A New Approach Based on Quantum Clustering and Wavelet Transform for Breast Cancer Classification: Comparative Study

Feature selection involves identifying a subset of the most useful features that produce the same results as the original set of features. In this paper, we present a new approach for improving classification accuracy. This approach is based on quantum clustering for feature subset selection and wavelet transform for features extraction. The feature selection is performed in three steps. First the mammographic image undergoes a wavelet transform then some features are extracted. In the second step the original feature space is partitioned in clusters in order to group similar features. This operation is performed using the Quantum Clustering algorithm. The third step deals with the selection of a representative feature for each cluster. This selection is based on similarity measures such as the correlation coefficient (CC) and the mutual information (MI). The feature which maximizes this information (CC or MI) is chosen by the algorithm. This approach is applied for breast cancer classification. The K-nearest neighbors (KNN) classifier is used to achieve the classification. We have presented classification accuracy versus feature type, wavelet transform and K neighbors in the KNN classifier. An accuracy of 100% was reached in some cases

Data clustering using a model granular magnet

We present a new approach to clustering, based on the physical properties of an inhomogeneous ferromagnet. No assumption is made regarding the underlying distribution of the data. We assign a Potts spin to each data point and introduce an interaction between neighboring points, whose strength is a decreasing function of the distance between the neighbors. This magnetic system exhibits three phases. At very low temperatures it is completely ordered; all spins are aligned. At very high temperatures the system does not exhibit any ordering and in an intermediate regime clusters of relatively strongly coupled spins become ordered, whereas different clusters remain uncorrelated. This intermediate phase is identified by a jump in the order parameters. The spin-spin correlation function is used to partition the spins and the corresponding data points into clusters. We demonstrate on three synthetic and three real data sets how the method works. Detailed comparison to the performance of other techniques clearly indicates the relative success of our method.Comment: 46 pages, postscript, 15 ps figures include

Advances in Feature Selection with Mutual Information

The selection of features that are relevant for a prediction or classification problem is an important problem in many domains involving high-dimensional data. Selecting features helps fighting the curse of dimensionality, improving the performances of prediction or classification methods, and interpreting the application. In a nonlinear context, the mutual information is widely used as relevance criterion for features and sets of features. Nevertheless, it suffers from at least three major limitations: mutual information estimators depend on smoothing parameters, there is no theoretically justified stopping criterion in the feature selection greedy procedure, and the estimation itself suffers from the curse of dimensionality. This chapter shows how to deal with these problems. The two first ones are addressed by using resampling techniques that provide a statistical basis to select the estimator parameters and to stop the search procedure. The third one is addressed by modifying the mutual information criterion into a measure of how features are complementary (and not only informative) for the problem at hand