Nonlinear mixture model for hyperspectral unmixing

Proceedings of International Conference - SPIE 7477, Image and Signal Processing for Remote Sensing XV - 28 September 2009

Enhancing the selection of a model-based clustering with external categorical variables

In cluster analysis, it can be useful to interpret the partition built from the data in the light of external categorical variables which are not directly involved to cluster the data. An approach is proposed in the model-based clustering context to select a number of clusters which both fits the data well and takes advantage of the potential illustrative ability of the external variables. This approach makes use of the integrated joint likelihood of the data and the partitions at hand, namely the model-based partition and the partitions associated to the external variables. It is noteworthy that each mixture model is fitted by the maximum likelihood methodology to the data, excluding the external variables which are used to select a relevant mixture model only. Numerical experiments illustrate the promising behaviour of the derived criterion. © 2014 Springer-Verlag Berlin Heidelberg.

Enhancing the selection of a model-based clustering with external categorical variables

In cluster analysis, it can be useful to interpret the partition built from the data in the light of external categorical variables which are not directly involved to cluster the data. An approach is proposed in the model-based clustering context to select a number of clusters which both fits the data well and takes advantage of the potential illustrative ability of the external variables. This approach makes use of the integrated joint likelihood of the data and the partitions at hand, namely the model-based partition and the partitions associated to the external variables. It is noteworthy that each mixture model is fitted by the maximum likelihood methodology to the data, excluding the external variables which are used to select a relevant mixture model only. Numerical experiments illustrate the promising behaviour of the derived criterion.

Agrupamento multi-orador

Actualmente tem-se observado um aumento do volume de sinais de fala em diversas aplicações, que reforçam a necessidade de um processamento automático dos ficheiros. No campo do processamento automático destacam-se as aplicações de “diarização de orador”, que permitem catalogar os ficheiros de fala com a identidade de oradores e limites temporais de fala de cada um, através de um processo de segmentação e agrupamento. No contexto de agrupamento, este trabalho visa dar continuidade ao trabalho intitulado “Detecção do Orador”, com o desenvolvimento de um algoritmo de “agrupamento multi-orador” capaz de identificar e agrupar correctamente os oradores, sem conhecimento prévio do número ou da identidade dos oradores presentes no ficheiro de fala. O sistema utiliza os coeficientes “Mel Line Spectrum Frequencies” (MLSF) como característica acústica de fala, uma segmentação de fala baseada na energia e uma estrutura do tipo “Universal Background Model - Gaussian Mixture Model” (UBM-GMM) adaptado com o classificador “Support Vector Machine” (SVM). No trabalho foram analisadas três métricas de discriminação dos modelos SVM e a avaliação dos resultados foi feita através da taxa de erro “Speaker Error Rate” (SER), que quantifica percentualmente o número de segmentos “fala” mal classificados. O algoritmo implementado foi ajustado às características da língua portuguesa através de um corpus com 14 ficheiros de treino e 30 ficheiros de teste. Os ficheiros de treino dos modelos e classificação final, enquanto os ficheiros de foram utilizados para avaliar o desempenho do algoritmo. A interacção com o algoritmo foi dinamizada com a criação de uma interface gráfica que permite receber o ficheiro de teste, processá-lo, listar os resultados ou gerar um vídeo para o utilizador confrontar o sinal de fala com os resultados de classificação.

Vertex component analysis: a fast algorithm to unmix hyperspectral data

Given a set of mixed spectral (multispectral or hyperspectral) vectors, linear spectral mixture analysis, or linear unmixing, aims at estimating the number of reference substances, also called endmembers, their spectral signatures, and their abundance fractions. This paper presents a new method for unsupervised endmember extraction from hyperspectral data, termed vertex component analysis (VCA). The algorithm exploits two facts: (1) the endmembers are the vertices of a simplex and (2) the affine transformation of a simplex is also a simplex. In a series of experiments using simulated and real data, the VCA algorithm competes with state-of-the-art methods, with a computational complexity between one and two orders of magnitude lower than the best available method.

Unmixing hyperspectral intimate mixtures

Proceedings of International Conference Conference Volume 7830 Image and Signal Processing for Remote Sensing XVI Lorenzo Bruzzone Toulouse, France | September 20, 2010

Feature selection for clustering categorical data with an embedded modelling approach

Research on the problem of feature selection for clustering continues to develop. This is a challenging task, mainly due to the absence of class labels to guide the search for relevant features. Categorical feature selection for clustering has rarely been addressed in the literature, with most of the proposed approaches having focused on numerical data. In this work, we propose an approach to simultaneously cluster categorical data and select a subset of relevant features. Our approach is based on a modification of a finite mixture model (of multinomial distributions), where a set of latent variables indicate the relevance of each feature. To estimate the model parameters, we implement a variant of the expectation-maximization algorithm that simultaneously selects the subset of relevant features, using a minimum message length criterion. The proposed approach compares favourably with two baseline methods: a filter based on an entropy measure and a wrapper based on mutual information. The results obtained on synthetic data illustrate the ability of the proposed expectation-maximization method to recover ground truth. An application to real data, referred to official statistics, shows its usefulness.

