Efficient triangular surface approximations using wavelets and quadtree data structures

We present a method for adaptive surface meshing and triangulation which controls the local level of detail of the surface approximation by local spectral estimates. These estimates are determined by a wavelet representation of the surface data. The basic idea is to decompose the initial data set by means of an orthogonal or semi orthogonal tensor product wavelet transform (WT) and to analyze the resulting coefficients. In surface regions, where the partial energy of the resulting coefficients is low, the polygonal approximation of the surface can be performed with larger triangles without losing too much fine grain details. However, since the localization of the WT is bound by the Heisenberg principle, the meshing method has to be controlled by the detail signals rather than directly by the coefficients. The dyadic scaling of the WT stimulated us to build an hierarchical meshing algorithm which transforms the initially regular data grid into a quadtree representation by rejection of unimportant mesh vertices. The optimum triangulation of the resulting quadtree cells is carried out by selection from a look up table. The tree grows recursively as controlled by detail signals which are computed from a modified inverse WT. In order to control the local level of detail, we introduce a new class of wavelet space filters acting as "magnifying glasses" on the data. We show that our algorithm performs a low algorithmic complexity, so that surface meshing can be achieved at interactive rates, such as required by flight simulators, however, other applications are possible as well.     

Parallel algorithms for tensor completion in the CP format

Low-rank tensor completion addresses the task of filling in missing entries in multi-dimensional data. It has proven its versatility in numerous applications, including context-aware recommender systems and multivariate function learning. To handle large-scale datasets and applications that feature high dimensions, the development of distributed algorithms is central. In this work, we propose novel, highly scalable algorithms based on a combination of the canonical polyadic (CP) tensor format with block coordinate descent methods. Although similar algorithms have been proposed for the matrix case, the case of higher dimensions gives rise to a number of new challenges and requires a different paradigm for data distribution. The convergence of our algorithms is analyzed and numerical experiments illustrate their performance on distributed-memory architectures for tensors from a range of different applications.     

动态层次Transformer序列推荐算法

序列化推荐任务根据用户历史行为序列,预测下一时刻即将交互的物品.大量研究表明:预测物品对用户历史行为序列的依赖是多层次的.已有的多尺度方法是针对隐式表示空间的启发式设计,不能显式地推断层次结构.为此,该文提出动态层次Transformer,来同时学习多尺度隐式表示与显式层次树.动态层次Transformer采用多层结构...     

Superquadric glyphs for symmetric second-order tensors

Symmetric second-order tensor fields play a central role in scientific and biomedical studies as well as in image analysis and feature-extraction methods. The utility of displaying tensor field samples has driven the development of visualization techniques that encode the tensor shape and orientation into the geometry of a tensor glyph. With some exceptions, these methods work only for positive-definite tensors (i.e. having positive eigenvalues, such as diffusion tensors). We expand the scope of tensor glyphs to all symmetric second-order tensors in two and three dimensions, gracefully and unambiguously depicting any combination of positive and negative eigenvalues. We generalize a previous method of superquadric glyphs for positive-definite tensors by drawing upon a larger portion of the superquadric shape space, supplemented with a coloring that indicates the quadratic form (including eigenvalue sign). We show that encoding arbitrary eigenvalue magnitudes requires design choices that differ fundamentally from those in previous work on traceless tensors that arise in the study of liquid crystals. Our method starts with a design of 2-D tensor glyphs guided by principles of scale-preservation and symmetry, and creates 3-D glyphs that include the 2-D glyphs in their axis-aligned cross-sections. A key ingredient of our method is a novel way of mapping from the shape space of three-dimensional symmetric second-order tensors to the unit square. We apply our new glyphs to stress tensors from mechanics, geometry tensors and Hessians from image analysis, and rate-of-deformation tensors in computational fluid dynamics.     

