Quasiconformal kernel common locality discriminant analysis with application to breast cancer diagnosis

Abstract

Dimensionality reduction (DR) is a popular method in recognition and classification in many areas, such as facial and medical imaging. In this paper, we propose a novel supervised DR method namely Quasiconformal Kernel Common Locality Discriminant Analysis (QKCLDA). QKCLDA preserves the local and discriminative relationships of the data. Moreover, it adjusts the kernel structure according to the distribution of the input data and thus possesses a classification advantage over traditional kernel-based methods. In QKCLDA, the parameter of the quasiconformal kernel is automatically calculated through optimizing an objective function of maximizing the class discriminative ability. QKCLDA is employed in breast cancer diagnoses, and some experiments using Wisconsin Diagnostic Breast Cancer (WDBC) and mini-MIAS databases have tested its feasibility and performance in assigning these diagnoses.

Introduction

Dimensionality reduction (DR) is the most popular approach for feature extraction. DR has wide applications in computer vision, pattern recognition, gene expression, paleontology, etc. Current DR methods are categorized into supervised learning, such as the linear discriminant analysis (LDA), unsupervised learning, such as the principal component analysis (PCA), and other semi-supervised learning methods that have been proposed in previous works [37], [35], [24].

In recent years, kernel-based methods have attracted attentions in pattern recognition area [9], [10], [22]. Recent many linear methods are proposed, for example, the kernel principal component analysis (KPCA) [26], [27], kernel discriminant analysis (KDA) [28], [18] and improved kernel-based learning methods [22], [34], and the support vector machine (SVM) [30].

Recently, many researchers have focused more on manifold learning, which is derived from PCA. PCA is generalized to principal curves [5] and principal surfaces [3]. Principal curves are essentially equivalent to self-organizing maps (SOM) [19], [25], [1]. As an extended version of SOM, visualization-induced SOM (ViSOM) preserves distance information on maps along with topologies [38], [23]. ViSOM represents a discrete principal curve or surface and produces a smooth and graded mesh in the data space that captures the nonlinear manifold of data [36]. Other nonlinear manifold algorithms have been developed, such as Isomap [31] and locally linear embedding (LLE) [26], [9], locality preserving projection (LPP) [6], and its extension of class-wise locality preserving projection (CLPP), which was proposed in our previous work [9].

In this paper, we present a novel dimensionality reduction method of Quasiconformal Kernel Common Locality Discriminant Analysis (QKCLDA), and in QKCLDA the quasiconformal kernel is applied. The kernel structure of the data is subjected to an adaptive adjustment according to the distribution of the input data. QKCLDA preserves the local and discriminative relationships of the data for classification. The rest of this paper is organized as follows. In Section 2, we analyze the popular algorithms. In Section 3, we describe common locality discriminant analysis (CLDA), and in Section 4, we extend CLDA with the quasiconformal kernel. The application to breast cancer diagnosis is presented in Section 5. Comprehensive evaluations are implemented in Sections 6 Experimental evaluation on feasibility of QKCLDA, 7 Performance evaluation on breast cancer diagnosis. Conclusions are drawn in Section 8.