A novel representation in three-dimensions for high dimensional data sets

Abstract

Data representation is an important topic in the field of data engineering. In this paper, we focus on the representation of high dimensional data sets. We present the construction method of the set-valued mapping in 3-C representation and propose a novel representation algorithm based on K-means clustering method. The main contribution is to obtain the cluster centers of these high dimensional data sets, and get the correspondence coordinates in 3-C space with the projection along the center's direction. To verify the effectiveness of the proposed method, three sections of experiments had been completed. The first one is ten data sets from UCI. The second one is web images from Corel5k. The last one is the syllabus, a data set consists of text documents from the MIT OpenCourseWare project. All of the results can make sure that the corresponding similarity of data points or attributes are displayed clearly and show that the proposed algorithm's feasibility and scalability. Especially, the results on web images and syllabus are very excellent. As a result, the proposed representation algorithm in three dimension space will make significant influence on data classification and dimensionality reduction.