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finish ca, should test
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@jdfekete
jdfekete committed Aug 6, 2015
1 parent 9c6748f commit 4f7b45c
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163 changes: 104 additions & 59 deletions reorder.v1.js
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Original file line number Diff line number Diff line change
Expand Up @@ -119,13 +119,16 @@ reorder.meancolumns = function(v) {
return m;
};

reorder.sum = function(v) {
function sum(v) {
var i = v.length,
s = v[0];
while(i-- > 1)
s += v[i];
s = 0;
while(i-- > 0)
if (! isNaN(v[i]))
s += v[i];
return s;
};
}

reorder.sum = sum;
function isNum(a, b) {
return !(isNaN(a) || isNaN(b) || a==Infinity || b == Infinity);
}
Expand Down Expand Up @@ -2303,7 +2306,7 @@ function normalize(v) {
if (norm === 0 || Math.abs(norm - 1) < 1e-7) return v;
while (i-- > 0)
v[i] /= norm;
return v;
return norm;
}

reorder.poweriteration = function(v, eps, init) {
Expand Down Expand Up @@ -2348,19 +2351,20 @@ reorder.poweriteration_n = function(v, p, init, eps, start) {
i, j, k, l,
bk, dot, row,
tmp = Array(n),
s = 100;
s = 100,
eigenvalue = Array(p);

reorder.assert(n == v[0].length, "poweriteration needs a square matrix");
if (! init) {
for (i = 0; i < p; i++) {
row = b[i] = reorder.random_array(n);
normalize(row);
eigenvalue[i] = normalize(row);
}
}
else {
for (i = 0; i < p; i++) {
b[i] = init[i].slice(); // copy
normalize(b[i]);
eigenvalue[i] = normalize(b[i]);
}
}
if (! start)
Expand All @@ -2382,14 +2386,14 @@ reorder.poweriteration_n = function(v, p, init, eps, start) {
for (j=0; j<n; j++)
tmp[i] += v[i][j] * bk[j];
}
normalize(tmp);
eigenvalue[k] = normalize(tmp);
if (reorder.dot(tmp, bk) > (1 - eps))
break;
bk = tmp; tmp = b[k]; b[k] = bk; // swap b/tmp
}
//console.log('eig[%d]=%j',k, bk);
}
return b;
return [b, eigenvalue];
};
// Compute te Fiedler vector, the smallest non-null eigenvector of a matrix.
// See:
Expand Down Expand Up @@ -2435,7 +2439,7 @@ function fiedler_vector(B, eps) {
}
var init = [ reorder.array1d(n, 1), reorder.random_array(n) ],
eig = reorder.poweriteration_n(Bhat, 2, init, eps, 1);
return eig[1];
return eig[0][1];
}

reorder.fiedler_vector = fiedler_vector;
Expand Down Expand Up @@ -2494,23 +2498,23 @@ reorder.pca_order = function(v, eps) {
//Corresponence Analysis
// see http://en.wikipedia.org/wiki/Correspondence_analysis

reorder.sumlines = function(v) {
function sumrows(v) {
var n = v.length,
o = v[0].length,
sumline = Array(n),
sumrow = Array(n),
i, j, row, s;

for (i = 0; i < n; i++) {
row = v[i];
s = 0;
for (j = 0; j < o; j++)
for (j = 0; j < o; j++)
s += row[j];
sumline[i] = s;
sumrow[i] = s;
}
return sumline;
};
return sumrow;
}

reorder.sumcols = function(v) {
function sumcols(v) {
var n = v.length,
o = v[0].length,
sumcol = reorder.zeroes(o),
Expand All @@ -2522,68 +2526,109 @@ reorder.sumcols = function(v) {
sumcol[j] += row[j];
}
return sumcol;
};
}

reorder.ca = function(v, eps) {
function multiply_by_transpose(a,b) {
var m = a.length,
n = b.length,
p = b[0].length,
i = -1,
j,
k;
if (p !== a[0].length) throw {"error": "columns(a) != rows(b); " + a[0].length + " != " + p};
var ab = new Array(m);
while (++i < m) {
ab[i] = new Array(n);
j = -1; while(++j < n) {
var s = 0;
k = -1; while (++k < p) s += a[i][k] * b[j][k];
ab[i][j] = s;
}
}
return ab;
}

