The Unsupervised Feature Selection Algorithms Based on Standard Deviation and Cosine Similarity for Genomic Data Analysis

To tackle the challenges in genomic data analysis caused by their tens of thousands of dimensions while having a small number of examples and unbalanced examples between classes, the technique of unsupervised feature selection based on standard deviation and cosine similarity is proposed in this paper. We refer to this idea as SCFS (Standard deviation and Cosine similarity based Feature Selection). It defines the discernibility and independence of a feature to value its distinguishable capability between classes and its redundancy to other features, respectively. A 2-dimensional space is constructed using discernibility as x-axis and independence as y-axis to represent all features where the upper right corner features have both comparatively high discernibility and independence. The importance of a feature is defined as the product of its discernibility and its independence (i.e., the area of the rectangular enclosed by the feature's coordinate lines and axes). The upper right corner features are by far the most important, comprising the optimal feature subset. Based on different definitions of independence using cosine similarity, there are three feature selection algorithms derived from SCFS. These are SCEFS (Standard deviation and Exponent Cosine similarity based Feature Selection), SCRFS (Standard deviation and Reciprocal Cosine similarity based Feature Selection) and SCAFS (Standard deviation and Anti-Cosine similarity based Feature Selection), respectively. The KNN and SVM classifiers are built based on the optimal feature subsets detected by these feature selection algorithms, respectively. The experimental results on 18 genomic datasets of cancers demonstrate that the proposed unsupervised feature selection algorithms SCEFS, SCRFS and SCAFS can detect the stable biomarkers with strong classification capability. This shows that the idea proposed in this paper is powerful. The functional analysis of these biomarkers show that the occurrence of the cancer is closely related to the biomarker gene regulation level. This fact will benefit cancer pathology research, drug development, early diagnosis, treatment and prevention.