--4.2 Feature selection of "Pattern Recognition and machine learning"

With n can be used as a classification of the measured value, in order to reduce (or minimize) the classification accuracy, reduce the dimension of the feature space to reduce the computational volume, it is necessary to select the M as a classification of the characteristics. Question: Which of the n measured values is selected as the classification feature, so that it has the smallest classification error?

The M features are selected from the n measured values, and there is a possible selection method in common. A kind of "exhaustive" method: the training sample is used for each method to classify, measure its correct classification rate, and then make the best performance choice, at this time to test the characteristics of a subset of species to reach the species, very time-consuming. It is necessary to find a simple and convenient criterion to determine the merits and demerits of each seed set indirectly. Scatter matrix criteria for general characteristics of selection criteria for independent features

For the selection criteria of the independent feature, the classification criterion should have the characteristic that the distance between the mean vectors of the different class pattern features should be the largest, and the pattern characteristics belonging to the same class should be the least. Assuming that the original characteristics of the measured values are statistically independent, at this time, only the training samples of the n measured values independently analyzed, from which to select the best m as a classification feature.

Discuss:

The applicability of the above-mentioned criterion based on distance measure is related to the distribution of pattern characteristics. Three different patterns of distribution (a) the distribution of characteristic xk is well separable, is it sufficient to separate? I and? J two categories, (b) the characteristics of the distribution of a large overlap, the XK can not reach a better classification, the need to increase other characteristics; (c)? The distribution of Class I feature XK has two maximum values, Although it does not overlap with the distribution of J, the calculation of GK is approximately equal to 0, and the use of GK as a sub-standard is inappropriate. Therefore, if the class probability density function is not or is not approximate to the normal distribution, the mean and variance are not sufficient to estimate the classification of categories, at which point the criterion function is not fully applicable.

The greater the dispersion between the class and the Inter-class dispersion matrix SW and the SB class, the smaller the dispersion in the class, the better the scalability. Scatter matrix Guidelines J1 and J2 form the largest subset of J1 or J2 as the selected classification feature. Note: The scatter matrix computed here is not limited by pattern distribution, but requires a sufficient number of pattern samples to obtain valid results

--4.2 Feature selection of "Pattern Recognition and machine learning"