Example

Application of these functions is illustrated on data set Wine from the UCI machine learning repository. This data set consists of 178 samples (each sample is 13-D). The number of classes is 3.

Figure 1: 2-D features corresponding to the samples of the Wine data. Colors indicate class memberships.

Fig. 1 shows the resulting 2-D feature plot taking all the 178 samples. For plotting the Wine feature space, the function plot_wine.m is posted. Note that the function is specifically tailored to the Wine data. Also note that it is assumed that a file wine.mat resides in the same directory as plot_wine.m. This file should contain a variable Data in the form of 178 x 14 matrix. The last column of this matrix contains class label indicators (integers), e.g. {0, 1, 2}. Type help plot_wine or take a look at the source code for further information on this function.

For example, running [T et] = plot_wine(2,1); from MATLAB^TMcommand prompt returns the following:

• The optimal feature extraction matrix T.
• The elapsed time et.

The input arguments represent:

• The size of the feature space m = 2 (passed to (1)).
• Plot indicator PlotFlag = 1 to enable the plotting of features.

Table 1: The performances (%) estimated through leave-one-out CV using linear and quadratic classifiers for dataset Wine

Dataset	m	1	3	5	13 (full)
	AIDA(L)	91.57		98.88	98.88
	ACC(L)	89.89	98.88	98.31	98.88
	MLT(L)	82.58	97.75	-	98.88
	Tubbs(L)	67.41	74.72	91.57	98.88
	LDA(L)	91.01	98.88	-	98.88
Wine	LPP(L)	92.13	98.31	98.31	98.88
	AIDA(Q)	92.13	99.44		99.44
	ACC(Q)	91.01	99.44	99.44	99.44
	MLT(Q)	85.95	99.44	-	99.44
	Tubbs(Q)	70.22	76.4	97.19	99.44
	LDA(Q)	91.57	99.44	-	99.44
	LPP(Q)	92.13	98.31	99.44	99.44

The performance of AIDA criterion was tested experimentally with the Wine dataset and compared to the performances of LDA, ACC [3], Tubbs [4], MLT [5] and LPP [6]. The performance was evaluated using linear and quadratic Bayesian classifiers, with prior probabilities estimated empirically from the data and the Gaussian approximation of the class-conditional probability density functions. A leave-one-out cross validation (CV) was used for performance evaluation. The admissible subspace dimensions are 1$\le$m$\le$c - 1 for LDA, 1$\le$m$\le$${\frac{{1}}{{2}}}$c(c - 1) for MLT [5], and 1$\le$m$\le$n - 1 for the AIDA, Tubbs, LPP and ACC methods. Table 1 shows results, represented by the estimated correct classification rates, for various dimensions of the feature space. The boxed values represent the best results for each classifier.