Random Projection (RP) technique has been widely applied in many scenarios because it can reduce high-dimensional features into low-dimensional space within short time and meet the need of real-time analysis of massive data. There is an urgent need of dimensionality reduction with fast increase of big genomics data. However, the performance of RP is usually lower. We attempt to improve classification accuracy of RP through combining other reduction dimension methods such as Principle Component Analysis (PCA), Linear Discriminant Analysis (LDA), and Feature Selection (FS). We compared classification accuracy and running time of different combination methods on three microarray datasets and a simulation dataset. Experimental results show a remarkable improvement of 14.77 in classification accuracy of FS followed by RP compared to RP on BC-TCGA dataset. LDA followed by RP also helps RP to yield a more discriminative subspace with an increase of 13.65 on classification accuracy on the same dataset. FS followed by RP outperforms other combination methods in classification accuracy on most of the datasets.
LDA tries to seek the best linear discriminant function in a supervised way @cite_20 . Compared to PCA, LDA explicitly attempts to model the difference between the classes of data. LDA projects original data onto subspace which has sufficient discriminant power. The dimension of the subspace is restricted to be less than the number of classes. In particular, the dimension of subspace for binary classification problem is 1.
@cite_20
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Fishers linear discriminant analysis (LDA) is a classical multivariate technique both for dimension reduction and classification. The data vectors are transformed into a low dimensional subspace such that the class centroids are spread out as much as possible. In this subspace LDA works as a simple prototype classifier with linear decision boundaries. However, in many applications the linear boundaries do not adequately separate the classes. We present a nonlinear generalization of discriminant analysis that uses the kernel trick of representing dot products by kernel functions. The presented algorithm allows a simple formulation of the EM-algorithm in terms of kernel functions which leads to a unique concept for unsupervised mixture analysis, supervised discriminant analysis and semi-supervised discriminant analysis with partially unlabelled observations in feature spaces.