.rotation.x = msg.pose.orientation.x
+ t.transform.rotation.y = msg.pose.orientation.y
+ t.transform.rotation.z = msg.pose.orientation.z
+ t.transform.rotation.w = msg.pose.orientation.w
+
+ cloud_out = do_transform_cloud(pc2_msg, t)
+ return cloud_out
+
+
+def convert_bag(bagfile, output_bag_name, save_all_topics=False):
+ topics = [
+ "/gnc/ekf",
+ "/hw/depth_haz/points",
+ "/hw/depth_haz/extended/amplitude_int",
+ ]
+ output_bag = rosbag.Bag(output_bag_name, "w")
+ topics_bag = [] if save_all_topics else topics
+
+ pc2_msg = None
+ with rosbag.Bag(bagfile, "r") as bag:
+ for topic, msg, t in bag.read_messages(topics_bag):
+ if topic == "/hw/depth_haz/points":
+ pc2_msg = msg
+ if topic == "/gnc/ekf" and pc2_msg is not None:
+ new_topic_name = "/hw/depth_haz/points/ground_truth"
+ pc2_body = translate_cam_frame(pc2_msg)
+ pc2_gt = ground_truth(msg, pc2_body)
+ output_bag.write(topic, msg, t)
+ output_bag.write(new_topic_name, pc2_gt, t)
+ pc2_msg = None
+ if save_all_topics:
+ output_bag.write(topic, msg, t)
+ output_bag.close()
+
+
+if __name__ == "__main__":
+ convert_bag(
+ "/home/jcsanto3/bagfile-data/ground_truth/groundtruth_20230419_1836_survey_run5.bag",
+ "./groundtruth_run5.bag",
+ )
diff --git a/anomaly/gmm-change-detection/scripts/preprocess_data.py b/anomaly/gmm-change-detection/scripts/preprocess_data.py
new file mode 100644
index 00000000..d151e9b9
--- /dev/null
+++ b/anomaly/gmm-change-detection/scripts/preprocess_data.py
@@ -0,0 +1,139 @@
+#!/usr/bin/env python
+# Copyright (c) 2017, United States Government, as represented by the
+# Administrator of the National Aeronautics and Space Administration.
+#
+# All rights reserved.
+#
+# The Astrobee platform is licensed under the Apache License, Version 2.0
+# (the "License"); you may not use this file except in compliance with the
+# License. You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
+# WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
+# License for the specific language governing permissions and limitations
+# under the License.
+
+
+# Converts ROS sensor_msgs:PointCloud2 to a
+# python-PCL-filtered numpy array
+
+import math
+import time
+
+import geometry_msgs
+import matplotlib.pyplot as plt
+import numpy as np
+import pcl
+import rosbag
+import rospy
+import sensor_msgs
+from PIL import Image
+
+
+# See https://stackoverflow.com/questions/39772424
+def convert_pc2_pcl(data):
+ data.__class__ = sensor_msgs.msg._PointCloud2.PointCloud2
+ offset_sorted = {f.offset: f for f in data.fields}
+ data.fields = [f for (_, f) in sorted(offset_sorted.items())]
+
+ pc = ros_numpy.numpify(data)
+ height = pc.shape[0]
+ if len(pc.shape) == 1: # Unordered PC2 structure
+ np_points = np.zeros((height, 3), dtype=np.float32)
+ np_points[:, 0] = np.resize(pc["x"], height)
+ np_points[:, 1] = np.resize(pc["y"], height)
+ np_points[:, 2] = np.resize(pc["z"], height)
+ p = pcl.PointCloud(np.array(np_points, dtype=np.float32))
+
+ else: # Ordered PC2 structure
+ width = pc.shape[1]
