30024651
Using Term Clustering and Supervised Term Affinity Construction to Boost Text Classification
The similarity measure is a crucial step in many machine learning problems. The traditional cosine similarity suffers from its inability to represent the semantic relationship of terms. This paper explores the kernel-based similarity measure by using term clustering. An affinity matrix of terms is constructed via the co-occurrence of the terms in both unsupervised and supervised ways. Normalized cut is employed to do the clustering to cut off the noisy edges. Diffusion kernel is adopted to measure the kernel-like similarity of the terms in the same cluster. Experiments demonstrate our methods can give satisfactory results, even when the training set is small.
33629250
Robust Visual Tracking Via Incremental Maximum Margin Criterion
Robust visual object tracking is one of the key problems in computer vision. Subspace based tracking method is a promising approach in handling appearance variability. Linear Discriminant Analysis(LDA) has been applied to this problem, but LDA is not a stable algorithm especially for visual tracking. Maximum Margin Criterion(MMC) is a recently proposed discriminant criterion. Its promising specialities make it a better choice for the tracking problem. In this paper, we present a novel subspace tracking algorithm based on MMC. We also proposed an incremental version of the corresponding algorithm so that the tracker can update in realtime. Experiments show our tracking algorithm is able to track objects well under large lighting, pose and expression variation.
6255110
Computing real inflection points of cubic algebraic curves
Shape modeling using planar cubic algebraic curves calls for computing the real inflection points of these curves since inflection points represents important shape feature. A real inflection point is also required for transforming projectively a planar cubic algebraic curve to the normal form, in order to facilitate further analysis of the curve. However, the naive method for computing the inflection points of a planar cubic algebraic curve f = 0 by directly intersecting f = 0 and its Hessian curve H(f) = 0 requires solving a degree nine univariate polynomial equation, and thus is relatively inefficient. In this paper we present an algorithm for computing the real inflection points of a real planar cubic algebraic curve. The algorithm follows Hilbert's solution for computing the inflection points of a cubic algebraic curve in the complex projective plane. Hilbert's solution is based on invariant theory and requires solving only a quartic polynomial equation and several cubic polynomial equations. Through a detailed study with emphasis on the distinction between real and imaginary inflection points, we adapt Hilbert's solution to efficiently compute only the real inflection points of a cubic algebraic curve f = 0, without exhaustive but unnecessary search and root testing. To compute the real inflection points of f = 0, only two cubic polynomial equations need to be solved in our algorithm and it is unnecessary to solve numerically the quartic equation prescribed in Hilbert's solution. In addition, the invariants of f = 0 are used to analyze the singularity of a singular curve, since the number of the real inflection points of f = 0 depends on its singularity type.
39024705
The Linear 2-Arboricity of Planar Graphs
Abstract. Let G be a planar graph with maximum degree Δ and girth g. The linear 2-arboricity la2(G) of G is the least integer k such that G can be partitioned into k edge-disjoint forests, whose component trees are paths of length at most 2. We prove that (1) la2(G)≤⌈(Δ+1)/2⌉+12; (2) la2(G)≤⌈(Δ+1)/2⌉+6 if g≥4; (3) la2(G)≤⌈(Δ+1)/2⌉+2 if g≥5; (4) la2(G)≤⌈(Δ+1)/2⌉+1 if g≥7.
12623712
A transparent rate adaptation algorithm for streaming video over the Internet
The lack of end-to-end quality of service support in the current Internet has caused significant difficulties to ensuring playback continuity in video streaming applications. This study addresses this challenge by investigating a new adaptation algorithm to adjust the bit-rate of video data in response to the network bandwidth available to improve playback continuity. Unlike previous works, the proposed algorithm is transparent to the video client, requires no parameter tuning, and yet can outperform existing algorithms. This paper presents this algorithm, evaluates and compares its performance with the best algorithm currently available using extensive trace-driven simulations.
14446380
OP-cluster: clustering by tendency in high dimensional space
Clustering is the process of grouping a set of objects into classes of similar objects. Because of unknownness of the hidden patterns in the data sets, the definition of similarity is very subtle. Until recently, similarity measures are typically based on distances, e.g Euclidean distance and cosine distance. We propose a flexible yet powerful clustering model, namely OP-cluster (Order Preserving Cluster). Under this new model, two objects are similar on a subset of dimensions if the values of these two objects induce the same relative order of those dimensions. Such a cluster might arise when the expression levels of (coregulated) genes can rise or fall synchronously in response to a sequence of environment stimuli. Hence, discovery of OP-Cluster is essential in revealing significant gene regulatory networks. A deterministic algorithm is designed and implemented to discover all the significant OP-Clusters. A set of extensive experiments has been done on several real biological data sets to demonstrate its effectiveness and efficiency in detecting coregulated patterns.
2372115
PoClustering: Lossless Clustering of Dissimilarity Data
Given a set of objects V with a dissimilarity measure between pairs of objects in V , a PoCluster is a collection of sets P ⊂ powerset(V ) partially ordered by the ⊂ relation such that S ⊂ T iff the maximal dissimilarity among objects in S is less than the maximal dissimilarity among objects in T . PoClusters capture categorizations of objects that are not strictly hierarchical, such as those found in ontologies. PoClusters can not, in general, be constructed using hierarchical clustering algorithms. In this paper, we examine the relationship between PoClusters and dissimilarity matrices and prove that PoClusters are in one-to-one correspondence with the set of dissimilarity matrices. The PoClustering problem is NP-Complete, and we present a heuristic algorithm for it in this paper. Experiments on both synthetic and real datasets demonstrate the quality and scalability of the algorithms.