autoTableOfReal PCA_and_Configuration_to_TableOfReal_reconstruct (PCA me, Configuration thee) {
try {
long npc = thy numberOfColumns;
if (thy numberOfColumns > my dimension) {
Melder_throw (U"The dimension of the Configuration must be less than or equal to the dimension of the PCA.");
}
if (npc > my numberOfEigenvalues) {
npc = my numberOfEigenvalues;
}
autoTableOfReal him = TableOfReal_create (thy numberOfRows, my dimension);
NUMstrings_copyElements (my labels, his columnLabels, 1, my dimension);
NUMstrings_copyElements (thy rowLabels, his rowLabels, 1, thy numberOfRows);
for (long i = 1; i <= thy numberOfRows; i++) {
double *hisdata = his data[i];
for (long k = 1; k <= npc; k++) {
double *evec = my eigenvectors[k], pc = thy data[i][k];
for (long j = 1; j <= my dimension; j++) {
hisdata[j] += pc * evec[j];
}
}
}
return him;
} catch (MelderError) {
Melder_throw (U"TableOfReal not reconstructed.");
}
}
autoTableOfReal Confusion_to_TableOfReal_marginals (Confusion me) {
try {
autoTableOfReal thee = TableOfReal_create (my numberOfRows + 1, my numberOfColumns + 1);
double total = 0.0;
for (long i = 1; i <= my numberOfRows; i++) {
double rowsum = 0.0;
for (long j = 1; j <= my numberOfColumns; j++) {
thy data[i][j] = my data[i][j];
rowsum += my data[i][j];
}
thy data[i][my numberOfColumns + 1] = rowsum;
total += rowsum;
}
thy data[my numberOfRows + 1][my numberOfColumns + 1] = total;
for (long j = 1; j <= my numberOfColumns; j++) {
double colsum = 0;
for (long i = 1; i <= my numberOfRows; i++) {
colsum += my data[i][j];
}
thy data[my numberOfRows + 1][j] = colsum;
}
NUMstrings_copyElements (my rowLabels, thy rowLabels, 1, my numberOfRows);
NUMstrings_copyElements (my columnLabels, thy columnLabels, 1, my numberOfColumns);
return thee;
} catch (MelderError) {
Melder_throw (me, U": table with marginals not created.");
}
}
autoConfusion Confusion_condense (Confusion me, const char32 *search, const char32 *replace,
long maximumNumberOfReplaces, int use_regexp) {
try {
long nmatches, nstringmatches;
if (my rowLabels == 0 || my columnLabels == 0) {
Melder_throw (U"No row or column labels.");
}
autostring32vector rowLabels (strs_replace (my rowLabels, 1, my numberOfRows, search, replace,
maximumNumberOfReplaces, &nmatches, &nstringmatches, use_regexp), 1, my numberOfRows);
autostring32vector columnLabels (strs_replace (my columnLabels, 1, my numberOfColumns, search, replace,
maximumNumberOfReplaces, &nmatches, &nstringmatches, use_regexp), 1, my numberOfColumns);
autoStrings srow = Thing_new (Strings);
srow -> numberOfStrings = my numberOfRows;
srow -> strings = rowLabels.transfer();
autoStrings scol = Thing_new (Strings);
scol -> numberOfStrings = my numberOfColumns;
scol -> strings = columnLabels.transfer();
/* Find dimension of new Confusion */
autoDistributions dcol = Strings_to_Distributions (scol.get());
long nresp = dcol -> numberOfRows;
autoDistributions drow = Strings_to_Distributions (srow.get());
long nstim = drow -> numberOfRows;
autoConfusion thee = Confusion_create (nstim, nresp);