+ np_points = np.zeros((height * width, 3), dtype=np.float32)
+ np_points[:, 0] = np.resize(pc["x"], height * width)
+ np_points[:, 1] = np.resize(pc["y"], height * width)
+ np_points[:, 2] = np.resize(pc["z"], height * width)
+ p = pcl.PointCloud(np.array(np_points, dtype=np.float32))
+ return p
+
+
+# Outlier and downsample filtering of data
+def filter_pcl(pcl_data):
+ p = pcl_data
+ pcl.save(p, "normal.pcd")
+
+ # Statistical Outlier Filter
+ fil = p.make_statistical_outlier_filter()
+ fil.set_mean_k(50)
+ fil.set_std_dev_mul_thresh(1.0)
+
+ # pcl.save(fil.filter(), "inliers.pcd")
+ # fil.set_negative(True)
+ # pcl.save(fil.filter(), "outliers.pcd")
+
+ # Downsample outlier filtered data
+ # fil = fil.make_voxel_grid_filter()
+ # fil.set_leaf_size(0.01, 0.01, 0.01)
+ # pcl.save(fil.filter(), "downsample.pcd")
+
+ # Conversion from pcl to numpy array
+ np_arr = fil.filter().to_array()
+ # np_arr = p.to_array()
+ return np_arr
+
+
+# Obtain and concatenate point clouds remapped with ground truth transform
+def concat_ground_truth_msgs(bagfile):
+ skipped = 100 # Number of messages to skip over
+ n_points = 171 * 224 # 171 rows x 224 columns
+ n_msgs = rosbag.Bag(bagfile).get_message_count("/hw/depth_haz/points/ground_truth")
+ n_msgs_used = math.floor(n_msgs / skipped)
+ merged_pcl = np.empty((n_msgs_used * n_points, 3), dtype=np.float32)
+
+ count = 0
+ i = 0
+ for topic, msg, t in rosbag.Bag(bagfile).read_messages():
+ if topic == "/hw/depth_haz/points/ground_truth":
+ count += 1
+ if count % skipped == 0:
+ np_arr = convert_pc2_pcl(msg).to_array()
+ merged_pcl[i : i + n_points, :] = np_arr
+ i += n_points
+
+ p = pcl.PointCloud(merged_pcl)
+ pcl.save(p, "ground_truth_run5.pcd")
+ return p
+
+
+# Process data from bagfile
+def read_pc2_msgs(bagfile):
+ for topic, msg, t in rosbag.Bag(bagfile).read_messages():
+ if topic == "/hw/depth_haz/extended/amplitude_int":
+ np_im = ros_numpy.image.image_to_numpy(msg)
+ data = Image.fromarray(np_im)
+
+ if (
+ topic == "/hw/depth_haz/points"
+ or topic == "/hw/depth_haz/points/ground_truth"
+ ):
+ p = convert_pc2_pcl(msg)
+ np_arr = filter_pcl(p)
+
+ if "data" in locals():
+ data.show()
+ data.save("image.png")
+ return np_arr
+ return np_arr
+
+
+# Process PCD point cloud directly
+def read_pcd(pcdfile):
+ p = pcl.load(pcdfile)
+ np_arr = filter_pcl(p)
+ return np_arr
+
+
+if __name__ == "__main__":
+ # filtered_data = read_pc2_msgs('/home/jcsanto3/bagfile-data/groundtruth/run5_precut.bag')
+ concat_ground_truth_msgs("./groundtruth_run5.bag")
diff --git a/anomaly/gmm-change-detection/scripts/saved_models/fake_data_1.pk b/anomaly/gmm-change-detection/scripts/saved_models/fake_data_1.pk
new file mode 100644
index 00000000..459643f0
Binary files /dev/null and b/anomaly/gmm-change-detection/scripts/saved_models/fake_data_1.pk differ
diff --git a/anomaly/gmm-change-detection/scripts/saved_models/fake_data_2.pk b/anomaly/gmm-change-detection/scripts/saved_models/fake_data_2.pk
new file mode 100644
index 00000000..8b64a8ef