Linear algebra for tensor problems

By a tensor problem in general, we mean one where all the data on input and output are given (exactly or approximately) in tensor formats, the number of data representation parameters being much smaller than the total amount of data. For such problems, it is natural to seek for algorithms working with data only in tensor formats maintaining the same small number of representation parameters—by the price of all results of computation to be contaminated by approximation (recompression) to occur in each operation. Since approximation time is crucial and depends on tensor formats in use, in this paper we discuss which are best suitable to make recompression inexpensive and reliable. We present fast recompression procedures with sublinear complexity with respect to the size of data and propose methods for basic linear algebra operations with all matrix operands in the Tucker format, mostly through calls to highly optimized level-3 BLAS/LAPACK routines. We show that for three-dimensional tensors the canonical format can be avoided without any loss of efficiency. Numerical illustrations are given for approximate matrix inversion via proposed recompression techniques.      

The Hierarchical Hidden Markov Model: Analysis and Applications

We introduce, analyze and demonstrate a recursive hierarchical generalization of the widely used hidden Markov models, which we name Hierarchical Hidden Markov Models (HHMM). Our model is motivated by the complex multi-scale structure which appears in many natural sequences, particularly in language, handwriting and speech. We seek a systematic unsupervised approach to the modeling of such structures. By extending the standard Baum-Welch (forward-backward) algorithm, we derive an efficient procedure for estimating the model parameters from unlabeled data. We then use the trained model for automatic hierarchical parsing of observation sequences. We describe two applications of our model and its parameter estimation procedure. In the first application we show how to construct hierarchical models of natural English text. In these models different levels of the hierarchy correspond to structures on different length scales in the text. In the second application we demonstrate how HHMMs can be used to automatically identify repeated strokes that represent combination of letters in cursive handwriting.     

On Camera Calibration with Linear Programming and Loop Constraint Linearization

A technique for calibrating a network of perspective cameras based on their graph of trifocal tensors is presented. After estimating a set of reliable epipolar geometries, a parameterization of the graph of trifocal tensors is proposed in which each trifocal tensor is linearly encoded by a 4-vector. The strength of this parameterization is that the homographies relating two adjacent trifocal tensors, as well as the projection matrices depend linearly on the parameters. Two methods for estimating these parameters in a global way taking into account loops in the graph are developed. Both methods are based on sequential linear programming: the first relies on a locally linear approximation of the polynomials involved in the loop constraints whereas the second uses alternating minimization. Both methods have the advantage of being non-incremental and of uniformly distributing the error across all the cameras. Experiments carried out on several real data sets demonstrate the accuracy of the proposed approach and its efficiency in distributing errors over the whole set of cameras.     

张量补全算法及其在人脸识别中的应用

数据丢失问题通常可以归结为矩阵补全问题,而矩阵补全是继压缩感知理论之后的又一种重要的信号获取方法。在实际应用中,数据样例往往具有多线性性,即数据集可以表示成高阶张量。本文研究了张量补全问题及其在人脸识别中的应用。基于张量的低维Tucker分解,提出张量补全的迭代算法,并且证明在算法的迭代过程中,估计张量与其Tucker逼近张量的距离是单调递减的。实验结果表明张量补全算法在补全张量和人脸识别上的可行性与有效性。     

Coarse-Grained Parallel Algorithms for Multi-Dimensional Wavelet Transforms

This paper presents parallel algorithms for computing multi-dimensional wavelet transforms on both shared memory and distributed memory machines. Traditional data partitioning methods for n-dimensional Discrete Wavelet Transforms (DWTs) call for data redistribution once a one dimensional wavelet transform is computed along each dimension. To avoid the data communication inherent in this redistribution, two new partitioning methods called CRBP (Communication Reduced Block Partitioning) and CRLP (Communication Reduced Layer Partitioning) are proposed. The efficiency of the algorithms is compared through several examples implemented on a cluster of SGI workstations. Two kinds of parallel approaches are used to compute multi-dimensional wavelet transforms on shared memory machines: homogeneous parallelism, and heterogeneous parallelism. Homogeneous parallelism uses traditional data partitioning while heterogeneous parallelism uses the CRBP approach. The effectiveness of these approaches is demonstrated through several examples implemented on an SGI Power Challenge. The paper discusses the effectiveness of each of the approaches on the two kinds of architectures.     

