Improvement And Applications Of Dimensionality Reduction Algorithms

Dimensionality reduction is a new tool to solve the curse of Dimensionality.Dimensionality reduction can map the data from high dimensional space to low dimensionalspace. Furthermore, it can extract essential feature of data. In recent years, dimensionalityreduction is in constant developed and its theoretical research has gained a great breakthrough.Dimensionality reduction has a wide range of applications, such as face recognition,image retrieval, and bioinformatics. It achieved good accuracy by extracting human faceimage feature in face recognition. Dimensionality reduction can improve the image retrievalprecision rate and recall rate by extracting the feature such as color, shape and texture. Withthe developing of gene chip, large amounts of high-dimensional biological data has beenarised. Dimensionality reduction processing provides a new solution for high-dimensionalgene expression profile data.In this paper, the main work is as follows:1. Dimensionality reduction algorithms can be divided into linear dimensionality reductionalgorithms and nonlinear dimensionality reduction algorithms. Linear dimensionality reductionalgorithms mainly include principal component analysis, linear discrimination analysis, andmultidimensional scale transformation, etc; Nonlinear dimensionality reduction algorithms mainlyinclude the locally linear embedding, ISOMAP, diffusion mapping, etc. We present density anddiscriminate–based weighted locally linear embedding (DDWLLE) and improved diffusion mapsbased on the locally linear embedding and diffusion mapping algorithm. DDWLLE extract datainformation by mining density characteristics with the consideration that each dataset has itsdata distribution structure. Experiments show that the proposed algorithm can achieve goodresults in artificial data set, expression profile data set and image retrieval data set.2. The dimensionality reduction algorithm and classification methods are combined inthe application of gene expression data. In order to retain the main characteristics, we usedPCA and LPP for reducing dimension. Support vector machine (SVM) algorithm is applied toclassify the normal sample data and disease sample data. The experiment result provesfeasibility and validity of the method.