Nonlinear manifold representation in natural systems: The SOMersault

Natural systems often contain rhythmically fluctuating individual components which, when combined, can result in nonlinear patterns such as cycles, helixes, and parabolas. The self-organizing map (SOM) is a widely used artificial neural network for exploratory data analysis of high dimensional, multivariate data sets, however it encounters limitations when dealing with such highly nonlinear patterns. The SOMersault method is an expansion of the SOM, effective for gaining an understanding of patterns and clusters in natural data sets containing a low dimensional nonlinear manifold set amongst complex high dimensional data measurements. Data clusters become ordered with respect to the nonlinear degrees of freedom in the data, and patterns extracted are closely related to the data they represent. Results are shown on synthetic and real world data, involving a global set of river basins, with clustering and pattern extraction improvements displayed visually and quantified through a new set of geodesic error measures.     

Clustering using PK-D: A connectivity and density dissimilarity

We present a new dissimilarity, which combines connectivity and density information. Usually, connectivity and density are conceived as mutually exclusive concepts; however, we discuss a novel procedure to merge both information sources. Once we have calculated the new dissimilarity, we apply MDS in order to find a low dimensional vector space representation. The new data representation can be used for clustering and data visualization, which is not pursued in this paper. Instead we use clustering to estimate the gain from our approach consisting of dissimilarity + MDS. Hence, we analyze the partitions’ quality obtained by clustering high dimensional data with various well known clustering algorithms based on density, connectivity and message passing, as well as simple algorithms like k-means and Hierarchical Clustering (HC). The quality gap between the partitions found by k-means and HC alone compared to k-means and HC using our new low dimensional vector space representation is remarkable. Moreover, our tests using high dimensional gene expression and image data confirm these results and show a steady performance, which surpasses spectral clustering and other algorithms relevant to our work.     

基于主题隐马尔科夫模型的人体异常行为识别

针对基于监控视频的人体异常行为识别问题,提出了基于主题隐马尔科夫模型的人体异常行为识别方法,即通过无任何人工标注的视频训练集自动学习人体行为模型,并能够应用学到的人体行为模型实时检测异常行为和识别正常行为。这一方法主要围绕"低层视频表示-中层语义行为建模-高层语义分类"3个方面进行:1)基于时-空间兴趣点构建了一种紧凑的和有效的视频表示方法。2)提出一种新颖的语义主题模型(Topic Model,TM)——主题隐马尔科夫模型(Topic Hidden Markov Model,THMM),它能够自然地分组视频中检测到的人体行为。主题隐马尔科夫模型基于已有的马尔科夫模型和主题模型构造,不但聚类运动词汇成简单动作,而且聚类简单动作成全局行为,同时建模了行为时间上的相关性。THMM是一个4层贝叶斯主题模型,它将视频序列建模为行为的马尔科夫链,同时行为是视频序列中某些视频剪辑(Clip)的概率分布;将视频剪辑建模为动作的随机组合,同时动作是视频剪辑中运动词汇的概率分布。克服了传统隐马尔科夫模型和主题模型在人体复杂行为建模过程中精度、鲁棒性和计算效率上的不足。3)提出运行时累积的异常性测度及其在线异常行为检测方法和基于在线似然比检验(Likelihood Ratio Test,LRT)的实时正常行为分类方法,从而克服了实时行为识别过程中由于缺乏充分的视觉证据而引发的行为类型歧义,能完较好地完成监控场景中实时异常行为检测和在线正常行为识别的任务。取自实际监控场景的实验数据集上的实验结果证明了本方法的有效性。     

Projective Blue‐Noise Sampling

We propose projective blue‐noise patterns that retain their blue‐noise characteristics when undergoing one or multiple projections onto lower dimensional subspaces. These patterns are produced by extending existing methods, such as dart throwing and Lloyd relaxation, and have a range of applications. For numerical integration, our patterns often outperform state‐of‐the‐art stochastic and low‐discrepancy patterns, which have been specifically designed only for this purpose. For image reconstruction, our method outperforms traditional blue‐noise sampling when the variation in the signal is concentrated along one dimension. Finally, we use our patterns to distribute primitives uniformly in 3D space such that their 2D projections retain a blue‐noise distribution.     

Unsupervised Learning of Image Manifolds by Semidefinite Programming

Can we detect low dimensional structure in high dimensional data sets of images? In this paper, we propose an algorithm for unsupervised learning of image manifolds by semidefinite programming. Given a data set of images, our algorithm computes a low dimensional representation of each image with the property that distances between nearby images are preserved. More generally, it can be used to analyze high dimensional data that lies on or near a low dimensional manifold. We illustrate the algorithm on easily visualized examples of curves and surfaces, as well as on actual images of faces, handwritten digits, and solid objects.     