NUMstrings_copyElements (drow -> rowLabels, thy rowLabels, 1, nstim);
NUMstrings_copyElements (dcol -> rowLabels, thy columnLabels, 1, nresp);
autoNUMvector<long> rowIndex (1, my numberOfRows);
create_index (srow -> strings, 1, my numberOfRows, drow -> rowLabels, 1, nstim, rowIndex.peek());
autoNUMvector<long> columnIndex (1, my numberOfColumns);
create_index (scol -> strings, 1, my numberOfColumns, dcol -> rowLabels, 1, nresp, columnIndex.peek());
for (long i = 1; i <= my numberOfRows; i++) {
for (long j = 1; j <= my numberOfColumns; j++) {
thy data [rowIndex [i]][columnIndex[j]] += my data[i][j];
}
}
return thee;
} catch (MelderError) {
Melder_throw (me, U": not condensed.");
}
}
/*
raw r[j]: eigenvec[i][j]
unstandardized u[j]: sqrt(N-g) * r[j]
standardized s[j]: u[j] sqrt (w[i][i] / (N-g))
*/
autoTableOfReal Discriminant_extractCoefficients (Discriminant me, int choice) {
try {
int raw = choice == 0, standardized = choice == 2;
long nx = my eigen -> dimension, ny = my eigen -> numberOfEigenvalues;
SSCP total = my total.get();
autoTableOfReal thee = TableOfReal_create (ny, nx + 1);
NUMstrings_copyElements (my total -> columnLabels, thy columnLabels, 1, nx);
autoSSCP within;
if (standardized) {
within = Discriminant_extractPooledWithinGroupsSSCP (me);
}
TableOfReal_setColumnLabel (thee.get(), nx + 1, U"constant");
TableOfReal_setSequentialRowLabels (thee.get(), 1, ny, U"function_", 1, 1);
double scale = sqrt (total -> numberOfObservations - my numberOfGroups);
double *centroid = my total -> centroid;
for (long i = 1; i <= ny; i++) {
double u0 = 0.0, ui;
for (long j = 1; j <= nx; j++) {
if (standardized) {
scale = sqrt (within -> data[j][j]);
}
thy data[i][j] = ui = scale * my eigen -> eigenvectors[i][j];;
u0 += ui * centroid[j];
}
thy data[i][nx + 1] = raw ? 0.0 : -u0;
}
return thee;
} catch (MelderError) {
Melder_throw (me, U": coefficients not extracted.");
}
}
TableOfReal CCA_and_TableOfReal_scores (CCA me, TableOfReal thee, long numberOfFactors)
{
TableOfReal him = NULL;
long n = thy numberOfRows;
long nx = my x -> dimension, ny = my y -> dimension;
if (ny + nx != thy numberOfColumns) return Melder_errorp7 (L"The number "
"of columns in the table (", Melder_integer (thy numberOfColumns), L") does not agree with "
"the dimensions of the CCA object (ny + nx = ", Melder_integer (ny), L" + ", Melder_integer (nx), L").");
if (numberOfFactors == 0) numberOfFactors = my numberOfCoefficients;
if (numberOfFactors < 1 || numberOfFactors > my numberOfCoefficients)
return Melder_errorp3 (L"The number of factors must be in interval "
"[1, ", Melder_integer (my numberOfCoefficients), L"].");
him = TableOfReal_create (n, 2 * numberOfFactors);
if (him == NULL) return NULL;
if (! NUMstrings_copyElements (thy rowLabels, his rowLabels, 1, thy numberOfRows) ||
! Eigen_and_TableOfReal_project_into (my y, thee, 1, ny, &him, 1, numberOfFactors) ||
! Eigen_and_TableOfReal_project_into (my x, thee, ny + 1,
thy numberOfColumns, &him, numberOfFactors + 1, his numberOfColumns) ||
