A Shrinking-Based Approach for Multi-Dimensional Data Analysis

This chapter discusses a shrinking-based approach for multi-dimensional analysis. Existing data analysis techniques have difficulty in handling multi-dimensional data. This chapter presents a novel data pre-processing technique called shrinking, which optimizes the inner structure of data inspired by the Newton’s Universal Law of Gravitation in the real world. This data reorganization concept can be applied in many fields, such as pattern recognition, data clustering, and signal processing. Then, as an important application of the data shrinking pre-processing, this chapter proposes a shrinking-based approach for multi-dimensional data analysis, which consists of three steps: data shrinking, cluster detection, and cluster evaluation and selection. The process of data shrinking moves data points along the direction of the density gradient, thus generating condensed, widely-separated clusters. Following data shrinking, clusters are detected by finding the connected components of dense cells. The data-shrinking and cluster-detection steps are conducted on a sequence of grids with different cell sizes. The clusters detected at these scales are compared by a cluster-wise evaluation measurement, and the best clusters are selected as the final result. The experimental results show that this approach can effectively and efficiently detect clusters in both low- and high-dimensional spaces.