function ca(v, eps) {
var n = v.length,
o = v[0].length,
sumline = reorder.sumlines(v),
sumcol = reorder.sumcols(v),
s = reorder.sum(sumcol),
i, j, row;

sumrow = sumrows(v),
sumcol = sumcols(v),
s = sum(sumcol),
i, j, row,
tmp = Array(n),
orig = v;

for (i = 0; i < n; i++) {
row = v[i];
for (j = 0; j < row.length; j++)
row = v[i].slice();
for (j = 0; j < o; j++) {
row[j] /= s;
}
tmp[i] = row;
sumrow[i] /= s;
}
sumline = reorder.sumlines(v);
sumcol = reorder.sumcols(v);

//reorder.printmat(v);
//console.log("lines: "+sumline);
//console.log("cols: "+sumcol);
for (j = 0; j < o; j++)
sumcol[j] /= s;

var v2 = Array(n), ep;
v = tmp; // get rid of original v
//console.log('normalized matrix:');
//reorder.printmat(v);
//console.log('sumrow:'+sumrow);
//console.log('sumcol:'+sumcol);

var pi = Array(n), // pre inertia matrix
ep; // don't store the expected values

for (i = 0; i < n; i++) {
v2[i] = Array(o);
row = pi[i] = Array(o);
for (j = 0; j < o; j++) {
ep = sumline[i]*sumcol[j];
v2[i][j] = (v[i][j] - ep) / Math.sqrt(ep);
ep = sumrow[i]*sumcol[j];
row[j] = (v[i][j] - ep) / Math.sqrt(ep);
}
}
//reorder.printmat(v2);
//console.log('Pre inertia:');
//reorder.printmat(pi);

var wc = Array(n); // weighted coordinates

for (i = 0; i < n; i++) {
row = wc[i] = Array(o);
for (j = 0; j < o; j++) {
ep = sumline[i]*sumcol[j];
v[i][j] = (v[i][j] - ep) / (sumcol[j]*Math.sqrt(sumline[i]));
ep = sumrow[i]*sumcol[j];
row[j] = (v[i][j] - ep) / (sumcol[j]*Math.sqrt(sumrow[i]));
}
}
//reorder.printmat(v);
//console.log('weighted coordinates:');
//reorder.printmat(wc);

var cov = Array(n);
for (i = 0; i < n; i++)
cov[i] = Array(n);
var inertia = multiply_by_transpose(pi, pi);
//console.log('inertia:');
//reorder.printmat(inertia);

var eigenvector = reorder.poweriteration_n(inertia,1, null, eps),
eigenvalue = eigenvector[1][0];
eigenvector = eigenvector[0][0];
//console.log('Eigenvalue: '+eigenvalue);

for (i = 0; i < n; i++)
for (j = i; j < n; j++)
cov[i][j] = cov[j][i] = reorder.covariance(v2[i], v2[j]);

//console.log("Variance-Covariance");
//reorder.printmat(cov,8);
var cols = Array(o);
for (j = 0; j < o; j++) {
cols[j] = wc[0][j]*eigenvalue;
}
//console.log('Col vector:'+cols);

var eigenvector1 = reorder.poweriteration(cov, eps),
eigenvalue1 = 0;
for (i = 0; i < n; i++)
eigenvalue1 += eigenvector1[i]*cov[i][0];
eigenvalue1 /= eigenvector1[0];
//console.log("Eigenvalue1="+eigenvalue1);
var rows = Array(n);
for (i = 0; i < n; i++) {
s = 0;
for (j = 0; j < o; j++) {
s += v[i][j]*cols[j];
}
rows[i] = s/(sumrow[i]*Math.sqrt(eigenvalue));
}
//console.log('Row vector:'+rows);

return eigenvector1;
};
return [rows, cols];
}

reorder.ca = ca;

/*jshint loopfunc:true */
reorder.cuthill_mckee = function(graph, comp) {
Expand Down
4 changes: 2 additions & 2 deletions reorder.v1.min.js
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