Independent factor discriminant analysis

Non-stationary feature fusion of face and palmprint multimodal biometrics

Passive polarization based imaging is a useful tool in computer vision and pattern recognition. A passive polarization imaging system forms a polarimetric image from the reflection of ambient light that contains useful information for computer vision tasks such as object detection (classification) and recognition. Applications of polarization based pattern recognition include material classification and automatic shape recognition. In this paper, we present two target detection algorithms for images captured by a passive polarimetric imaging system. The proposed detection algorithms are based on Bayesian decision theory. In these approaches, an object can belong to one of any given number classes and classification involves making decisions that minimize the average probability of making incorrect decisions. This minimum is achieved by assigning an object to the class that maximizes the a posteriori probability. Computing a posteriori probabilities requires estimates of class conditional probability density functions (likelihoods) and prior probabilities. A Probabilistic neural network (PNN), which is a nonparametric method that can compute Bayes optimal boundaries, and a -nearest neighbor (KNN) classifier, is used for density estimation and classification. The proposed algorithms are applied to polarimetric image data gathered in the laboratory with a liquid crystal-based system. The experimental results validate the effectiveness of the above algorithms for target detection from polarimetric data.

Efficient dimensionality reduction can involve generative latent variable models such as probabilistic principal component analysis (PPCA) or independent component analysis (ICA). Such models aim to extract a reduced set of variables (latent variables) from the original ones. In most cases, the learning of these models occur within an unsupervised framework where only unlabeled samples are used. In this paper, we investigate the possibility of estimating an independent factor analysis model (IFA), and thus projecting original data onto a lower dimensional space, when prior knowledge on the cluster membership of some training samples is incorporated. We propose to allow this model to learn within a semi-supervised framework in which likelihood of both labeled and unlabeled samples is maximized by a generalized expectation-maximization (GEM) algorithm. Experimental results with real data sets are provided to demonstrate the ability of our approach to find a low dimensional manifold with good explanatory power.

In this paper, we propose a fast and versatile blind source separation including closed-form estimation of sources' probability density functions (PDFs), where the ICA's activation function is automatically adapted to various noise conditions. In the proposed method, closed-form second-order ICA and closed-form PDF estimation are introduced as a computational-cost-efficient preprocessing to extract sources' PDFs. Compared with various type of conventional ICAs, e.g., fixed activation-function type and ML-based type, our proposed algorithm can give a faster and higher convergence. Experimental assessment reveals that the proposed method is versatile for handling non-speech sound sources.

The non-line-of-sight (NLOS) propagation caused by intermittently blocking of the direct path between the base station and the mobile station is the main difficulty for mobile user location in cellular wireless communication system. So it is indispensable to investigate the techniques about the NLOS error identification and correction. In this paper, we suggest a robust and accurate approach using probability density function (PDF) estimator to identify the NLOS situation, and then an improved biased Kalman filter which depends on PDF estimator as the nonlinearity weighting coefficient in recursive operation is used to mitigate the NLOS error for time of arrival (TOA) measurements. As the PDF estimator is calculated from actual TOA samples, it is adaptive for the complex practical NLOS environments. The simulation results also indicate that with the less prior information about communication environments, the approach we present has a good location performance even in severe NLOS situations.

The error estimate of Borgonovo's moment-independent index δi is considered, and it shows that the possible computational complexity of δi is mainly due to the probability density function (PDF) estimate because the PDF estimate is an ill-posed problem and its convergence rate is quite slow. So it reminds us to compute Borgonovo's index using other methods. To avoid the PDF estimate, δi, which is based on the PDF, is first approximatively represented by the cumulative distribution function (CDF). The CDF estimate is well posed and its convergence rate is always faster than that of the PDF estimate. From the representation, a stable approach is proposed to compute δi with an adaptive procedure. Since the small probability multidimensional integral needs to be computed in this procedure, a computational strategy named asymptotic space integration is introduced to reduce a high-dimensional integral to a one-dimensional integral. Then we can compute the small probability multidimensional integral by adaptive numerical integration in one dimension with an improved convergence rate. From the comparison of numerical error analysis of some examples, it can be shown that the proposed method is an effective approach to uncertainty importance measure computation.