Time series pattern discovery by a PIP-based evolutionary approach

Time series are an important and interesting research field due to their many different applications. In our previous work, we proposed a time-series segmentation approach by combining a clustering technique, discrete wavelet transformation (DWT) and a genetic algorithm to automatically find segments and patterns from a time series. In this paper, we propose a perceptually important points (PIP)-based evolutionary approach, which uses PIP instead of DWT, to effectively adjust the length of subsequences and find appropriate segments and patterns, as well as avoid some problems that arose in the previous approach. To achieve this, an enhanced suitability factor in the fitness function is designed, modified from the previous approach. The experimental results on a real financial dataset show the effectiveness of the proposed approach.     

运动串:一种用于行为分割的运动捕获数据表示方法

运动数据的行为分割是运动捕获过程中非常重要的一环.针对现有分割方法的不足,提出了一种可用于行为分割的运动数据表示方法,并基于该表示实现了数据的行为分割.运动数据经过谱聚类(spectral clustering)、时序恢复和最大值滤波法(max filtering)后生成一个字符串,该字符串称为运动串,然后采用后缀树(suffix tree)分析运动串,提取出所有静态子串和周期子串,对这些子串进行行为标注,从而实现运动数据的行为分割.实验表明,基于运动串的分割具有较好的鲁棒性和分割效果.     

Object Location by Parallel Pose Clustering

This paper describes the location of 3D objects in either depth or intensity data using parallel pose clustering. A leader-based partitional algorithm is used that allows the number of clusters to be selected on the basis of the input data, which is important because the number of pose clusters cannot usually be determined in advance. In comparison with previous work, no assumptions are made about the number or distribution of data patterns, or that the processor topology should be matched to this distribution. After overcoming a parallel bottleneck, we show that our approach exhibits superlinear speedup, since the overall computation is reduced in the parallel system. Isolated pose estimates may be eliminated from the cluster space after an initial stage, which may be done with low probability of missing a true cluster. The algorithm has been tested using real and synthetic data on a transputer-based MIMD architecture.     

Vector Image Segmentation by Piecewise Continuous Approximation

In this article we present an approach to the segmentation problem by a piecewise approximation of the given image with continuous functions. Unlike the common approach of Mumford and Shah in our formulation of the problem the number of segments is a parameter, which can be estimated. The problem can be stated as: Compute the optimal segmentation with a fixed number of segments, then reduce the number of segments until the segmentation result fulfills a given suitability. This merging algorithm results in a multi-objective optimization, which is not only resolved by a linear combination of the contradicting error functions. To constrain the problem we use a finite dimensional vector space of functions in our approximation and we restrict the shape of the segments. Our approach results in a multi-objective optimization: On the one hand the number of segments is to be minimized, on the other hand the approximation error should also be kept minimal. The approach is sound theoretically and practically: We show that for L ²-images a Pareto-optimal solution exists and can be computed for the discretization of the image efficiently.     

高维数据离群点检测的局部线性嵌入方法

由于高维空间中数据点比较稀疏,用传统方法来检测高维空间中的离群点不能达到预期效果。提出了一种基于局部线性嵌入的离群点检测方法（OLLE）。在OLLE降维方法中,建立了一种有效的粗糙集模型,使数据集的下近似中的点保持局部线性结构。同时构造两个权重,使所有样本点保持局部近邻结构,且保证在降维的过程中使离群点远离正常点。最后,在低维空间中,采用基于最小生成树的k-最近邻启发式方法来检测离群点。通过一系列的模拟实验,证明OLLE方法能达到很好的降维效果,并且在低维空间中可以有效地检测出离群点。     

Structure and motion from line segments in multiple images

This paper presents a new method for recovering the three dimensional structure of a scene composed of straight line segments using the image data obtained from a moving camera. The recovery algorithm is formulated in terms of an objective function which measures the total squared distance in the image plane between the observed edge segments and the projections (perspective) of the reconstructed lines. This objective function is minimized with respect to the line parameters and the camera positions to obtain an estimate for the structure of the scene. The effectiveness of this approach is demonstrated quantitatively through extensive simulations and qualitatively with actual image sequences. The implementation is being made publicly available     

Discovering nontrivial repeating patterns in music data

A repeating pattern in music data is defined as a sequence of notes which appears more than once in a music object. The themes are a typical kind of repeating patterns. The themes and other nontrivial repeating patterns are important music features which can be used for both content-based retrieval of music data and music data analysis. In this paper, we propose two approaches for fast discovering nontrivial repeating patterns in music objects. In the first approach, we develop a data structure called correlative matrix and its associated algorithms for extracting the repeating patterns. In the second approach, we introduce a string-join operation and a data structure called RP-tree for the same purpose. Experiments are performed to compare these two approaches with others. The results are further analyzed to show the efficiency and the effectiveness of our approaches     