! TableOfReal_setSequentialColumnLabels (him, 1, numberOfFactors, L"y_", 1, 1) ||
! TableOfReal_setSequentialColumnLabels (him, numberOfFactors + 1,
his numberOfColumns, L"x_", 1, 1)) forget (him);
return him;
}
TableOfReal CCA_and_TableOfReal_scores (CCA me, TableOfReal thee, long numberOfFactors) {
try {
long n = thy numberOfRows;
long nx = my x -> dimension, ny = my y -> dimension;
if (ny + nx != thy numberOfColumns) {
Melder_throw (U"The number of columns in the table (", thy numberOfColumns,
U") does not agree with the dimensions of the CCA object (ny + nx = ", ny, U" + ", nx, U").");
}
if (numberOfFactors == 0) {
numberOfFactors = my numberOfCoefficients;
}
if (numberOfFactors < 1 || numberOfFactors > my numberOfCoefficients) {
Melder_throw (U"The number of factors must be in interval [1, ", my numberOfCoefficients, U"].");
}
autoTableOfReal him = TableOfReal_create (n, 2 * numberOfFactors);
TableOfReal phim = him.peek();
NUMstrings_copyElements (thy rowLabels, his rowLabels, 1, thy numberOfRows);
Eigen_and_TableOfReal_project_into (my y, thee, 1, ny, &phim, 1, numberOfFactors);
Eigen_and_TableOfReal_project_into (my x, thee, ny + 1, thy numberOfColumns, &phim, numberOfFactors + 1, his numberOfColumns);
TableOfReal_setSequentialColumnLabels (him.peek(), 1, numberOfFactors, U"y_", 1, 1);
TableOfReal_setSequentialColumnLabels (him.peek(), numberOfFactors + 1, his numberOfColumns, U"x_", 1, 1);
return him.transfer();
} catch (MelderError) {
Melder_throw (me, U": no TableOfReal with scores created.");
}
}
autoConfusion Confusion_groupStimuli (Confusion me, const char32 *labels, const char32 *newLabel, long newpos) {
try {
long ncondense = Melder_countTokens (labels);
autoNUMvector<long> irow (1, my numberOfRows);
for (long i = 1; i <= my numberOfRows; i++) {
irow[i] = i;
}
for (char32 *token = Melder_firstToken (labels); token != nullptr; token = Melder_nextToken ()) {
for (long i = 1; i <= my numberOfRows; i++) {
if (Melder_equ (token, my rowLabels[i])) {
irow[i] = 0;
break;
}
}
}
long nfound = 0;
for (long i = 1; i <= my numberOfRows; i++) {
if (irow[i] == 0) {
nfound ++;
}
}
if (nfound == 0) {
Melder_throw (U"Invalid stimulus labels.");
}
if (nfound != ncondense) {
Melder_warning (U"One or more of the given stimulus labels are suspect.");
}
long newnstim = my numberOfRows - nfound + 1;
if (newpos < 1) {
newpos = 1;
}
if (newpos > newnstim) {
newpos = newnstim;
}
autoConfusion thee = Confusion_create (newnstim, my numberOfColumns);
NUMstrings_copyElements (my columnLabels, thy columnLabels, 1, my numberOfColumns);
TableOfReal_setRowLabel (thee.get(), newpos, newLabel);
long inewrow = 1;
for (long i = 1; i <= my numberOfRows; i++) {
long rowpos = newpos;
if (irow[i] > 0) {
if (inewrow == newpos) {
inewrow++;
}
rowpos = inewrow;
inewrow++;
TableOfReal_setRowLabel (thee.get(), rowpos, my rowLabels[i]);
}
for (long j = 1; j <= my numberOfColumns; j++) {
thy data[rowpos][j] += my data[i][j];
}
}
return thee;
} catch (MelderError) {
Melder_throw (me, U": stimuli not grouped.");
}
}
