Subspace clustering groups data into several lowrank subspaces. In this paper, we propose a theoretical framework to analyze a popular optimization-based algorithm, Sparse Subspace Clustering (SSC), when the data dimension is compressed via some random projection algorithms. We show SSC provably succeeds if the random projection is a subspace embedding, which includes random Gaussian projection...

Neighborhood Preserving Embedding (NPE) is a subspace learning algorithm. Since NPE is a linear approximation to Locally Linear Embedding (LLE) algorithm, it has good neighborhood-preserving properties. Although NPE has been applied in many fields, it has limitations to solve recognition task. In this paper, a novel subspace method, named Kernel Fisher Neighborhood Preserving Embedding (KFNPE),...

We present an (1+ε)-approximation algorithm for computing the minimum-spanning tree of points in a planar arrangement of lines, where the metric is the number of crossings between the spanning tree and the lines. The expected running time of the algorithm is near linear. We also show how to embed such a crossing metric of hyperplanes in d-dimensions, in subquadratic time, into high-dimensions s...

This paper presents an efficient topology information extraction algorithm that is capable of extracting primary topological relations, such as, interior, boundary, and exterior from a single spatial or spatio-temporal object stored in a linear constraint database. Any non-spatial constraints will be preserved so that the input spatiotemporal object’s temporal constraints will not be sacrificed...

We consider the problem to disseminate a file to all peers on a peer-to-peer network. We prove the file dissemination problem is NP-hard for arbitrary networks (modeled as undirected graphs) while polynomial time solvable if the network topology is a tree. We also provide an optimal algorithm for disseminate a file on Chord-like graphs. One salient feature of this algorithm is that it fully mak...

Recently, Bilu and Linial [6] formalized an implicit assumption often made when choosing a clustering objective: that the optimum clustering to the objective should be preserved under small multiplicative perturbations to distances between points. Balcan and Liang [4] generalized this to a relaxed notion where the optimal clustering after perturbation is allowed to change slightly. In this pape...

In this paper we propose a two-dimensional (2D) Laplacianfaces method for face recognition. The new algorithm is developed based on two techniques, i.e., locality preserved embedding and image based projection. The 2D Laplacianfaces method is not only computationally more efficient but also more accurate than the one-dimensional (1D) Laplacianfaces method in extracting the facial features for h...

A reliable symbolic-numeric algorithm for solving nonlinear systems over the reals is designed. The symbolic step generates a new system, such the formulas are different but the solutions are preserved, through partial factorizations of polynomial expressions, and constraint inversion. The numeric step is a branch-and-prune algorithm based on interval constraint propagation to compute a set of ...

In this paper, we design an approach which is a combination of k-means clustering and probability neural network method to classify the remote sensing image. The proposed method allows the implementation of Kaufman approach to get clustering centers, which are used as initial centers in k-means algorithm. Then the image is divided into k number of clusters by using the k-means algorithm. Finall...

For optic ow computation the Horn and Schunck algorithm is one of the most used and powerful. Some drawbacks are, nevertheless, intrinsically related to the approach that it is used. A smoothness constraint is imposed to the ow eld in order to produce a solution. This constraint causes the estimated eld to be uncorrect where motion discontinuities are present. In this paper the weight of this s...