Clustering is a mathematical method of data analysis which identifies trends in data by efficiently separating data into a specified number of clusters so is incredibly useful and widely applicable for questions of interrelatedness of data. Two methods of clustering are considered here. K-means clustering defines clusters in relation to the centroid, or center, of a cluster. Spectral clustering...

Similarity matrix is critical to the performance of spectral clustering. Mercer kernels have become popular largely due to its successes in applying kernel methods such as kernel PCA. A novel spectral clustering method is proposed based on local neighborhood in kernel space (SC-LNK), which assumes that each data point can be linearly reconstructed from its neighbors. The SC-LNK algorithm tries ...

Spectral clustering consists of two distinct stages: (a) construct an affinity graph from the dataset and (b) cluster the data points through finding an optimal partition of the affinity graph. The focus of the paper is the first step. Existing spectral clustering algorithms adopt Gaussian function to define the affinity graph since it is easy to implement. However, Gaussian function is hard to...

Cluster ensemble has been shown to be an effective thought of improving the accuracy and stability of single clustering algorithms. It consists of generating a set of partition results from a same data set and combining them into a final one. In this paper, we develop a novel cluster ensemble method named Cluster Ensemble algorithm using the Binary k-means and Spectral Clustering (CEBKSC). By u...

Spectral clustering is a powerful clustering method for document data set. However, spectral clustering needs to solve an eigenvalue problem of the matrix converted from the similarity matrix corresponding to the data set. Therefore, it is not practical to use spectral clustering for a large data set. To overcome this problem, we propose the method to reduce the similarity matrix size. First, u...

Abstract. Spectral co-clustering is a generic method of computing coclusters of relational data, such as sets of documents and their terms. Latent semantic analysis is a method of document and term smoothing that can assist in the information retrieval process. In this article we examine the process behind spectral clustering for documents and terms, and compare it to Latent Semantic Analysis. ...

In many applications, we need to cluster largescale data objects. However, some recently proposed clustering algorithms such as spectral clustering can hardly handle large-scale applications due to the complexity issue, although their effectiveness has been demonstrated in many previous work. In this paper, we propose a fast solver for spectral clustering. In contrast to traditional spectral cl...

Spectral clustering and co-clustering are well-known techniques in data analysis, and recent work has extended spectral clustering to square, symmetric tensors and hypermatrices derived from a network. We develop a new tensor spectral co-clustering method that simultaneously clusters the rows, columns, and slices of a nonnegative three-mode tensor and generalizes to tensors with any number of m...

We are given n data points x1, . . . , xn and some way to compute similarities between them, call si,j the similarity between the n points. Assume that the similarity function is symmetric, so si,j = sj,i. For the purposes of this lecture let us just consider the simplified clustering problem where we would like to split the dataset into two clusters. We would like to find a subset S ⊂ [n] of s...

We study a number of open issues in spectral clustering: (i) Selecting the appropriate scale of analysis, (ii) Handling multi-scale data, (iii) Clustering with irregular background clutter, and, (iv) Finding automatically the number of groups. We first propose that a ‘local’ scale should be used to compute the affinity between each pair of points. This local scaling leads to better clustering e...