10.1.1.61.5511 - A Survey on Wavelet Applications in Data...

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A Survey on Wavelet Applications in Data Mining Tao Li Department of Computer Science Univ. of Rochester Rochester, NY 14627 [email protected] Qi Li Dept. of Computer & Information Sciences Univ. of Delaware Newark, DE 19716 [email protected] Shenghuo Zhu Department of Computer Science Univ. of Rochester Rochester, NY 14627 [email protected] Mitsunori Ogihara Department of Computer Science Univ. of Rochester Rochester, NY 14627 [email protected] ABSTRACT Recently there has been significant development in the use of wavelet methods in various data mining processes. However, there has been written no comprehensive survey available on the topic. The goal of this is paper to fill the void. First, the paper presents a high-level data-mining framework that reduces the overall process into smaller components. Then applications of wavelets for each component are reviewd. The paper concludes by discussing the impact of wavelets on data mining research and outlining potential future research directions and applications. 1. INTRODUCTION The wavelet transform is a synthesis of ideas that emerged over many years from different fields, such as mathematics and signal processing. Generally speaking, the wavelet transform is a tool that divides up data, functions, or operators into different frequency components and then studies each component with a resolution matched to its scale [52]. Therefore, the wavelet transform is antic- ipated to provide economical and informative mathematical repre- sentation of many objects of interest [1]. Nowadays many computer software packages contain fast and efficient algorithms to perform wavelet transforms. Due to such easy accessibility wavelets have quickly gained popularity among scientists and engineers, both in theoretical research and in applications. Above all, wavelets have been widely applied in such computer science research areas as im- age processing, computer vision, network management, and data mining. Over the past decade data mining, or knowledge discovery in databases (KDD), has become a significant area both in academia and in industry. Data mining is a process of automatic extraction of novel, useful and understandable patterns from a large collection of data. Wavelet theory could naturally play an important role in data mining since it is well founded and of very practical use. Wavelets have many favorable properties, such as vanishing moments, hier- archical and multiresolution decomposition structure, linear time and space complexity of the transformations, decorrelated coeffi- cients, and a wide variety of basis functions. These properties could provide considerably more efficient and effective solutions to many data mining problems. First, wavelets could provide presentations of data that make the mining process more efficient and accurate.
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