Least squares QR-based decomposition provides an efficient way of computing optimal regularization parameter in photoacoustic tomography

A computationally efficient approach that computes the optimal regularization parameter for the Tikhonov-minimization scheme is developed for photoacoustic imaging. This approach is based on the least squares-QR decomposition which is a well-known dimensionality reduction technique for a large system of equations. It is shown that the proposed framework is effective in terms of quantitative and qualitative reconstructions of initial pressure distribution enabled via finding an optimal regularization parameter. The computational efficiency and performance of the proposed method are shown using a test case of numerical blood vessel phantom, where the initial pressure is exactly known for quantitative comparison. (C) 2013 Society of Photo-Optical Instrumentation Engineers (SPIE)

A NEAR OPTIMAL PROJECTION FOR SPARSE REPRESENTATION BASED CLASSIFICATION

Sparse representation based classification (SRC) is one of the most successful methods that has been developed in recent times for face recognition. Optimal projection for Sparse representation based classification (OPSRC)1] provides a dimensionality reduction map that is supposed to give optimum performance for SRC framework. However, the computational complexity involved in this method is too high. Here, we propose a new projection technique using the data scatter matrix which is computationally superior to the optimal projection method with comparable classification accuracy with respect OPSRC. The performance of the proposed approach is benchmarked with various publicly available face database.

Redução de dimensionalidade em equilíbrio de fases fluidas

Atualmente, existem modelos matemáticos capazes de preverem acuradamente as relações entre propriedades de estado; e esta tarefa é extremamente importante no contexto da Engenharia Química, uma vez que estes modelos podem ser empregados para avaliar a performance de processos químicos. Ademais, eles são de fundamental importância para a simulação de reservatórios de petróleo e processos de separação. Estes modelos são conhecidos como equações de estado, e podem ser usados em problemas de equilíbrios de fases, principalmente em equilíbrios líquido-vapor. Recentemente, um teorema matemático foi formulado (Teorema de Redução), fornecendo as condições para a redução de dimensionalidade de problemas de equilíbrios de fases para misturas multicomponentes descritas por equações de estado cúbicas e regras de mistura e combinação clássicas. Este teorema mostra como para uma classe bem definidade de modelos termodinâmicos (equações de estado cúbicas e regras de mistura clássicas), pode-se reduzir a dimensão de vários problemas de equilíbrios de fases. Este método é muito vantajoso para misturas com muitos componentes, promovendo uma redução significativa no tempo de computação e produzindo resultados acurados. Neste trabalho, apresentamos alguns experimentos numéricos com misturas-testes usando a técnica de redução para obter pressões de ponto de orvalho sob especificação de temperaturas.

Mapeamento de difusão no reconhecimento e reconstrução de sinais

Em muitas representações de objetos ou sistemas físicos se faz necessário a utilização de técnicas de redução de dimensionalidade que possibilitam a análise dos dados em baixas dimensões, capturando os parâmetros essenciais associados ao problema. No contexto de aprendizagem de máquina esta redução se destina primordialmente à clusterização, reconhecimento e reconstrução de sinais. Esta tese faz uma análise meticulosa destes tópicos e suas conexões que se encontram em verdadeira ebulição na literatura, sendo o mapeamento de difusão o foco principal deste trabalho. Tal método é construído a partir de um grafo onde os vértices são os sinais (dados do problema) e o peso das arestas é estabelecido a partir do núcleo gaussiano da equação do calor. Além disso, um processo de Markov é estabelecido o que permite a visualização do problema em diferentes escalas conforme variação de um determinado parâmetro t: Um outro parâmetro de escala, Є, para o núcleo gaussiano é avaliado com cuidado relacionando-o com a dinâmica de Markov de forma a poder aprender a variedade que eventualmente seja o suporte do dados. Nesta tese é proposto o reconhecimento de imagens digitais envolvendo transformações de rotação e variação de iluminação. Também o problema da reconstrução de sinais é atacado com a proposta de pré-imagem utilizando-se da otimização de uma função custo com um parâmetro regularizador, γ, que leva em conta também o conjunto de dados iniciais.

