A Multi-Target Tracking and GMM-Classifier for Intelligent Vehicles

The expectation maximisation (EM) algorithm is an iterative maximum likelihood procedure often used for estimating the parameters of a mixture model. Theoretically, increases in the likelihood function are guaranteed as the algorithm iteratively improves upon previously derived parameter estimates. The algorithm is considered to converge when all parameter estimates become stable and no further improvements can be made to the likelihood value. However, to reduce computational time, it is often common practice for the algorithm to be stopped before complete convergence using heuristic approaches. In this paper, we consider various stopping criteria and evaluate their effect on fitting Gaussian mixture models (GMMs) to patient length of stay (LOS) data. Although the GMM can be successfully fitted to positively skewed data such as LOS, the fitting procedure often requires many iterations of the EM algorithm. To our knowledge, no previous study has evaluated the effect of different stopping criteria on fitting GMMs to skewed distributions. Hence, the aim of this paper is to evaluate the effect of various stopping criteria in order to select and justify their use within a patient spell classification methodology. Results illustrate that criteria based on the difference in the likelihood value and on the GMM parameters may not always be a good indicator for stopping the algorithm. In fact we show that the values of the difference in the variance parameters should be used instead, as these parameters are the last to stabilise. In addition, we also specify threshold values for the other stopping criteria.

In a distribution power network, the load model has no certain pattern or predicted behaviour due to large range of data and changes in energy consumption for end-user consumers. Thus, a powerful analysis based on probabilistic structure is required. For this paper Gaussian Mixture Model (GMM) has been used. GMM is a powerful probability model that allows different types of load distributions to be presented as a combination of several Gaussian distributions. The parameters of GMM is unknown for large random data such as real load data and these parameters can be identified by Expectation Maximization (EM) algorithm. This paper presents a method to evaluate probabilistic load data concerning the time-evolution of any type of distribution load for any duration of time. The proposed method is explained through generated load data of 100 residential houses for duration of one year.

The accurate modeling of uncertain variables, such as wind power and load uncertainty, is an essential foundation for the planning operation and scheduling decisions in power systems. Currently, Gaussian mixture model (GMM) and Dirichlet process mixture model (DPMM) are the primary techniques used to characterize uncertainties in power systems, which are commonly solved by expectation-maximization (EM) algorithm. However, for the massive data of uncertain variables, the algorithm encounters challenges in accurately obtaining GMM and DPMM with a lower time consumption. To address this issue, we propose a method for GMM uncertainty modeling in power systems considering the mutual assistance of latent variables. Specifically, the GMM of uncertain variables is first constructed, and the conditional probability is employed to characterize the mutual assistance of latent variables. Then, an improved EM algorithm is developed to obtain the optimal GMM parameters, in which the expectation step (E-step) and maximization step (M-step) of the algorithm are revised using the conditional probability. Importantly, the closed-form solutions for GMM parameters are rederived in the revised E-step and M-step. Finally, the proposed uncertainty modeling method is compared with the traditional GMM and DPMM on actual wind power and load data from Australia. The proposed method performs the efficiency and accuracy in characterizing uncertainty.

Salient object detection in a real-time environment demands high accuracy with less computation time. It is a changeling task to investigate a saliency model which improves saliency detection accuracy as well as reduces computation time. In this paper, we propose a hybrid model that improves detection accuracy with low computational time. The input image is simplified and clustered at multiple scales using SLIC and K-means clustering algorithms respectively. Gaussian Mixture Model (GMM) is developed on various color components of the digital image at multiple scales. The parameters of GMM are learnt using Expectation Maximization (EM) algorithm. The spatial variance of each color component is determined using GMM parameters and hence object position is estimated. Further, spatial variance of color components and object position is exploited to compute saliency map at a scale level. Afterwards, all the saliency maps generated across various scales are linearly combined to produce the final saliency map. The performance of the proposed model is compared in terms of Precision, Recall, F-Measure, Area under the Curve (AUC), Receiver Operating Characteristics (ROC) and Mean Absolute Error (MAE). Extensive experiments on six publicly available datasets viz. MSRA10K, DUT-OMRON, ECSSD, PASCAL-S, SED2, and THUR15K show that the proposed model outperforms or comparable against 11 state-of-the-art methods of the last decade. The key features of the proposed method are object completeness and efficiency in terms of computational time.

