Spectral clustering algorithm has been shown to be more effective in finding clusters than most traditional algorithms. However, spectral clustering suffers from a scalability problem in both memory use and computational time when a dataset size is large. To perform clustering on large datasets, we propose to parallelize both memory use and computation on distributed computers. Through an empir...

In recent years there has been a growing interest in clustering methods stemming from the spectral decomposition of the data affinity matrix, which are shown to present good results on a wide variety of situations. However, a complete theoretical understanding of these methods in terms of data distributions is not yet well understood. In this paper, we propose a spectral clustering based mode m...

Figure 15.1: k=3 clusters with red points chosen as facilities. Consider a situation where we have n point locations and we wish to place k facilities among these points to provide some service. It is desirable to have these facilities close to the points they are serving, but the notion of “close” can have different interpretations. The k-means problem seeks to place k facilities so as to mini...

Biological and social systems consist of myriad interacting units. The interactions can be represented in the form of a graph or network. Measurements of these graphs can reveal the underlying structure of these interactions, which provides insight into the systems that generated the graphs. Moreover, in applications such as connectomics, social networks, and genomics, graph data are accompanie...

In this study we propose a systematic methodology for constructing a sparse affinity matrix to be used in an advantageous spectral clustering approach. Newton’s equations of motion are employed to concentrate the data points around their cluster centers, using an appropriate potential. During this process possibly overlapping clusters are separated, and simultaneously, useful similarity informa...

In the past decades, Spectral Clustering (SC) has become one of the most effective clustering approaches. Although it has been widely used, one significant drawback of SC is its expensive computation cost. Many efforts have been devoted to accelerating SC algorithms and promising results have been achieved. However, most of the existing algorithms rely on the assumption that data can be stored ...

In this paper, we analyze the second eigenvector technique of spectral partitioning on the planted partition random graph model, by constructing a recursive algorithm using the second eigenvectors in order to learn the planted partitions. The correctness of our algorithm is not based on the ratio-cut interpretation of the second eigenvector, but exploits instead the stability of the eigenvector...

Spectral techniques, off late, have been in limelight in the machine learning community and has drawn attention of many serious machine learners. They are being used in a variety of applications like gene clustering, document analysis, image segmentation, dimensionality reduction etc. They are very simple to understand and provide highly accurate results even for difficult clustering problems. ...

The construction of a similarity matrix is one significant step for the spectral clustering algorithm; while the Gaussian kernel function is one of the most common measures for constructing the similarity matrix. However, with a fixed scaling parameter, the similarity between two data points is not adaptive and appropriate for multi-scale datasets. In this paper, through quantitating the value ...

Spectral clustering is a novel clustering method which can detect complex shapes of data clusters. However, it requires the eigen decomposition of the graph Laplacian matrix, which is proportion to O(n) and thus is not suitable for large scale systems. Recently, many methods have been proposed to accelerate the computational time of spectral clustering. These approximate methods usually involve...