Multi-dimensional conditional moment closure modelling applied to a heavy-duty common-rail diesel engine

A multi-dimensional combustion code implementing the Conditional Moment Closure turbulent combustion model interfaced with a well-established RANS two- phase flow field solver has been employed to study a broad range of operating conditions for a heavy duty direct-injection common-rail Diesel engine. These conditions include different loads (25%, 50%, 75% and full load) and engine speeds (1250 and 1830 RPM) and, with respect to the fuel path, different injection timings and rail pressures. A total of nine cases have been simulated. Excellent agreement with experimental data has been found for the pressure traces and the heat release rates, without adjusting any model constants. The chemical mechanism used contains a detailed NOx sub-mechanism. The predicted emissions agree reasonably well with the experimental data considering the range of operating points and given no adjustments of any rate constants have been employed. In an effort to identify CPU cost reduction potential, various dimensionality reduction strategies have been assessed. Furthermore, the sensitivity of the predictions with respect to resolution in particular relating to the CMC grid has been investigated. Overall, the results suggest that the presented modelling strategy has considerable predictive capability concerning Diesel engine combustion without requiring model constant calibration based on experimental data. This is true particularly for the heat release rates predictions and, to a lesser extent, for NOx emissions where further progress is still necessary. © 2009 SAE International.

On the relation of slow feature analysis and Laplacian eigenmaps

The past decade has seen a rise of interest in Laplacian eigenmaps (LEMs) for nonlinear dimensionality reduction. LEMs have been used in spectral clustering, in semisupervised learning, and for providing efficient state representations for reinforcement learning. Here, we show that LEMs are closely related to slow feature analysis (SFA), a biologically inspired, unsupervised learning algorithm originally designed for learning invariant visual representations. We show that SFA can be interpreted as a function approximation of LEMs, where the topological neighborhoods required for LEMs are implicitly defined by the temporal structure of the data. Based on this relation, we propose a generalization of SFA to arbitrary neighborhood relations and demonstrate its applicability for spectral clustering. Finally, we review previous work with the goal of providing a unifying view on SFA and LEMs. © 2011 Massachusetts Institute of Technology.

Geometric optimization methods for independent component analysis applied on gene expression data

DNA microarrays provide a huge amount of data and require therefore dimensionality reduction methods to extract meaningful biological information. Independent Component Analysis (ICA) was proposed by several authors as an interesting means. Unfortunately, experimental data are usually of poor quality- because of noise, outliers and lack of samples. Robustness to these hurdles will thus be a key feature for an ICA algorithm. This paper identifies a robust contrast function and proposes a new ICA algorithm. © 2007 IEEE.

Manopt, a matlab toolbox for optimization on manifolds

Optimization on manifolds is a rapidly developing branch of nonlinear optimization. Its focus is on problems where the smooth geometry of the search space can be leveraged to design effcient numerical algorithms. In particular, optimization on manifolds is well-suited to deal with rank and orthogonality constraints. Such structured constraints appear pervasively in machine learning applications, including low-rank matrix completion, sensor network localization, camera network registration, independent component analysis, metric learning, dimensionality reduction and so on. The Manopt toolbox, available at www.manopt.org, is a user-friendly, documented piece of software dedicated to simplify experimenting with state of the art Riemannian optimization algorithms. By dealing internally with most of the differential geometry, the package aims particularly at lowering the entrance barrier. © 2014 Nicolas Boumal.

Computational information geometry and its applications

Digitization is the main feature of modern Information Science. Conjoining the digits and the coordinates, the relation between Information Science and high-dimensional space is consanguineous, and the information issues are transformed to the geometry problems in some high-dimensional spaces. From this basic idea, we propose Computational Information Geometry (CIG) to make information analysis and processing. Two kinds of applications of CIG are given, which are blurred image restoration and pattern recognition. Experimental results are satisfying. And in this paper, how to combine with groups of simple operators in some 2D planes to implement the geometrical computations in high-dimensional space is also introduced. Lots of the algorithms have been realized using software.

