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Spectral Methods for Data Clustering

Spectral Methods for Data Clustering
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Author(s): Wenyuan Li (Nanyang Technological University, Singapore)
Copyright: 2009
Pages: 7
Source title: Encyclopedia of Data Warehousing and Mining, Second Edition
Source Author(s)/Editor(s): John Wang (Montclair State University, USA)
DOI: 10.4018/978-1-60566-010-3.ch278

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Abstract

With the rapid growth of the World Wide Web and the capacity of digital data storage, tremendous amount of data are generated daily from business and engineering to the Internet and science. The Internet, financial realtime data, hyperspectral imagery, and DNA microarrays are just a few of the common sources that feed torrential streams of data into scientific and business databases worldwide. Compared to statistical data sets with small size and low dimensionality, traditional clustering techniques are challenged by such unprecedented high volume, high dimensionality complex data. To meet these challenges, many new clustering algorithms have been proposed in the area of data mining (Han & Kambr, 2001). Spectral techniques have proven useful and effective in a variety of data mining and information retrieval applications where massive amount of real-life data is available (Deerwester et al., 1990; Kleinberg, 1998; Lawrence et al., 1999; Azar et al., 2001). In recent years, a class of promising and increasingly popular approaches — spectral methods — has been proposed in the context of clustering task (Shi & Malik, 2000; Kannan et al., 2000; Meila & Shi, 2001; Ng et al., 2001). Spectral methods have the following reasons to be an attractive approach to clustering problem: • Spectral approaches to the clustering problem offer the potential for dramatic improvements in efficiency and accuracy relative to traditional iterative or greedy algorithms. They do not intrinsically suffer from the problem of local optima. • Numerical methods for spectral computations are extremely mature and well understood, allowing clustering algorithms to benefit from a long history of implementation efficiencies in other fields (Golub & Loan, 1996). • Components in spectral methods have the naturally close relationship with graphs (Chung, 1997). This characteristic provides an intuitive and semantic understanding of elements in spectral methods. It Spectral Methods for Data Clustering Wenyuan Li Nanyang Technological University, Singapore Wee Keong Ng Nanyang Technological University, Singapore is important when the data is graph-based, such as links of WWW, or can be converted to graphs. In this paper, we systematically discuss applications of spectral methods to data clustering.

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