Human behavior clustering for anomaly detection

This paper aims to address the problem of modeling human behavior patterns captured in surveillance videos for the application of online normal behavior recognition and anomaly detection. A novel framework is developed for automatic behavior modeling and online anomaly detection without the need for manual labeling of the training data set. The framework consists of the following key components. 1) A compact and effective behavior representation method is developed based on spatial-temporal interest point detection. 2) The natural grouping of behavior patterns is determined through a novel clustering algorithm, topic hidden Markov model (THMM) built upon the existing hidden Markov model (HMM) and latent Dirichlet allocation (LDA), which overcomes the current limitations in accuracy, robustness, and computational efficiency. The new model is a four-level hierarchical Bayesian model, in which each video is modeled as a Markov chain of behavior patterns where each behavior pattern is a distribution over some segments of the video. Each of these segments in the video can be modeled as a mixture of actions where each action is a distribution over spatial-temporal words. 3) An online anomaly measure is introduced to detect abnormal behavior, whereas normal behavior is recognized by runtime accumulative visual evidence using the likelihood ratio test (LRT) method. Experimental results demonstrate the effectiveness and robustness of our approach using noisy and sparse data sets collected from a real surveillance scenario.     

一种高维数据聚类遗传算法

聚类分析是数据挖掘中的一个重要研究课题。在许多实际应用中,聚类分析的数据往往具有很高的维度,例如文档数据、基因微阵列等数据可以达到上千维,而在高维数据空间中,数据的分布较为稀疏。受这些因素的影响,许多对低维数据有效的经典聚类算法对高维数据聚类常常失效。针对这类问题,本文提出了一种基于遗传算法的高维数据聚类新方法。该方法利用遗传算法的全局搜索能力对特征空间进行搜索,以找出有效的聚类特征子空间。同时,为了考察特征维在子空间聚类中的特征,本文设计出一种基于特征维对子空间聚类贡献率的适应度函数。人工数据、真实数据的实验结果以及与k-means算法的对比实验证明了该方法的可行性和有效性。     

基于相邻频繁模式段的闭合序列模式挖掘算法

直接对生物序列进行频繁模式挖掘会产生很多冗余模式,闭合模式更能表达出序列的功能和结构。根据生物序列的特点,提出了基于相邻闭合频繁模式段的模式挖掘算法－JCPS。首先产生闭合相邻频繁模式段,然后对这些闭合频繁模式段进行组合,同时进行闭合检测,产生新的闭合频繁模式。通过对真实的蛋白质序列家族库的处理,证明该算法能有效处理生物序列数据。     

Visualizing High‐Dimensional Structures by Dimension Ordering and Filtering using Subspace Analysis

High‐dimensional data visualization is receiving increasing interest because of the growing abundance of high‐dimensional datasets. To understand such datasets, visualization of the structures present in the data, such as clusters, can be an invaluable tool. Structures may be present in the full high‐dimensional space, as well as in its subspaces. Two widely used methods to visualize high‐dimensional data are the scatter plot matrix (SPM) and the parallel coordinate plot (PCP). SPM allows a quick overview of the structures present in pairwise combinations of dimensions. On the other hand, PCP has the potential to visualize not only bi‐dimensional structures but also higher dimensional ones. A problem with SPM is that it suffers from crowding and clutter which makes interpretation hard. Approaches to reduce clutter are available in the literature, based on changing the order of the dimensions. However, usually this reordering has a high computational complexity. For effective visualization of high‐dimensional structures, also PCP requires a proper ordering of the dimensions. In this paper, we propose methods for reordering dimensions in PCP in such a way that high‐dimensional structures (if present) become easier to perceive. We also present a method for dimension reordering in SPM which yields results that are comparable to those of existing approaches, but at a much lower computational cost. Our approach is based on finding relevant subspaces for clustering using a quality criterion and cluster information. The quality computation and cluster detection are done in image space, using connected morphological operators. We demonstrate the potential of our approach for synthetic and astronomical datasets, and show that our method compares favorably with a number of existing approaches.     

具有多项式密度分布的直线骨架卷积曲面

给出了一个具有多项式密度分布的直线骨架卷积曲面的解析表达式，并提出了基于控制曲线的密度控制方法，实验结果表明，该方法的自然景物，海生物等光滑物体造型中具有很大的应用价值。     

基于簇内乘积量化的最近邻检索方法

本文针对大规模高维数据近邻检索中的瓶颈问题,提出基于向量量化的一种检索方法—簇内乘积量化树方法.该方法运用向量量化和乘积量化的多层树状结构高效表征大规模高维数据集,与现有方法相比降低了索引表空桶率;其次提出基于贪心队列的近邻簇筛选方法减小了计算复杂度,加快了近邻检索速度;最后提出面量化方法用于近似计算候选数据集向量与查询向量间的距离,与点量化和线量化方法相比量化误差更小,提高了近邻查询准确率.本文提出的簇内乘积量化树算法在算子Sift和Gist描述的大规模高维数据集上与乘积量化树技术相比,首次召回准确率提高了57.7%,索引表空桶率降低幅度在50%以上,与局部优化乘积量化技术相比,查全率高达97%,而查询时间却仅需原来的1/9.实验结果表明本文提出的基于簇内乘积量化的近邻方法提升了近邻检索性能,为大规模高维数据集近邻检索提供了理论支持.