Deterministic Column-Based Matrix Decomposition

In this paper, we propose a deterministic column-based matrix decomposition method. Conventional column-based matrix decomposition (CX) computes the columns by randomly sampling columns of the data matrix. Instead, the newly proposed method (termed as CX_D) selects columns in a deterministic manner, which well approximates singular value decomposition. The experimental results well demonstrate the power and the advantages of the proposed method upon three real-world data sets.

Discriminative Orthogonal Neighborhood-Preserving Projections for Classification

Orthogonal neighborhood-preserving projection (ONPP) is a recently developed orthogonal linear algorithm for overcoming the out-of-sample problem existing in the well-known manifold learning algorithm, i.e., locally linear embedding. It has been shown that ONPP is a strong analyzer of high-dimensional data. However, when applied to classification problems in a supervised setting, ONPP only focuses on the intraclass geometrical information while ignores the interaction of samples from different classes. To enhance the performance of ONPP in classification, a new algorithm termed discriminative ONPP (DONPP) is proposed in this paper. DONPP 1) takes into account both intraclass and interclass geometries; 2) considers the neighborhood information of interclass relationships; and 3) follows the orthogonality property of ONPP. Furthermore, DONPP is extended to the semisupervised case, i.e., semisupervised DONPP (SDONPP). This uses unlabeled samples to improve the classification accuracy of the original DONPP. Empirical studies demonstrate the effectiveness of both DONPP and SDONPP.

一种基于改进LLE方法的传感器故障诊断方法研究

针对非线性系统传感器故障诊断难以解决的问题,提出了一种新的基于局部嵌入映射(LLE)的方法,解决了非线性数据的特征映射问题。首先,改进了基于分形维估计的内在维数的估计,通过线性拟合解决了线性区域的自动确定。然后,将故障状态与空间分布结合起来,通过确定数据点在空间超球内的分布完成故障的检测,在这个过程中将超球的确定与LLE算法中基于核函数的样本外数据扩展结合起来,大大减少了计算量,提高了算法的实时性,从而为复杂非线性传感器的故障诊断提供了一种新的有效的方法。

Restructuring Sparse High Dimensional Data for Effective Retrieval

The task in text retrieval is to find the subset of a collection of documents relevant to a user's information request, usually expressed as a set of words. Classically, documents and queries are represented as vectors of word counts. In its simplest form, relevance is defined to be the dot product between a document and a query vector--a measure of the number of common terms. A central difficulty in text retrieval is that the presence or absence of a word is not sufficient to determine relevance to a query. Linear dimensionality reduction has been proposed as a technique for extracting underlying structure from the document collection. In some domains (such as vision) dimensionality reduction reduces computational complexity. In text retrieval it is more often used to improve retrieval performance. We propose an alternative and novel technique that produces sparse representations constructed from sets of highly-related words. Documents and queries are represented by their distance to these sets. and relevance is measured by the number of common clusters. This technique significantly improves retrieval performance, is efficient to compute and shares properties with the optimal linear projection operator and the independent components of documents.

The Role of Knowledge in Visual Shape Representation

This report shows how knowledge about the visual world can be built into a shape representation in the form of a descriptive vocabulary making explicit the important geometrical relationships comprising objects' shapes. Two computational tools are offered: (1) Shapestokens are placed on a Scale-Space Blackboard, (2) Dimensionality-reduction captures deformation classes in configurations of tokens. Knowledge lies in the token types and deformation classes tailored to the constraints and regularities ofparticular shape worlds. A hierarchical shape vocabulary has been implemented supporting several later visual tasks in the two-dimensional shape domain of the dorsal fins of fishes.

Fuzzy-Rough Sets Assisted Attribute Selection

R. Jensen and Q. Shen. Fuzzy-Rough Sets Assisted Attribute Selection. IEEE Transactions on Fuzzy Systems, vol. 15, no. 1, pp. 73-89, 2007.