Binary files /dev/null and b/anomaly/gmm-change-detection/scripts/saved_models/fake_data_2.pk differ
diff --git a/anomaly/gmm-change-detection/scripts/visualization.py b/anomaly/gmm-change-detection/scripts/visualization.py
new file mode 100644
index 00000000..c47adf2e
--- /dev/null
+++ b/anomaly/gmm-change-detection/scripts/visualization.py
@@ -0,0 +1,85 @@
+# Based on the GMM visualization code:
+# https://github.com/sitzikbs/gmm_tutorial/blob/master/visualization.py
+# with modifications to accomodate using the model data
+import matplotlib.cm as cmx
+import matplotlib.pyplot as plt
+import numpy as np
+from matplotlib.axes._axes import _log as matplotlib_axes_logger
+from mpl_toolkits.mplot3d import Axes3D
+
+# Suppress matplotlib warnings
+matplotlib_axes_logger.setLevel("ERROR")
+
+
+def plot_sphere(w=0, c=[0, 0, 0], r=[1, 1, 1], subdev=10, ax=None, sigma_multiplier=3):
+ """
+ plot a sphere surface
+ Input:
+ c: 3 elements list, sphere center
+ r: 3 element list, sphere original scale in each axis ( allowing to draw elipsoids)
+ subdiv: scalar, number of subdivisions (subdivision^2 points sampled on the surface)
+ ax: optional pyplot axis object to plot the sphere in.
+ sigma_multiplier: sphere additional scale (choosing an std value when plotting gaussians)
+ Output:
+ ax: pyplot axis object
+ """
+
+ if ax is None:
+ fig = plt.figure()
+ ax = fig.add_subplot(111, projection="3d")
+ pi = np.pi
+ cos = np.cos
+ sin = np.sin
+ phi, theta = np.mgrid[
+ 0.0 : pi : complex(0, subdev), 0.0 : 2.0 * pi : complex(0, subdev)
+ ]
+ x = sigma_multiplier * r[0] * sin(phi) * cos(theta) + c[0]
+ y = sigma_multiplier * r[1] * sin(phi) * sin(theta) + c[1]
+ z = sigma_multiplier * r[2] * cos(phi) + c[2]
+ cmap = cmx.ScalarMappable()
+ cmap.set_cmap("jet")
+ c = cmap.to_rgba(w)
+
+ ax.plot_surface(x, y, z, color=c, alpha=0.2, linewidth=1)
+
+ return ax
+
+
+def visualize_3d_gmm(points, predictions, w, mu, stdev, n_gaussians, axes=None):
+ """
+ plots points and their corresponding gmm model in 3D
+ Input:
+ points: N X 3, sampled points
+ w: n_gaussians, gmm weights
+ mu: 3 X n_gaussians, gmm means
+ stdev: 3 X n_gaussians, gmm standard deviation (assuming diagonal covariance matrix)
+ Output:
+ None
+ """
+
+ N = int(np.round(points.shape[0] / n_gaussians))
+
+ # Visualize data
+ axes = axes or plt.gca()
+ plt.set_cmap("Set1")
+ colors = cmx.Set1(np.linspace(0, 1, n_gaussians))
+ for i in range(n_gaussians):
+ idx = np.where(predictions == i)
+ axes.scatter(
+ points[idx, 0],
+ points[idx, 1],
+ points[idx, 2],
+ alpha=0.07,
+ c=colors[i],
+ s=0.7,
+ )
+
+ for i in range(w.shape[0]):
+ plot_sphere(w=w[i], c=mu[:, i], r=stdev[:, i], ax=axes)
+
+ return axes
+ # plt.title('3D GMM')
+ # axes.set_xlabel('X')
+ # axes.set_ylabel('Y')
+ # axes.set_zlabel('Z')
+ # plt.show()
diff --git a/anomaly/readme.md b/anomaly/readme.md
index 5f86a5ca..31f15e39 100644
--- a/anomaly/readme.md
+++ b/anomaly/readme.md
@@ -8,3 +8,4 @@ Anomaly Detectors
\subpage semantic_anomaly
\subpage image_anomaly
\subpage volumetric_anomaly
+\subpage gmm