An Expert Support System for Breast Cancer Diagnosis using Color Wavelet Features

Abstract

Breast cancer diagnosis can be done through the pathologic assessments of breast tissue samples such as core needle biopsy technique. The result of analysis on this sample by pathologist is crucial for breast cancer patient. In this paper, nucleus of tissue samples are investigated after decomposition by means of the Log-Gabor wavelet on HSV color domain and an algorithm is developed to compute the color wavelet features. These features are used for breast cancer diagnosis using Support Vector Machine (SVM) classifier algorithm. The ability of properly trained SVM is to correctly classify patterns and make them particularly suitable for use in an expert system that aids in the diagnosis of cancer tissue samples. The results are compared with other multivariate classifiers such as Naïves Bayes classifier and Artificial Neural Network. The overall accuracy of the proposed method using SVM classifier will be further useful for automation in cancer diagnosis.

Appendix A

First order statistical features: Some of the first order statistical features used for this study are Mean, Standard deviation, Skewness, Uniformity and Entropy using the standard expression derived in [63–65] as follows;

$$ Mean\left( {{f_1}} \right) = \sum\limits_{{i = 0}}^{{N - 1}} {{z_i}} p\left( {{z_i}} \right) $$

(A.1)

$$ Standard\;deviation\left( {{f_2}} \right) = \sum\limits_{{i = 0}}^{{N - 1}} {{{\left( {{z_i} - {f_1}} \right)}^2}} p\left( {{z_i}} \right) $$

(A.2)

$$ Skewness\left( {{f_3}} \right) = \sum\limits_{{i = 0}}^{{N - 1}} {{{\left( {{z_i} - {f_1}} \right)}^3}} p\left( {{z_i}} \right) $$

(A.3)

$$ Uniformity\left( {{f_4}} \right) = \sum\limits_{{i = 0}}^{{L - 1}} {{p^2}\left( {{z_i}} \right)} $$

(A.4)

$$ Entropy\left( {{f_5}} \right) = - \sum\limits_{{i = 0}}^{{N - 1}} {p\left( {{z_i}} \right)} \;lo{g_2}p\left( {{z_i}} \right) $$

(A.5)

where, z _i is a random variable indicating intensity, p(z) is the histogram of the intensity levels in a region, N is the number of possible intensity levels.

Second order statistical features: Gray level co-occurrence matrix (GLCM) method is used for extracting wavelet co-occurrence statistical features in this study. The matrices are constructed at a distance of d = 1 and for orientation θ given as 0°, 45°, 90°, and 135°. The statistical parameters such as Contrast, Cluster prominence, Energy, Dissimilarity, Sum of squares: variance, Sum entropy and Difference entropy have taken for this study, amongst several statistical measures [63–65] that derive from each color co-occurrence matrix.

$$ Contrast\left( {{f_6}} \right) = \sum\limits_{{i,j = 1}}^N {{C_{{i,j}}}} {\left( {i - j} \right)^2} $$

(A.6)

$$ Cluster\;Prominence\left( {{f_7}} \right) = \sum\limits_{{i,j = 1}}^N {{{\left( {\left( {i - {\mu_i}} \right) + \left( {j - {\mu_j}} \right)} \right)}^4}{C_{{i,j}}}} $$

(A.7)

$$ Energy\left( {{f_8}} \right) = \sum\limits_{{i,j = 1}}^N {C_{{i,j}}^2} $$

(A.8)

$$ Dissimilarity\left( {{f_9}} \right) = \sum\limits_{{i,j = 1}}^N {\left| {i - j} \right|{C_{{i,j}}}} $$

(A.9)

$$ Sum\;of\;squares:variance\left( {{f_{{10}}}} \right) = \sum\limits_{{i,j = 1}}^N {{{\left( {i - \mu } \right)}^2}{C_{{i,j}}}} $$

(A.10)

$$ Sum\;Entropy\left( {{f_{{11}}}} \right) = - \sum\limits_{{i = 2}}^{{2{N_g}}} {{C_{{x + y}}}(i)\log \left\{ {{C_{{x + y}}}(i)} \right\}} $$

(A.11)

$$ Difference\;Entropy\left( {{f_{{12}}}} \right) = - \sum\limits_{{i = 0}}^{{{N_g} - 1}} {{C_{{x - y}}}(i)\log \left\{ {{C_{{x - y}}}(i)} \right\}} $$

(A.12)

where, C _{i, j} is the element [i, j] of the co-occurrence matrix, N _g is the number of gray levels, μ is the mean, σ ² is the variance of the intensities in the co-occurrence matrix, where x and y are the coordinates (row and column) of an array in the co-occurrence matrix, and C _x+y is the probability of co-occurrence matrix coordinates summing to x+y where as C _x-y is the probability of co-occurrence matrix coordinates differentiating to x-y.