Vibration modelling with fast Gaussian wavelet algorithm

Vibration signals are considered as nonstationary signals with transients. Conventional harmonic Fourier analysis finds it difficult to model the vibration signals. In this paper, a novel approach using the global Fourier transforms and local wavelet analysis is presented for vibration analysis and modelling. Time–frequency wavelet analysis has been proven a useful tool for the detection of vibration transients. However, current algorithms with discrete or continuous wavelet transforms for vibration analysis are either low resolution of features or very time consuming. We developed a fast Gaussian wavelet algorithm with very narrow band-pass filtering technique. The time–frequency maps with high frequency resolution enable us to observe the evolution in time of significant frequencies identified by global Fourier analysis, so that the transients and the regular signals can be distinguished. These regular significant frequencies are selected to be the basis of vibration modelling. The coefficients of the model are identified by a least-squares algorithm, which ensures that the error is minimised. To demonstrate this approach a machine spindle vibration signal is analysed, and the main features of the vibration signal are extracted, which are useful for system monitoring and further analysis.     

Dimensionality reduction and topographic mapping of binary tensors

In this paper, a decomposition method for binary tensors, generalized multi-linear model for principal component analysis (GMLPCA) is proposed. To the best of our knowledge at present there is no other principled systematic framework for decomposition or topographic mapping of binary tensors. In the model formulation, we constrain the natural parameters of the Bernoulli distributions for each tensor element to lie in a sub-space spanned by a reduced set of basis (principal) tensors. We evaluate and compare the proposed GMLPCA technique with existing real-valued tensor decomposition methods in two scenarios: (1) in a series of controlled experiments involving synthetic data; (2) on a real-world biological dataset of DNA sub-sequences from different functional regions, with sequences represented by binary tensors. The experiments suggest that the GMLPCA model is better suited for modelling binary tensors than its real-valued counterparts. Furthermore, we extended our GMLPCA model to the semi-supervised setting by forcing the model to search for a natural parameter subspace that represents a user-specified compromise between the modelling quality and the degree of class separation.     

基于位置聚类和张量分解的Web服务推荐算法

基于服务质量（QoS）的Web服务推荐能在众多功能相似的Web服务中发现最能满足用户非功能需求的Web服务,但QoS属性值预测算法仍存在预测准确度不高和数据稀疏性的问题。针对以上问题,提出了一种基于位置聚类和分层张量分解的QoS预测算法ClustTD,该算法基于用户和服务的位置属性将用户和服务聚类成多个局部组,分别对局部组和全局的用户、服务和时间上下文进行张量建模和分解,将局部和全局张量分解的QoS预测值进行加权组合,同时考虑了局部和全局因素,获得最终QoS预测值。实验结果表明,该算法具有较高的QoS预测准确率和Web服务推荐质量,并能在一定程度上解决数据稀疏性问题。     

结合梯度和区域信息的多尺度水平集图像分割

提出了一种结合梯度和区域信息的多尺度水平集图像分割算法。该算法结合梯度和区域信息构造能量函数,在梯度约束项中,构建了一个基于小波高频分量的边缘检测函数,在区域约束项中,运用经典C-V模型的区域项,得到混合C-V模型,采用变分法求解,并消除了水平集的重初始化。利用小波变换首先在逼近图像中运用混合C-V模型得到粗分辨图像的一个粗尺度分割,再对当前粗尺度下的最终轮廓线作内插操作,将得到的近似轮廓曲线作为初始水平集函数在原图像中运用消除重初始化的C-V模型演化得到最终的分割。实验结果表明,在同样的模型参数条件下,该方法具有比传统方法更高的演化效率和分割质量。     

Mining billion-scale tensors: algorithms and discoveries

How can we analyze large-scale real-world data with various attributes? Many real-world data (e.g., network traffic logs, web data, social networks, knowledge bases, and sensor streams) with multiple attributes are represented as multi-dimensional arrays, called tensors. For analyzing a tensor, tensor decompositions are widely used in many data mining applications: detecting malicious attackers in network traffic logs (with source IP, destination IP, port-number, timestamp), finding telemarketers in a phone call history (with sender, receiver, date), and identifying interesting concepts in a knowledge base (with subject, object, relation). However, current tensor decomposition methods do not scale to large and sparse real-world tensors with millions of rows and columns and ‘fibers.’ In this paper, we propose HaTen2, a distributed method for large-scale tensor decompositions that runs on the MapReduce framework. Our careful design and implementation of HaTen2 dramatically reduce the size of intermediate data and the number of jobs leading to achieve high scalability compared with the state-of-the-art method. Thanks to HaTen2, we analyze big real-world sparse tensors that cannot be handled by the current state of the art, and discover hidden concepts.     

