idx = fscchi2 (X, Y) tests each predictor, a column of the matrix X, for independence from the class labels Y with a chi-square test, and ranks the predictors by the result. idx is a row vector of column indices, from the most important predictor to the least; predictors of equal score keep their order.

X is a real matrix of type double or single with one row per observation. Y holds one class label per row of X: a numeric or logical vector, a categorical vector, a cell array of character vectors, a string array, or a character matrix with one row per observation.

idx = fscchi2 (Tbl, ResponseVarName) takes the predictors and the class labels from the table Tbl: ResponseVarName names the variable holding the labels and every other variable is a predictor. idx = fscchi2 (Tbl, formula) names them with a model formula instead, 'Y ~ x1 + x2', which holds main effects only, and ranks only the predictors it names, idx indexing them in the order the table holds them. idx = fscchi2 (Tbl, Y) takes the predictors from the table and the labels from Y. A logical, categorical, text or string variable of the table is a categorical predictor; an ordinal categorical one is continuous, its categories in their order.

[idx, scores] = fscchi2 (…) also returns the score of each predictor, a row vector in the order of the predictors, so that scores(idx) is in decreasing order. The score is -log (p), p being the p-value of the predictor’s test, so a larger score marks a more important predictor; it is Inf where p is 0. A predictor that cannot separate the classes, being constant or wholly missing, scores 0, and so does every predictor when the labels hold a single class.

A continuous predictor is first binned. Its n known values are sorted, the upper edge of bin k is the value at position ceil (k * n / NumBins), and a value goes to the first bin whose edge it does not exceed. The bins so hold equal numbers of observations as nearly as the ties allow, the first ones taking any remainder, and equal values always share a bin, which may leave fewer bins than asked for. A categorical predictor takes its categories as they are. The test is Pearson’s chi-square test of independence on the table of weighted counts of the bins or categories against the classes, the empty ones left out.

Each predictor is tested on the observations it is known for. Their weights are scaled within each class so that the class carries its prior probability, and over all so that they sum to the number of those observations. The empirical prior, the default, is the weighted share of each class among those observations, which leaves the weights as given. An observation whose class label is missing is left out of every test.

The following Name-Value pairs are supported:

The option names are not case sensitive but must be given in full. With a matrix, the categorical predictors cannot be named, the predictors having no names, as in MATLAB.

See also: fsrftest, relieff, sequentialfs, crosstab

Source Code: fscchi2