In this paper, the Gaussian mixture model (GMM) is introduced to implement channel multipath clustering. The GMM incorporates the covariance structure and the mean information of the channel multipaths, thus it can effectively reveal the similarity of the channel multipaths. First, the expectation-maximization (EM) algorithm is utilized to search for the posterior estimation of the GMM parameters. Then, the variational Bayesian (VB) algorithm is employed to optimize the GMM parameters to enhance the searching ability of EM and further to determine the optimal number of Gaussian distributions without resorting to cross-validation. Finally, a compact index (CI) is proposed to validate the clustering results reasonably. Thanks to the proposed CI, it is possible to find a close relationship among the GMM clustering mechanism, the multipath propagation characteristics and the CI evaluation index. Experiments with synthetic data and outdoor-to-indoor (O2I) channel data are presented to demonstrate the effectiveness of the proposed method.

In the work presented here, we consider state and parameter estimation of a semi-nonlinear Markov jump system in a non-Gaussian noise environment. The non-Gaussian measurement noise is approximated by a finite Gaussian mixture model (GMM). We propose a maximum likelihood (ML) solution to this state estimation problem which leads to two expectation-maximization (EM) algorithms. The first is a batch EM method which takes all the available data in the conditional expectation of the state in the E-step. An interacting multiple model (IMM) smoother is employed to evaluate the conditional expectation of the state by which a suboptimal estimate of system state is directly obtained. The Gaussian mixture parameters are then updated in the M-step. The second is a recursive EM algorithm which results from a stochastic approximation procedure and uses a standard IMM filter. For performance evaluation, posterior Cramer-Rao bound (PCRB) on the state estimation is adopted. Simulation results verify the effectiveness of the proposed algorithms.

We present a novel approach for prediction of satellite image frame that uses a fuzzy rule based framework. The input-output membership functions for the premise and consequent parts of the rules are derived using a Gaussian Mixture Model (GMM). The weights of the fuzzy rules are represented as the prior probabilities of the respective Gaussian components. For obtaining the predictive fuzzy model, the GMM parameters are estimated via EM algorithm using a spatiotemporal representation of image sequence or video clips. Minimum Description Length (MDL) criterion is used to obtain a suitable predictive fuzzy model. The resulting model is successfully applied on a sequence of satellite images of tropical cyclone, Nargis, that made landfall in Myanmar on May 2, 2008. The quality of the predicted image is assessed using two criteria. The proposed approach is found to predict image frame successfully.

In this paper we apply generative modeling to Gaussian Mixture Models (GMM) as a solution to high dimensional novel event detection and analysis on radio frequency (RF) power generators. A family of Denoising and β-Disentangling Variational Autoencoders β-DVAE) is used to encode datasets into lower and more salient dimensions. The reduced feature sets are modeled using GMMs where model parameters are learned using the Expectation Maximization (EM) algorithm. The data is obtained from two different generator models operating under normal as well as known not-normal conditions. This approach is also tested on standard classification sets. Robust testing is reported to achieve a target class accuracy of 98.16% for the target RF generator. Additionally, the GMM parameters are decoded by the generative model to the original data space for calculating per-variable fitness in order to provide an initial novel event analysis for engineers and technicians. This per-variable fitness is very critical for determining each variable's contribution to a novelty so that engineers can perform informed trouble shooting and maintenance of the RF generators.

Condition assessment of cables by pattern recognition of vehicle-induced cable tension ratio

The Expectation-Maximization algorithm is a very popular approach for estimating the parameters of Gaussian mixture models (GMMs). A known issue with GMM estimation is its sensitivity to outliers, which can lead to poor estimation performance depending on the dataset under consideration. A common approach to deal with this issue is robust estimation, which typically consists of reducing the influence of the outliers on the estimators by weighting the impact of some samples of the dataset considered as outliers. In an unsupervised context, it is difficult to know which sample from the database corresponds to a normal observation. To that extent, we propose to use within the EM algorithm an outlier detection step that attributes an anomaly score to each sample of the database in an unsupervised way. A modified Bayesian Information Criterion is also introduced to efficiently select the appropriate amount of outliers contained in a dataset. The proposed method is tested on a benchmark remote sensing dataset coming from the UCI Machine Learning Repository. The experimental results show the interest of the proposed robustification when compared to other benchmark imputation procedures.