autoConfusion Confusion_groupResponses (Confusion me, const char32 *labels, const char32 *newLabel, long newpos) {
try {
long ncondense = Melder_countTokens (labels);
autoNUMvector<long> icol (1, my numberOfColumns);
for (long i = 1; i <= my numberOfColumns; i++) {
icol[i] = i;
}
for (char32 *token = Melder_firstToken (labels); token != 0; token = Melder_nextToken ()) {
for (long i = 1; i <= my numberOfColumns; i++) {
if (Melder_equ (token, my columnLabels[i])) {
icol[i] = 0;
break;
}
}
}
long nfound = 0;
for (long i = 1; i <= my numberOfColumns; i++) {
if (icol[i] == 0) {
nfound ++;
}
}
if (nfound == 0) {
Melder_throw (U"Invalid response labels.");
}
if (nfound != ncondense) {
Melder_warning (U"One or more of the given response labels are suspect.");
}
long newnresp = my numberOfColumns - nfound + 1;
if (newpos < 1) {
newpos = 1;
}
if (newpos > newnresp) {
newpos = newnresp;
}
autoConfusion thee = Confusion_create (my numberOfRows, newnresp);
NUMstrings_copyElements (my rowLabels, thy rowLabels, 1, my numberOfRows);
TableOfReal_setColumnLabel (thee.get(), newpos, newLabel);
long inewcol = 1;
for (long i = 1; i <= my numberOfColumns; i++) {
long colpos = newpos;
if (icol[i] > 0) {
if (inewcol == newpos) {
inewcol++;
}
colpos = inewcol;
inewcol++;
TableOfReal_setColumnLabel (thee.get(), colpos, my columnLabels[i]);
}
for (long j = 1; j <= my numberOfRows; j++) {
thy data[j][colpos] += my data[j][i];
}
}
return thee;
} catch (MelderError) {
Melder_throw (me, U": responses not grouped.");
}
}
autoPCA TableOfReal_to_PCA_byRows (TableOfReal me) {
try {
autoPCA thee = NUMdmatrix_to_PCA (my data, my numberOfRows, my numberOfColumns, false);
NUMstrings_copyElements (my columnLabels, thy labels, 1, my numberOfColumns);
return thee;
} catch (MelderError) {
Melder_throw (me, U": PCA not created.");
}
}
autoPCA TableOfReal_to_PCA (I) {
iam (TableOfReal);
try {
long m = my numberOfRows, n = my numberOfColumns;
if (! TableOfReal_areAllCellsDefined (me, 0, 0, 0, 0)) {
Melder_throw (U"Undefined cells.");
}
if (m < 2) {
Melder_throw (U"There is not enough data to perform a PCA.\nYour table has less than 2 rows.");
}
if (m < n) {
Melder_warning (U"The number of rows in your table is less than the \nnumber of columns. ");
}
if (NUMfrobeniusnorm (m, n, my data) == 0) {
Melder_throw (U"All values in your table are zero.");
}
autoPCA thee = Thing_new (PCA);
autoNUMmatrix<double> a (NUMmatrix_copy (my data, 1, m, 1, n), 1, 1);
thy centroid = NUMvector<double> (1, n);
for (long j = 1; j <= n; j++) {
double colmean = a[1][j];
for (long i = 2; i <= m; i++) {
colmean += a[i][j];
}
colmean /= m;
for (long i = 1; i <= m; i++) {
a[i][j] -= colmean;
}
thy centroid[j] = colmean;
}
Eigen_initFromSquareRoot (thee.peek(), a.peek(), m, n);
thy labels = NUMvector<char32 *> (1, n);
NUMstrings_copyElements (my columnLabels, thy labels, 1, n);
PCA_setNumberOfObservations (thee.peek(), m);
/*
The covariance matrix C = A'A / (N-1). However, we have calculated
the eigenstructure for A'A. This has no consequences for the
eigenvectors, but the eigenvalues have to be divided by (N-1).
