Variable Width Elliptic Gaussian Kernels for Probability Density Estimation

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.

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.

Multivariate online kernel density estimation with Gaussian kernels

Reduction techniques are important tools in machine learning and pattern recognition. In this article, we demonstrate how a kernel-based density estimator can be used as a tool for understanding human category representation. Despite the dominance of exemplar models of categorization, there is still ambiguity about the number of exemplars stored in memory. Here, we illustrate that by omitting exemplars categorization performance is not affected.

In this paper we discuss non-parametric estimation of the probability density function (PDF) of a univariate random variable. This problem has been the subject of a vast amount of scientific literature in many domains: while statisticians are mainly interested in the analysis of the properties of proposed estimators, engineers treat the histogram as a ready-to-use tool for dataset analysis. By considering histogram data as a numerical sequence, a simple PDF estimator is presented in this paper. It is based on basic notions related to the reconstruction of a continuous-time signal from a sequence of samples and it is as accurate as kernel-based estimators, widely adopted in the statistical literature. The major properties of the proposed PDF estimator are discussed and then verified by simulations related to the common case of a normal density function.

Many statistic based machine learning methods depend on the estimation of probability density function from observations. Non-parametric density estimation algorithms based on minimizing expirical risk using support vector machine (SVM) are quite general and powerful, but have a significant disadvantage in the smoothness of estimation result. In this paper, we studies the vicinal risk minimization based estimation algorithm, and propose a new construction algorithm of vicinity function. Experiments are carried out which prove that the performance of new algorithm is obviously improved.

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.

Unimodal density estimation using Bernstein polynomials

Pareto Density Estimation (PDE) as defined in this work is a method for the estimation of probability density functions using hyperspheres. The radius of the hyperspheres is derived from optimizing information while minimizing set size. It is shown, that PDE is a very good estimate for data containing clusters of Gaussian structure. The behavior of the method is demonstrated with respect to cluster overlap, number of clusters, different variances in different clusters and application to high dimensional data. For high dimensional data PDE is found to be appropriate for the purpose of cluster analysis. The method is tested successfully on a difficult high dimensional real world problem: stock picking in falling markets.

Boosting feature selection for Neural Network based regression

As there has been a paradigm shift in the learning load from a human subject to a computer, machine learning has been considered as a useful tool for Brain-Computer Interfaces (BCIs). In this paper, we propose a novel Bayesian framework for discriminative feature extraction for motor imagery classification in an EEG-based BCI in which the class-discriminative frequency bands and the corresponding spatial filters are optimized by means of the probabilistic and information-theoretic approaches. In our framework, the problem of simultaneous spatiospectral filter optimization is formulated as the estimation of an unknown posterior probability density function (pdf) that represents the probability that a single-trial EEG of predefined mental tasks can be discriminated in a state. In order to estimate the posterior pdf, we propose a particle-based approximation method by extending a factored-sampling technique with a diffusion process. An information-theoretic observation model is also devised to measure discriminative power of features between classes. From the viewpoint of classifier design, the proposed method naturally allows us to construct a spectrally weighted label decision rule by linearly combining the outputs from multiple classifiers. We demonstrate the feasibility and effectiveness of the proposed method by analyzing the results and its success on three public databases.

Non-parametric representation of pixel intensity distribution is quite effective to construct proper background model and to detect foreground objects accurately. However, from the viewpoint of practical application, the computation cost of the distribution estimation should be reduced. In this paper, we present fast estimation of the probability density function (PDF) of pixel value using Parzen density estimation and foreground object detection based on the estimated PDF. Here, the PDF is computed by partially updating the PDF estimated at the previous frame, and it greatly reduces the computation cost of the PDF estimation. Thus, the background model adapts quickly to changes in the scene and, therefore, foreground objects can be robustly detected. Several experiments show the effectiveness of our approach.

AI’s 10 to Watch, 2022