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.

Lymphocyte count (LC) is an important hematological parameter in dairy cows. Historical studies establishing LC reference intervals often included cows that were not tested for bovine leukosis virus (BLV). As a result, BLV-infected cows showing subclinical lymphocytosis were possibly included in those studies, leading to higher LC reference intervals. Because BLV (among other pathogens or processes) can cause persistent lymphocytosis, including BLV-infected cows when establishing LC reference intervals could lead to their overestimation. Our objectives were to propose updated LC reference intervals for Holstein cows and to estimate the most discriminant LC threshold for differentiating cows belonging to the low- versus high-LC distributions. We conducted a cross-sectional observational study to collected blood samples from 631 Holstein cows, irrespective of their BLV status, across 8 herds in Québec, Canada. Blood samples were analyzed on the day of collection to determine LC in 109 cells/L. Using Gaussian finite mixture models, we identified the 2 most probable Gaussian LC distributions representing healthy versus abnormal cows within the complete dataset (i.e., all sampled lactating cows analyzed together, regardless of age), and within 2 age groups: young (2-4 yr-old lactating cows) and older cows (>4-year-old lactating cows). We used the identified distributions to propose LC reference intervals for Holstein cows. Then, we determined the most discriminant LC thresholds to distinguish cows belonging to the low- versus high-LC distributions (the latter being presumed to be affected by either a short-term or chronic immunological alteration). To assess persistent lymphocytosis, we collected a second set of blood samples 4 mo later from cows with an initial LC ≥5.5 × 109 cells/L. The LC reference intervals were 1.5 to 5.5 × 109 cells/L in the complete dataset, and 1.9 to 6.0 and 1.6 to 4.5 × 109 cells/L, in young and older cows, respectively. The most discriminant LC thresholds were ≥5.5 × 109 cells/L in the complete dataset, ≥5.5 × 109 cells/L for young cows, and ≥4.5 × 109 cells/L for older cows. The probability of belonging to the Gaussian LC distribution representing presumably abnormal values from cows affected by either a short-term or chronic immunological alteration increased markedly with increasing LC but was also high for cows with a very low LC (<1.5 × 109 cells/L). Persistent lymphocytosis was observed in 77% (49/64) of cows in the young group and 98% (55/56) of cows in the older group. The reference LC intervals proposed are lower than those reported in previous studies and reflect an expected age-related variation. The proposed LC thresholds provide a practical marker of chronic lymphocytosis.

How to use historical data of public smart card to predict user behaviour attracts a lot of attention. This paper aims at modelling travel patterns and predicting future travel behaviour of metro system smart card holders. We apply Gaussian mixture model (GMM) on time series to model user behaviour. We propose a new method based on the perplexity for finite GMM and use expectation-maximisation (EM) algorithm to estimate parameters of GMM. In order to predict the future travel behaviour, we introduce the Gaussian process regression (GPR) to define distributions over GMM, which can not only tell the probability of travelling at a certain moment but also tell the reliability of the prediction. Experimental results show that our whole system in the centre of GMM and GPR can effectively mine the hidden knowledge of historical data of smart card, and thus model the travel patterns and predict future travel behaviour.

EM algorithm is a very popular iteration-based method to estimate the parameters of Gaussian Mixture Model from a large observation set. However, in most cases, EM algorithm is not guaranteed to converge to the global optimum. Instead, it stops at some local optimums, which can be much worse than the global optimum. Therefore, it is usually required to run multiple procedures of EM algorithm with different initial configurations and return the best solution. To improve the efficiency of this scheme, we propose a new method which can estimate an upper bound on the logarithm likelihood of the local optimum, based on the current configuration after the latest EM iteration. This is accomplished by first deriving some region bounding the possible locations of local optimum, followed by some upper bound estimation on the maximum likelihood. With this estimation, we can terminate an EM algorithm procedure if the estimated local optimum is definitely worse than the best solution seen so far. Extensive experiments show that our method can effectively and efficiently accelerate conventional multiple restart EM algorithm.

A view-based statistical system for multi-view face detection and pose estimation