*/
for (long i = 1; i <= thy numberOfEigenvalues; i++) {
thy eigenvalues[i] /= (m - 1);
}
return thee;
} catch (MelderError) {
Melder_throw (me, U": PCA not created.");
}
}
autoTableOfReal Eigen_and_TableOfReal_project (Eigen me, TableOfReal thee, long from, long numberOfComponents) {
try {
if (numberOfComponents == 0) {
numberOfComponents = my numberOfEigenvalues;
}
autoTableOfReal him = TableOfReal_create (thy numberOfRows, numberOfComponents);
Eigen_and_TableOfReal_project_into (me, thee, from, thy numberOfColumns, him.peek(), 1, numberOfComponents);
NUMstrings_copyElements (thy rowLabels, his rowLabels, 1, thy numberOfRows);
return him.transfer();
} catch (MelderError) {
Melder_throw (U"TableOfReal not created from projection.");
}
}
autoConfiguration PCA_and_TableOfReal_to_Configuration (PCA me, TableOfReal thee, long numberOfDimensionsToKeep) {
try {
if (numberOfDimensionsToKeep == 0 || numberOfDimensionsToKeep > my numberOfEigenvalues) {
numberOfDimensionsToKeep = my numberOfEigenvalues;
}
autoConfiguration him = Configuration_create (thy numberOfRows, numberOfDimensionsToKeep);
Eigen_and_TableOfReal_into_TableOfReal_projectRows (me, thee, 1, him.get(), 1, numberOfDimensionsToKeep);
NUMstrings_copyElements (thy rowLabels, his rowLabels, 1, thy numberOfRows);
TableOfReal_setSequentialColumnLabels (him.get(), 0, 0, U"pc", 1, 1);
return him;
} catch (MelderError) {
Melder_throw (U"Configuration not created from PCA & TableOfReal.");
}
}
autoTableOfReal Discriminant_extractGroupCentroids (Discriminant me) {
try {
long m = my groups -> size, n = my eigen -> dimension;
autoTableOfReal thee = TableOfReal_create (m, n);
for (long i = 1; i <= m; i ++) {
SSCP sscp = my groups->at [i];
TableOfReal_setRowLabel (thee.get(), i, Thing_getName (sscp));
NUMvector_copyElements (sscp -> centroid, thy data [i], 1, n);
}
NUMstrings_copyElements (my groups->at [m] -> columnLabels, thy columnLabels, 1, n);
return thee;
} catch (MelderError) {
Melder_throw (me, U": group centroids not extracted.");
}
}
TableOfReal CCA_and_Correlation_factorLoadings (CCA me, Correlation thee)
{
TableOfReal him;
long i, j, k, ny = my y -> dimension, nx = my x -> dimension;
double t, **evecy = my y -> eigenvectors, **evecx = my x -> eigenvectors;
if (ny + nx != thy numberOfColumns) return Melder_errorp1 (L"The number "
"of columns in the Correlation object must equal the sum of the "
"dimensions in the CCA object");
him = TableOfReal_create (2 * my numberOfCoefficients, thy numberOfColumns);
if (him == NULL) return NULL;
if (! NUMstrings_copyElements (thy columnLabels, his columnLabels,
1, thy numberOfColumns) ||
! TableOfReal_setSequentialRowLabels (him, 1, my numberOfCoefficients,
L"dv", 1, 1) ||
! TableOfReal_setSequentialRowLabels (him, my numberOfCoefficients + 1,
2 * my numberOfCoefficients, L"iv", 1, 1))
{
forget (him);
return NULL;
}
for (i = 1; i <= thy numberOfRows; i++)
{
for (j = 1; j <= my numberOfCoefficients; j++)
{
t = 0;
for (k = 1; k <= ny; k++)
{
t += thy data[i][k] * evecy[j][k];
}
his data[j][i] = t;
}
for (j = 1; j <= my numberOfCoefficients; j++)
{
t = 0;
for (k = 1; k <= nx; k++)
{
t += thy data[i][ny + k] * evecx[j][k];
}
his data[my numberOfCoefficients + j][i] = t;
}
}
return him;
}
autoTableOfReal Discriminant_extractGroupStandardDeviations (Discriminant me) {
try {
long m = my groups->size, n = my eigen -> dimension;
autoTableOfReal thee = TableOfReal_create (m, n);
for (long i = 1; i <= m; i ++) {
