This paper exploits the properties of the commute time between nodes of a graph for the purposes of clustering and embedding, and explores its applications to image segmentation and multi-body motion tracking. Our starting point is the lazy random walk on the graph, which is determined by the heatkernel of the graph and can be computed from the spectrum of the graph Laplacian. We characterize the random walk using the commute time (i.e. the expected time taken for a random walk to travel between two nodes and return) and show how this quantity may be computed from the Laplacian spectrum using the discrete Green’s function. Our motivation is that the commute time can be anticipated to be a more robust measure of the proximity of data than the raw proximity matrix. In this paper, we explore two applications of the commute time. The first is to develop a method for image segmentation using the eigenvector corresponding to the smallest eigenvalue of the commute time matrix. We show that our commute time segmentation method has the property of enhancing the intra-group coherence while weakening inter-group coherence and is superior to the normalized cut. The second application is to develop a robust multi-body motion tracking method using an embedding based on the commute time. Our embedding procedure preserves commute time, and is closely akin to kernel PCA, the Laplacian eigenmap and the diffusion map. We illustrate the results both on synthetic image sequences and real world video sequences, and compare our results with several alternative methods.

Spectral clustering methods are common graph-based approaches to clustering of data. Spectral clustering algorithms typically start from local information encoded in a weighted graph on the data and cluster according to the global eigenvectors of the corresponding (normalized) similarity matrix. One contribution of this paper is to present fundamental limitations of this general local to global approach. We show that based only on local information, the normalized cut functional is not a suitable measure for the quality of clustering. Further, even with a suitable similarity measure, we show that the first few eigenvectors of such adjacency matrices cannot successfully cluster datasets that contain structures at different scales of size and density. Based on these findings, a second contribution of this paper is a novel diffusion based measure to evaluate the coherence of individual clusters. Our measure can be used in conjunction with any bottom-up graph-based clustering method, it is scale-free and can determine coherent clusters at all scales. We present both synthetic examples and real image segmentation problems where various spectral clustering algorithms fail. In contrast, using this coherence measure finds the expected clusters at all scales.

We describe a video indexing system that aims at indexing large video files in relation to the presence of similar faces. The detection of near-frontal view faces is done with a cascade of weak classifier. Face tracking is done through a particle filter and generate trajectories. Face clusters are found based on a spectral clustering approach. We compare the performance of various spectral clustering techniques based on 2DPCA features. The system performance is evaluated against a public face database as well as on a real full-length feature movie. 1.

In this paper a new completely unsupervised mesh segmentation algorithm is proposed, which is based on the PCA interpretation of the Laplacian eigenvectors of the mesh and on parametric clustering using Gaussian mixtures. We analyse the geometric properties of these vectors and we devise a practical method that combines single-vector analysis with multiple-vector analysis. We attempt to characterize the projection of the graph onto each one of its eigenvectors based on PCA properties of the eigenvectors. We devise an unsupervised probabilistic method, based on one-dimensional Gaussian mixture modeling with model selection, to reveal the structure of each eigenvector. Based on this structure, we select a subset of eigenvectors among the set of the smallest non-null eigenvectors and we embed the mesh into the isometric space spanned by this selection of eigenvectors. The final clustering is performed via unsupervised classification based on learning a multi-dimensional Gaussian mixture model of the embedded graph. 1.

Abstract. An implicit assumption in psychometrics and educational statistics is that the generative model for student scores on test questions is governed by the

Heroin and cocaine gas chromatography data are analyzed using several clustering techniques. A database with clusters confirmed by police investigation is used to assess the potential of the analysis of the chemical signature of these drugs in the investigation process. Results are compared to standard methods in the field of chemical drug profiling and show that conventional approaches miss the inherent structure in the data, which is highlighted by methods such as spectral clustering and its variants. Also, an approach based on genetic programming is presented in order to tune the affinity matrix of the spectral clustering algorithm. Results indicate that all algorithms show a quite different behavior on the two datasets, but in both cases, the data exhibits a level of clustering, since there is at least one type of clustering algorithm that performs significantly better than chance. This confirms the relevancy of using chemical drugs databases in the process of understanding the illicit drugs market, as information regarding drug trafficking networks can likely be extracted from the chemical composition of drugs.

The progress in the acquisition of 3-D data from multicamera set-ups has opened the way to a new way of loking at motion analysis. This paper proposes a solution to the motion segmentation in the context of sparse scene flow. In particular, our interest focuses on the disassociation of motions belonging to different rigid objects, starting from the 3-D trajectories of features lying on their surfaces. We analyze these trajectories and propose a representation suitable for defining robust-pairwise similarity measures between trajectories and handling missing data. The motion segmentation is treated as graph multi-cut problem, and solved with spectral clustering techniques (two algorithms are presented). Experiments are done over simulated and real data in the form of sparse scene-flow; we also evaluate the results on trajectories from motion capture data. A discussion is provided on the results for each algorithm, the parameters and the possible use of these results in motion analysis. 1.