Clustering is a powerful tool for data classification; however, its application has been limited to analysis of static snapshots of data which may be time-evolving. This work presents a clustering algorithm that employs a fixed time interval and a time-aggregated similarity measure to determine classification. The fixed time interval and a weighting parameter are tuned to the system’s dynamics;...

Spectral clustering algorithm has been shown to be more effective in finding clusters than some traditional algorithms such as k-means. However, spectral clustering suffers from a scalability problem in both memory use and computational time when the size of a data set is large. To perform clustering on large data sets, we investigate two representative ways of approximating the dense similarit...

We propose a principled account on multiclass spectral clustering. Given a discrete clustering formulation, we first solve a relaxed continuous optimization problem by eigendecomposition. We clarify the role of eigenvectors as a generator of all optimal solutions through orthonormal transforms. We then solve an optimal discretization problem, which seeks a discrete solution closest to the conti...

Consistency is a key property of all statistical procedures analyzing randomly sampled data. Surprisingly, despite decades of work, little is known about consistency of most clustering algorithms. In this paper we investigate consistency of the popular family of spectral clustering algorithms, which clusters the data with the help of eigenvectors of graph Laplacian matrices. We develop new meth...

Clustering is the task of grouping a set of examples so that similar examples are grouped into the same cluster while dissimilar examples are in different clusters. The quality of a clustering depends on two problem-dependent factors which are i) the chosen similarity metric and ii) the data representation. Supervised clustering approaches, which exploit labeled partitioned datasets have thus b...

Spectral clustering is a powerful technique in data analysis that has found increasing support and application in many areas. This report is geared to give an introduction to its methods, presenting the most common algorithms, discussing advantages and disadvantages of each, rather than endorsing one of them as the best, because, arguably, there is no black-box algorithm, which performs equally...

Spectral clustering has become a popular technique due to its high performance in many contexts. It comprises three main steps: create a similarity graph between N objects to cluster, compute the first k eigenvectors of its Laplacian matrix to define a feature vector for each object, and run k-means on these features to separate objects into k classes. Each of these three steps becomes computat...

Data mining has become one of the fastest growing research topics in mathematics and computer science. Data such as high dimensional signals, magnetic resonance images, and hyperspectral images can be costly to acquire or it could be unobtainable to make even simple direct comparisons. Compressed sensing is a technique that addresses this issue. It is used for exact recovery of sparse signals u...

Transferring knowledge from auxiliary datasets has been proved useful in machine learning tasks. Its adoption in clustering however is still limited. Despite of its superior performance, spectral clustering has not yet been incorporated with knowledge transfer or transfer learning. In this paper, we make such an attempt and propose a new algorithm called transfer spectral clustering (TSC). It i...

An important form of prior information in clustering comes in form of cannot-link and must-link constraints. We present a generalization of the popular spectral clustering technique which integrates such constraints. Motivated by the recently proposed 1-spectral clustering for the unconstrained problem, our method is based on a tight relaxation of the constrained normalized cut into a continuou...