SSCP sscp = my groups->at [i];
TableOfReal_setRowLabel (thee.get(), i, Thing_getName (sscp));
long numberOfObservationsm1 = (long) floor (sscp -> numberOfObservations) - 1;
for (long j = 1; j <= n; j ++) {
thy data [i] [j] = numberOfObservationsm1 > 0 ? sqrt (sscp -> data [j] [j] / numberOfObservationsm1) : NUMundefined;
}
}
NUMstrings_copyElements (my groups->at [m] -> columnLabels, thy columnLabels, 1, n);
return thee;
} catch (MelderError) {
Melder_throw (me, U": group standard deviations not extracted.");
}
}
TableOfReal Eigen_and_TableOfReal_project (I, thou, long from,
long numberOfComponents)
{
iam (Eigen);
thouart (TableOfReal);
TableOfReal him;
if (numberOfComponents == 0) numberOfComponents = my numberOfEigenvalues;
him = TableOfReal_create (thy numberOfRows, numberOfComponents);
if (him != NULL)
{
if (! Eigen_and_TableOfReal_project_into (me, thee, from,
thy numberOfColumns, & him, 1, numberOfComponents) ||
! NUMstrings_copyElements (thy rowLabels, his rowLabels,
1, thy numberOfRows)) forget (him);
}
return him;
}
autoTableOfReal PCA_and_TableOfReal_to_TableOfReal_zscores (PCA me, TableOfReal thee, long numberOfDimensions) {
try {
if (numberOfDimensions == 0 || numberOfDimensions > my numberOfEigenvalues) {
numberOfDimensions = my numberOfEigenvalues;
}
autoTableOfReal him = TableOfReal_create (thy numberOfRows, numberOfDimensions);
for (long i = 1; i <= thy numberOfRows; i++) { /* row */
for (long j = 1; j <= numberOfDimensions; j++) {
double r = 0, sigma = sqrt (my eigenvalues[j]);
for (long k = 1; k <= my dimension; k++) {
// eigenvector in row, data in row
r += my eigenvectors[j][k] * (thy data[i][k] - my centroid[k]) / sigma;
}
his data[i][j] = r;
}
}
NUMstrings_copyElements (thy rowLabels, his rowLabels, 1, thy numberOfRows);
TableOfReal_setSequentialColumnLabels (him.get(), 0, 0, U"pc", 1, 1);
return him;
} catch (MelderError) {
Melder_throw (U"TableOfReal (zscores) not created from PCA & TableOfReal.");
}
}
ClassificationTable Discriminant_and_TableOfReal_to_ClassificationTable (Discriminant me, TableOfReal thee,
int poolCovarianceMatrices, int useAprioriProbabilities) {
try {
long g = Discriminant_getNumberOfGroups (me);
long p = Eigen_getDimensionOfComponents (me);
long m = thy numberOfRows;
if (p != thy numberOfColumns) Melder_throw
(U"The number of columns does not agree with the dimension of the discriminant.");
autoNUMvector<double> log_p (1, g);
autoNUMvector<double> log_apriori (1, g);
autoNUMvector<double> ln_determinant (1, g);
autoNUMvector<double> buf (1, p);
autoNUMvector<SSCP> sscpvec (1, g);
autoSSCP pool = SSCPs_to_SSCP_pool (my groups);
autoClassificationTable him = ClassificationTable_create (m, g);
NUMstrings_copyElements (thy rowLabels, his rowLabels, 1, m);
// Scale the sscp to become a covariance matrix.
for (long i = 1; i <= p; i++) {
for (long k = i; k <= p; k++) {
pool -> data[k][i] = (pool -> data[i][k] /= (pool -> numberOfObservations - g));
}
}
double lnd;
autoSSCPs agroups = 0; SSCPs groups;
if (poolCovarianceMatrices) {
/*
Covariance matrix S can be decomposed as S = L.L'. Calculate L^-1.
L^-1 will be used later in the Mahalanobis distance calculation:
v'.S^-1.v == v'.L^-1'.L^-1.v == (L^-1.v)'.(L^-1.v).
*/
NUMlowerCholeskyInverse (pool -> data, p, &lnd);
for (long j = 1; j <= g; j++) {
ln_determinant[j] = lnd;
sscpvec[j] = pool.peek();
}
groups = (SSCPs) my groups;
} else {
// Calculate the inverses of all group covariance matrices.