Parallel method for sparse semisupervised hyperspectral unmixing

Parallel hyperspectral unmixing problem is considered in this paper. A semisupervised approach is developed under the linear mixture model, where the abundance's physical constraints are taken into account. The proposed approach relies on the increasing availability of spectral libraries of materials measured on the ground instead of resorting to endmember extraction methods. Since Libraries are potentially very large and hyperspectral datasets are of high dimensionality a parallel implementation in a pixel-by-pixel fashion is derived to properly exploits the graphics processing units (GPU) architecture at low level, thus taking full advantage of the computational power of GPUs. Experimental results obtained for real hyperspectral datasets reveal significant speedup factors, up to 164 times, with regards to optimized serial implementation.

Blind hyperspectral unmixing

Hyperspectral unmixing methods aim at the decomposition of a hyperspectral image into a collection endmember signatures, i.e., the radiance or reflectance of the materials present in the scene, and the correspondent abundance fractions at each pixel in the image. This paper introduces a new unmixing method termed dependent component analysis (DECA). This method is blind and fully automatic and it overcomes the limitations of unmixing methods based on Independent Component Analysis (ICA) and on geometrical based approaches. DECA is based on the linear mixture model, i.e., each pixel is a linear mixture of the endmembers signatures weighted by the correspondent abundance fractions. These abundances are modeled as mixtures of Dirichlet densities, thus enforcing the non-negativity and constant sum constraints, imposed by the acquisition process. The endmembers signatures are inferred by a generalized expectation-maximization (GEM) type algorithm. The paper illustrates the effectiveness of DECA on synthetic and real hyperspectral images.

Fast unsupervised extraction of endmembers spectra from hyperspectral data

Linear unmixing decomposes an hyperspectral image into a collection of re ectance spectra, called endmember signatures, and a set corresponding abundance fractions from the respective spatial coverage. This paper introduces vertex component analysis, an unsupervised algorithm to unmix linear mixtures of hyperpsectral data. VCA exploits the fact that endmembers occupy vertices of a simplex, and assumes the presence of pure pixels in data. VCA performance is illustrated using simulated and real data. VCA competes with state-of-the-art methods with much lower computational complexity.

Categorical data clustering using a minimum message length criterion

Research on cluster analysis for categorical data continues to develop, new clustering algorithms being proposed. However, in this context, the determination of the number of clusters is rarely addressed. We propose a new approach in which clustering and the estimation of the number of clusters is done simultaneously for categorical data. We assume that the data originate from a finite mixture of multinomial distributions and use a minimum message length criterion (MML) to select the number of clusters (Wallace and Bolton, 1986). For this purpose, we implement an EM-type algorithm (Silvestre et al., 2008) based on the (Figueiredo and Jain, 2002) approach. The novelty of the approach rests on the integration of the model estimation and selection of the number of clusters in a single algorithm, rather than selecting this number based on a set of pre-estimated candidate models. The performance of our approach is compared with the use of Bayesian Information Criterion (BIC) (Schwarz, 1978) and Integrated Completed Likelihood (ICL) (Biernacki et al., 2000) using synthetic data. The obtained results illustrate the capacity of the proposed algorithm to attain the true number of cluster while outperforming BIC and ICL since it is faster, which is especially relevant when dealing with large data sets.

Determining the number of clusters in categorical data

Cluster analysis for categorical data has been an active area of research. A well-known problem in this area is the determination of the number of clusters, which is unknown and must be inferred from the data. In order to estimate the number of clusters, one often resorts to information criteria, such as BIC (Bayesian information criterion), MML (minimum message length, proposed by Wallace and Boulton, 1968), and ICL (integrated classification likelihood). In this work, we adopt the approach developed by Figueiredo and Jain (2002) for clustering continuous data. They use an MML criterion to select the number of clusters and a variant of the EM algorithm to estimate the model parameters. This EM variant seamlessly integrates model estimation and selection in a single algorithm. For clustering categorical data, we assume a finite mixture of multinomial distributions and implement a new EM algorithm, following a previous version (Silvestre et al., 2008). Results obtained with synthetic datasets are encouraging. The main advantage of the proposed approach, when compared to the above referred criteria, is the speed of execution, which is especially relevant when dealing with large data sets.

H → Zr in the complex two Higgs doublet model

The latest LHC data confirmed the existence of a Higgs-like particle and made interesting measurements on its decays into gamma gamma, ZZ*, WW*, tau(+)tau(-), and b (b) over bar. It is expected that a decay into Z gamma might be measured at the next LHC round, for which there already exists an upper bound. The Higgs-like particle could be a mixture of scalar with a relatively large component of pseudoscalar. We compute the decay of such a mixed state into Z gamma, and we study its properties in the context of the complex two Higgs doublet model, analysing the effect of the current measurements on the four versions of this model. We show that a measurement of the h -> Z gamma rate at a level consistent with the SM can be used to place interesting constraints on the pseudoscalar component. We also comment on the issue of a wrong sign Yukawa coupling for the bottom in Type II models.