Limited dataset and inherent complexity of subsurface applications make the deep learning (DL) model prone to overfitting. Dimension reduction (DR) optimizes DL training by extracting latent variables with fewer numbers and retaining most data features. Existing DR approaches, both conventional and DL-based, inadequately address the complexities of 3D saturation data with sparse nature and abrupt changes at plume boundaries, underscoring the need for a more robust and efficient solution.Motivation Grid cell fractions with non-zero values in 2D and 3D CO 2 saturation data Develop DL-based workflow to effectively extract latent variables of complex 3D CO 2 saturation data and correspondingly reconstruct highdimensional data from latent variables, facilitating more efficient analysis and processing of 3D saturation data. Apply the developed workflow to the Illinois Basin Decatur Project (IBDP) simulation data, which contain sufficient variations in CO 2 plume shapes and distributions.Research Objectives 3D CO 2 saturation (Baffle at middle) 3D CO 2 saturation (No Baffle) Step 1: PCA models for DR and reconstruction of 2D saturation fields. Obtained by averaging in three directions: X, Y, and Z. More effective non-zero values, making dimension reduction easier. Latent variable numbers: 300 for X, Y, and 200 for Z saturation separately.800 latent variables in total. Step 2: Training of 3D reconstruction model. Inputs: 2D average saturation data in X, Y, and Z directions, and geological data. Output: 3D saturation data. Include three view-based reconstruction model, followed with a multi-view fusion model. Apply trained workflow to 3D saturation data. DR step: Averaging operations (X, Y, and, Z) and PCA. Reconstruction step: Inverse PCA and 3D reconstruction model.Methodology DL-based Workflow PCA for 2D saturation data.Top

We propose a generative mixture model classifier that allows for the class conditional densities to be represented by mixtures having certain subsets of their components shared or common among classes. We argue that, when the total number of mixture components is kept fixed, the most efficient classification model is obtained by appropriately determining the sharing of components among class conditional densities. In order to discover such an efficient model, a training method is derived based on the EM algorithm that automatically adjusts component sharing. We provide experimental results with good classification performance.

Probability density function (PDF) estimation is a fundamentally important problem for statistical pattern recognition. Independent component analysis (ICA) can be applied to the feature vectors so that the PDF estimation of a high dimensional vector can be converted to the PDF estimation of several 1-dimensional variables. However in practice we find that this PDF is in poor generalization ability for pattern classification because of the implied noise. Hence, this paper proposes an improvement of ICA based PDF estimation method. A latent variable model is built to separate the noise from the feature vector so that the pattern information and the noise can be dealt with respectively. Based on the latent variable model, a modified ICA based PDF is deduced. The validity of our proposed method is demonstrated by the experiments of off-line handwritten numeral recognition.

Estimation of probability density functions based on available data is important problem arising in various fields, such as telecommunications, machine learning, data mining, pattern recognition and computer vision. In this paper, we consider Kernel-based non-parametric density estimation methods and derive formulae for variable kernel density estimation using generalized, elliptic Gaussian kernels. The proposed technique is verified on simulated data.

We present probabilistic models which are suitable for class conditional density estimation and can be regarded as shared kernel models where sharing means that each kernel may contribute to the estimation of the conditional densities of an classes. We first propose a model that constitutes an adaptation of the classical radial basis function (RBF) network (with full sharing of kernels among classes) where the outputs represent class conditional densities. In the opposite direction is the approach of separate mixtures model where the density of each class is estimated using a separate mixture density (no sharing of kernels among classes). We present a general model that allows for the expression of intermediate cases where the degree of kernel sharing can be specified through an extra model parameter. This general model encompasses both the above mentioned models as special cases. In all proposed models the training process is treated as a maximum likelihood problem and expectation-maximization algorithms have been derived for adjusting the model parameters.

Entropy-metric estimation of the small data models with stochastic parameters

Multivariate online kernel density estimation with Gaussian kernels

In this paper we seek a Gaussian mixture model (GMM) of an n-variate probability density function. Usually the parameters of GMMs are determined in the original n-dimensional space by optimizing a maximum likelihood (ML) criterion. A practical deficiency of this method of fitting GMMs is its poor performance when dealing with high-dimensional data since a large sample size is needed to match the accuracy that is possible in low dimensions. We propose a method for fitting the GMM based on the projection pursuit strategy. This GMM is highly constrained and hence its ability to model structure in subspaces is enhanced, compared to a direct ML fitting of a GMM in high dimensions. Our method is closely related to recently developed independent factor analysis (IFA) mixture models. The comparisons with ML fitting of GMM in n-dimensions and IFA mixtures show that the proposed method is an attractive choice for fitting GMMs using small sizes of training sets.

The high dimensionality of global gene expression profiles, where number of variables (genes) is very large compared to the number of observations (samples), presents challenges that affect generalizability and applicability of microarray analysis. Latent variable modeling offers a promising approach to deal with high-dimensional microarray data. The latent variable model is based on a few latent variables that capture most of the gene expression information. Here, we describe how to accomplish a reduction in dimension by a latent variable methodology, which can greatly reduce the number of features used to characterize microarray data. We propose a general latent variable framework for prediction of predefined classes of samples using gene expression profiles from microarray experiments. The framework consists of (i) selection of smaller number of genes that are most differentially expressed between samples, (ii) dimension reduction using hierarchical clustering, where each cluster partition is identified as latent variable, (iii) discretization of gene expression matrix, (iv) fitting the Rasch item response model for genes in each cluster partition to estimate the expression of latent variable, and (v) construction of prediction model with latent variables as covariates to study the relationship between latent variables and phenotype. Two different microarray data sets are used to illustrate a general framework of the approach. We show that the predictive performance of our method is comparable to the current best approach based on an all-gene space. The method is general and can be applied to the other high-dimensional data problems.