// In case of a singular matrix, substitute inverse of pooled.
agroups.reset (Data_copy ( (SSCPs) my groups)); groups = agroups.peek();
long npool = 0;
for (long j = 1; j <= g; j++) {
SSCP t = (SSCP) groups -> item[j];
long no = (long) floor (SSCP_getNumberOfObservations (t));
for (long i = 1; i <= p; i++) {
for (long k = i; k <= p; k++) {
t -> data[k][i] = (t -> data[i][k] /= (no - 1));
}
}
sscpvec[j] = (SSCP) groups -> item[j];
try {
NUMlowerCholeskyInverse (t -> data, p, &ln_determinant[j]);
} catch (MelderError) {
// Try the alternative: the pooled covariance matrix.
// Clear the error.
Melder_clearError ();
if (npool == 0) {
NUMlowerCholeskyInverse (pool -> data, p, &lnd);
}
npool++;
sscpvec[j] = pool.peek();
ln_determinant[j] = lnd;
}
}
if (npool > 0) {
Melder_warning (npool, U" groups use pooled covariance matrix.");
}
}
// Labels for columns in ClassificationTable
for (long j = 1; j <= g; j++) {
const char32 *name = Thing_getName ( (Thing) my groups -> item[j]);
if (! name) {
name = U"?";
}
TableOfReal_setColumnLabel (him.peek(), j, name);
}
// Normalize the sum of the apriori probabilities to 1.
// Next take ln (p) because otherwise probabilities might be too small to represent.
NUMvector_normalize1 (my aprioriProbabilities, g);
double logg = log (g);
for (long j = 1; j <= g; j++) {
log_apriori[j] = useAprioriProbabilities ? log (my aprioriProbabilities[j]) : - logg;
}
// Generalized squared distance function:
// D^2(x) = (x - mu)' S^-1 (x - mu) + ln (determinant(S)) - 2 ln (apriori)
for (long i = 1; i <= m; i++) {
double norm = 0, pt_max = -1e38;
for (long j = 1; j <= g; j++) {
SSCP t = (SSCP) groups -> item[j];
double md = mahalanobisDistanceSq (sscpvec[j] -> data, p, thy data[i], t -> centroid, buf.peek());
double pt = log_apriori[j] - 0.5 * (ln_determinant[j] + md);
if (pt > pt_max) {
pt_max = pt;
}
log_p[j] = pt;
}
for (long j = 1; j <= g; j++) {
norm += (log_p[j] = exp (log_p[j] - pt_max));
}
for (long j = 1; j <= g; j++) {
his data[i][j] = log_p[j] / norm;
}
}
return him.transfer();
} catch (MelderError) {
Melder_throw (U"ClassificationTable from Discriminant & TableOfReal not created.");
}
}
autoClassificationTable Discriminant_and_TableOfReal_to_ClassificationTable_dw (Discriminant me, TableOfReal thee, int poolCovarianceMatrices, int useAprioriProbabilities, double alpha, double minProb, autoTableOfReal *displacements) {
try {
long g = Discriminant_getNumberOfGroups (me);
long p = Eigen_getDimensionOfComponents (my eigen.get());
long m = thy numberOfRows;
if (p != thy numberOfColumns) Melder_throw
(U"The number of columns does not agree with the dimension of the discriminant.");
autoNUMvector<double> log_p (1, g);
autoNUMvector<double> log_apriori (1, g);
autoNUMvector<double> ln_determinant (1, g);
autoNUMvector<double> buf (1, p);
autoNUMvector<double> displacement (1, p);
autoNUMvector<double> x (1, p);
autoNUMvector<SSCP> sscpvec (1, g);
autoSSCP pool = SSCPList_to_SSCP_pool (my groups.get());
autoClassificationTable him = ClassificationTable_create (m, g);
NUMstrings_copyElements (thy rowLabels, his rowLabels, 1, m);
autoTableOfReal adisplacements = Data_copy (thee);
// Scale the sscp to become a covariance matrix.
for (long i = 1; i <= p; i ++) {
for (long k = i; k <= p; k ++) {
pool -> data [k] [i] = pool -> data [i] [k] /= pool -> numberOfObservations - g;
}
}
double lnd;
autoSSCPList agroups;
SSCPList groups;
if (poolCovarianceMatrices) {
// Covariance matrix S can be decomposed as S = L.L'. Calculate L^-1.
