Matrix Factorization for Recommender Systems

A set of tools for investigating algorithms described in Matrix Factorization Techniques for Recommender Systems.

This minimal implementation supports the following features:

1. Fitting a model is handled via a command line interface that reads training data from a file, performs Stochastic Gradient Descent (for a specified number of epochs) and writes the model to a file.

2. Raw data is read in text format, where each record is a triple <i,j,r> that represents the entry r[i,j] of a "ratings" matrix.

3. A fitted model is represented as a protobuf object.

4. A separate CL interface is provided for evaluating a fitted model on test data and emitting the predicted ratings.

The model

Suppose the user space has dimension M and the item space dimension N, so that the ratings matrix has dimension M-by-N and is sparse. We use bracket notation (a la numpy) instead of subscripts. For a L-dimensional latent factor model, the predicted ratings are given by:

h[i,j] = Pbias[i] + Qbias[j] + Pwts[i,:] * Qwts[j,:]

The names correspond to fields in the model definition. In particular, Pwts is an M-by-L matrix, Qwts an N-by-L matrix, and Pwts[i,:] * Qwts[j,:] is the Euclidean product of their i-th and j-th rows. The Pbias and Qbias terms are vectors of dimension M and N respectively.

Stochastic gradient descent

The loss function for a single training example <i,j> is given by

E = ((h[i,j] - r[i,j])^2 - lambda * l2(Pwts[i,:])^2 + mu * l2(Qwts[j,:])^2) / 2.

Where l2() denotes L2-norm of a vector. Note that regularization is applied only to the Pwts and Qwts terms, not the bias terms. From this loss function, the "delta" to update the terms Pbias[i], Qbias[j], Pwts[i,:], Qwts[j,:] is computed and applied at each step.

The package github.com/drjerry/mfrs/mfsgd is a command-line interface for applying SGD to a file of training data. It loads all training data into memory and performs SGD over the entire set for a specified number of "epochs." The arguments it takes are:

• nrow, ncol, ldim: specify the dimensions M, N, and L in advance
• lambda, mu: the regularization parameters in the loss function
• learning "rate": rescales the delta (for each term) in the SGD update
• epochs: number of times to repeat SGD through the entire data set

Building

The package includes its own minimal set of wrappers around CBLAS methods, and this library needs to be present on the target architecture. Installing the package requires compiler and linker flags to be passed via CGO environment variables. If your GOPATH is set up and CBLAS is installed in a standard location, the following should just work:

$ CGO_LDFLAGS=-lcblas go install github.com/drjerry/mfrs/mfsgd
$ CGO_LDFLAGS=-lcblas go install github.com/drjerry/mfrs/mfeval

If CBLAS is installed in a non-standard location, the "-L" and "-I" flags may need to be passed as well.