基于多尺度的声测量搅拌釜内物料特征

通过声波信号在线分析反应器内物料特征具有快速、无损、安全、不侵入流场的优点。讨论了利用声发射信号在线分析搅拌釜内物料浓度与粒度的方法。先通过小波变换多尺度分解原始声信号,然后以分解后各细节信号小波系数幅值绝对值加和为特征变量,釜内物料浓度或颗粒平均粒度和声发射信号的关系再用判别分析方法加以区分,考察了信号长度、分解尺度以及不同小波对判别准确性的影响,结果表明,当物料的浓度一定时,基于多尺度分析的声测量方法可以准确地对釜内物料的粒度进行分类。     

体数据的多尺度张量表达与可视化

图形硬件的发展为实时体数据可视化提供了硬件保证,然而随着扫描技术的发展,大数据可视化仍然面临显存不足问题,因此研究保持数据特征的压缩表达方法就非常重要。应用张量近似思想建立了体数据的多尺度表达与可视化方法,一方面多尺度张量近似实现了数据压缩,解决了大数据的绘制问题;另一方面,张量近似的自适应压缩基保持了体数据的尺度特征。实验结果表明,该方法是有效的。     

Glyphs for Asymmetric Second‐Order 2D Tensors

Tensors model a wide range of physical phenomena. While symmetric tensors are sufficient for some applications (such as diffusion), asymmetric tensors are required, for example, to describe differential properties of fluid flow. Glyphs permit inspecting individual tensor values, but existing tensor glyphs are fully defined only for symmetric tensors. We propose a glyph to visualize asymmetric second‐order two‐dimensional tensors. The glyph includes visual encoding for physically significant attributes of the tensor, including rotation, anisotropic stretching, and isotropic dilation. Our glyph design conserves the symmetry and continuity properties of the underlying tensor, in that transformations of a tensor (such as rotation or negation) correspond to analogous transformations of the glyph. We show results with synthetic data from computational fluid dynamics.     

小波多尺度水平集算法与心脏超声图像鲁棒分割

由于斑点噪声的存在,超声图像的灰度分布是非高斯的,传统的基于高斯模型的图像分割方法不能解决心脏超声图像分割问题。但小波分解后的高阶低频小波系数近似服从高斯分布,利用这个特点,论文提出一种新颖的小波多分辨率框架下的水平集曲线演化算法。首先对超声心脏图像做小波分解,得到各层的低频图像。从小波分解的顶层低频图像开始,利用边界和区域复合约束动态轮廓线模型(ActiveContourModel)寻找左心室内边界;然后通过插值将结果向下一尺度低频图像传递,并利用尺度间形状约束和边界约束复合ACM进一步细化曲线,使其符合局部图像特征,如此逐层重复直至原始图像。由于采用了小波多尺度框架和尺度间形状约束,算法具有曲线演化结果稳健鲁棒、不易陷入局部极小和发生边界泄漏等优点,非常适合心脏超声图像噪声高、对比度低、边界灰度梯度不显著的特点。在实际临床三维超声图像上的实验表明,算法分割结果和人工分割结果很接近。     

A flexible approach for visual data mining

The exploration of heterogenous information spaces requires suitable mining methods as well as effective visual interfaces. Most of the existing systems concentrate either on mining algorithms or on visualization techniques. This paper describes a flexible framework for visual data mining which combines analytical and visual methods to achieve a better understanding of the information space. We provide several pre-processing methods for unstructured information spaces, such as a flexible hierarchy generation with user-controlled refinement. Moreover, we develop new visualization techniques, including an intuitive focus+context technique to visualize complex hierarchical graphs. A special feature of our system is a new paradigm for visualizing information structures within their frame of reference