// L^-1 will be used later in the Mahalanobis distance calculation:
// v'.S^-1.v == v'.L^-1'.L^-1.v == (L^-1.v)'.(L^-1.v).
NUMlowerCholeskyInverse (pool -> data, p, & lnd);
for (long j = 1; j <= g; j ++) {
ln_determinant [j] = lnd;
sscpvec [j] = pool.get();
}
groups = my groups.get();
} else {
//Calculate the inverses of all group covariance matrices.
// In case of a singular matrix, substitute inverse of pooled.
agroups = Data_copy (my groups.get());
groups = agroups.get();
long npool = 0;
for (long j = 1; j <= g; j ++) {
SSCP t = groups->at [j];
long no = (long) floor (SSCP_getNumberOfObservations (t));
for (long i = 1; i <= p; i ++) {
for (long k = i; k <= p; k ++) {
t -> data [k] [i] = t -> data [i] [k] /= no - 1;
}
}
sscpvec [j] = groups->at [j];
try {
NUMlowerCholeskyInverse (t -> data, p, & ln_determinant [j]);
} catch (MelderError) {
// Try the alternative: the pooled covariance matrix.
// Clear the error.
Melder_clearError ();
if (npool == 0) {
NUMlowerCholeskyInverse (pool -> data, p, & lnd);
}
npool ++;
sscpvec [j] = pool.get();
ln_determinant [j] = lnd;
}
}
if (npool > 0) {
Melder_warning (npool, U" groups use pooled covariance matrix.");
}
}
// Labels for columns in ClassificationTable
for (long j = 1; j <= g; j ++) {
const char32 *name = Thing_getName (my groups->at [j]);
if (! name) {
name = U"?";
}
TableOfReal_setColumnLabel (him.get(), j, name);
}
// Normalize the sum of the apriori probabilities to 1.
// Next take ln (p) because otherwise probabilities might be too small to represent.
double logg = log (g);
NUMvector_normalize1 (my aprioriProbabilities, g);
for (long j = 1; j <= g; j ++) {
log_apriori[j] = ( useAprioriProbabilities ? log (my aprioriProbabilities[j]) : - logg );
}
// Generalized squared distance function:
// D^2(x) = (x - mu)' S^-1 (x - mu) + ln (determinant(S)) - 2 ln (apriori)
for (long i = 1; i <= m; i ++) {
SSCP winner;
double norm = 0, pt_max = -1e308;
long iwinner = 1;
for (long k = 1; k <= p; k ++) {
x [k] = thy data [i] [k] + displacement [k];
}
for (long j = 1; j <= g; j ++) {
SSCP t = groups->at [j];
double md = mahalanobisDistanceSq (sscpvec [j] -> data, p, x.peek(), t -> centroid, buf.peek());
double pt = log_apriori [j] - 0.5 * (ln_determinant [j] + md);
if (pt > pt_max) {
pt_max = pt;
iwinner = j;
}
log_p [j] = pt;
}
for (long j = 1; j <= g; j ++) {
norm += log_p [j] = exp (log_p [j] - pt_max);
}
for (long j = 1; j <= g; j ++) {
his data [i] [j] = log_p [j] / norm;
}
// Save old displacement, calculate new displacement
winner = groups->at [iwinner];
for (long k = 1; k <= p; k ++) {
adisplacements -> data [i] [k] = displacement [k];
if (his data [i] [iwinner] > minProb) {
double delta_k = winner -> centroid [k] - x [k];
displacement [k] += alpha * delta_k;
}
}
}
*displacements = adisplacements.move();
return him;
} catch (MelderError) {
Melder_throw (U"ClassificationTable for Weenink procedure not created.");
}
}