Population structure-learned classifier for high-dimension low-sample-size class-imbalanced problem

The Classification on high-dimension low-sample-size data (HDLSS) is a challenging problem and it is common to have class-imbalanced data in most application fields. We term this as Imbalanced HDLSS (IHDLSS). Recent theoretical results reveal that the classification criterion and tolerance similarity are crucial to HDLSS, which emphasizes the maximization of within-class variance on the premise of class separability. Based on this idea, a novel linear binary classifier, termed Population Structure-learned Classifier (PSC), is proposed. The proposed PSC can obtain better generalization performance on IHDLSS by maximizing the sum of inter-class scatter matrix and intra-class scatter matrix on the premise of class separability and assigning different intercept values to majority and minority classes. The salient features of the proposed approach are: (1) It works well on IHDLSS; (2) The inverse of high dimensional matrix can be solved in low dimensional space; (3) It is self-adaptive in determining the intercept term for each class; (4) It has the same computational complexity as the SVM. A series of evaluations are conducted on one simulated data set and eight real-world benchmark data sets on IHDLSS on gene analysis. Experimental results demonstrate that the PSC is superior to the state-of-art methods in IHDLSS.

The classification for High-dimension low-sample size data

Huge amount of applications in various fields, such as gene expression analysis or computer vision, undergo data sets with high-dimensional low-sample-size (HDLSS), which has putted forward great challenges for standard statistical and modern machine learning methods. In this paper, we propose a novel classification criterion on HDLSS, tolerance similarity, which emphasizes the maximization of within-class variance on the premise of class separability. According to this criterion, a novel linear binary classifier is designed, denoted by No-separated Data Maximum Dispersion classifier (NPDMD). The objective of NPDMD is to find a projecting direction w in which all of training samples scatter in as large an interval as possible. NPDMD has several characteristics compared to the state-of-the-art classification methods. First, it works well on HDLSS. Second, it combines the sample statistical information and local structural information (supporting vectors) into the objective function to find the solution of projecting direction in the whole feature spaces. Third, it solves the inverse of high dimensional matrix in low dimensional space. Fourth, it is relatively simple to be implemented based on Quadratic Programming. Fifth, it is robust to the model specification for various real applications. The theoretical properties of NPDMD are deduced. We conduct a series of evaluations on one simulated and six real-world benchmark data sets, including face classification and mRNA classification. NPDMD outperforms those widely used approaches in most cases, or at least obtains comparable results.

Population-Guided Large Margin Classifier for High-Dimension Low -Sample-Size Problems

Various applications in different fields, such as gene expression analysis or computer vision, suffer from data sets with high-dimensional low-sample-size (HDLSS), which has posed significant challenges for standard statistical and modern machine learning methods. In this paper, we propose a novel linear binary classifier, denoted by population-guided large margin classifier (PGLMC), which is applicable to any sorts of data, including HDLSS. PGLMC is conceived with a projecting direction w given by the comprehensive consideration of local structural information of the hyperplane and the statistics of the training samples. Our proposed model has several advantages compared to those widely used approaches. First, it is not sensitive to the intercept term b. Second, it operates well with imbalanced data. Third, it is relatively simple to be implemented based on Quadratic Programming. Fourth, it is robust to the model specification for various real applications. The theoretical properties of PGLMC are proven. We conduct a series of evaluations on two simulated and six real-world benchmark data sets, including DNA classification, digit recognition, medical image analysis, and face recognition. PGLMC outperforms the state-of-the-art classification methods in most cases, or at least obtains comparable results.