Model-Based Clustering and Classification of Functional Data

The problem of complex data analysis is a central topic of modern statistical science and learning systems and is becoming of broader interest with the increasing prevalence of high-dimensional data. The challenge is to develop statistical models and autonomous algorithms that are able to acquire knowledge from raw data for exploratory analysis, which can be achieved through clustering techniques or to make predictions of future data via classification (i.e., discriminant analysis) techniques. Latent data models, including mixture model-based approaches are one of the most popular and successful approaches in both the unsupervised context (i.e., clustering) and the supervised one (i.e, classification or discrimination). Although traditionally tools of multivariate analysis, they are growing in popularity when considered in the framework of functional data analysis (FDA). FDA is the data analysis paradigm in which the individual data units are functions (e.g., curves, surfaces), rather than simple vectors. In many areas of application, the analyzed data are indeed often available in the form of discretized values of functions or curves (e.g., time series, waveforms) and surfaces (e.g., 2d-images, spatio-temporal data). This functional aspect of the data adds additional difficulties compared to the case of a classical multivariate (non-functional) data analysis. We review and present approaches for model-based clustering and classification of functional data. We derive well-established statistical models along with efficient algorithmic tools to address problems regarding the clustering and the classification of these high-dimensional data, including their heterogeneity, missing information, and dynamical hidden structure. The presented models and algorithms are illustrated on real-world functional data analysis problems from several application area

Recent advances in directional statistics

Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. An overview of currently available software for analysing directional data is also provided, and potential future developments discussed.Comment: 61 page

Nonparametric discriminant HMM and application to facial expression recognition

Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2009, p. 2090-2096This paper presents a nonparametric discriminant HMM and applies it to facial expression recognition. In the proposed HMM, we introduce an effective nonparametric output probability estimation method to increase the discrimination ability at both hidden state level and class level. The proposed method uses a nonparametric adaptive kernel to utilize information from all classes and improve the discrimination at class level. The discrimination between hidden states is increased by defining membership coefficients which associate each reference vector with hidden states. The adaption of such coefficients is obtained by the Expectation Maximization (EM) method. Furthermore, we present a general formula for the estimation of output probability, which provides a way to develop new HMMs. Finally, we evaluate the performance of the proposed method on the CMU expression database and compare it with other nonparametric HMMs. © 2009 IEEE.published_or_final_versio

Speaker Identification Based On Discriminative Vector Quantization And Data Fusion

Speaker Identification (SI) approaches based on discriminative Vector Quantization (VQ) and data fusion techniques are presented in this dissertation. The SI approaches based on Discriminative VQ (DVQ) proposed in this dissertation are the DVQ for SI (DVQSI), the DVQSI with Unique speech feature vector space segmentation for each speaker pair (DVQSI-U), and the Adaptive DVQSI (ADVQSI) methods. The difference of the probability distributions of the speech feature vector sets from various speakers (or speaker groups) is called the interspeaker variation between speakers (or speaker groups). The interspeaker variation is the measure of template differences between speakers (or speaker groups). All DVQ based techniques presented in this contribution take advantage of the interspeaker variation, which are not exploited in the previous proposed techniques by others that employ traditional VQ for SI (VQSI). All DVQ based techniques have two modes, the training mode and the testing mode. In the training mode, the speech feature vector space is first divided into a number of subspaces based on the interspeaker variations. Then, a discriminative weight is calculated for each subspace of each speaker or speaker pair in the SI group based on the interspeaker variation. The subspaces with higher interspeaker variations play more important roles in SI than the ones with lower interspeaker variations by assigning larger discriminative weights. In the testing mode, discriminative weighted average VQ distortions instead of equally weighted average VQ distortions are used to make the SI decision. The DVQ based techniques lead to higher SI accuracies than VQSI. DVQSI and DVQSI-U techniques consider the interspeaker variation for each speaker pair in the SI group. In DVQSI, speech feature vector space segmentations for all the speaker pairs are exactly the same. However, each speaker pair of DVQSI-U is treated individually in the speech feature vector space segmentation. In both DVQSI and DVQSI-U, the discriminative weights for each speaker pair are calculated by trial and error. The SI accuracies of DVQSI-U are higher than those of DVQSI at the price of much higher computational burden. ADVQSI explores the interspeaker variation between each speaker and all speakers in the SI group. In contrast with DVQSI and DVQSI-U, in ADVQSI, the feature vector space segmentation is for each speaker instead of each speaker pair based on the interspeaker variation between each speaker and all the speakers in the SI group. Also, adaptive techniques are used in the discriminative weights computation for each speaker in ADVQSI. The SI accuracies employing ADVQSI and DVQSI-U are comparable. However, the computational complexity of ADVQSI is much less than that of DVQSI-U. Also, a novel algorithm to convert the raw distortion outputs of template-based SI classifiers into compatible probability measures is proposed in this dissertation. After this conversion, data fusion techniques at the measurement level can be applied to SI. In the proposed technique, stochastic models of the distortion outputs are estimated. Then, the posteriori probabilities of the unknown utterance belonging to each speaker are calculated. Compatible probability measures are assigned based on the posteriori probabilities. The proposed technique leads to better SI performance at the measurement level than existing approaches

Generalized multi-stream hidden Markov models.

For complex classification systems, data is usually gathered from multiple sources of information that have varying degree of reliability. In fact, assuming that the different sources have the same relevance in describing all the data might lead to an erroneous behavior. The classification error accumulates and can be more severe for temporal data where each sample is represented by a sequence of observations. Thus, there is compelling evidence that learning algorithms should include a relevance weight for each source of information (stream) as a parameter that needs to be learned. In this dissertation, we assumed that the multi-stream temporal data is generated by independent and synchronous streams. Using this assumption, we develop, implement, and test multi- stream continuous and discrete hidden Markov model (HMM) algorithms. For the discrete case, we propose two new approaches to generalize the baseline discrete HMM. The first one combines unsupervised learning, feature discrimination, standard discrete HMMs and weighted distances to learn the codebook with feature-dependent weights for each symbol. The second approach consists of modifying the HMM structure to include stream relevance weights, generalizing the standard discrete Baum-Welch learning algorithm, and deriving the necessary conditions to optimize all model parameters simultaneously. We also generalize the minimum classification error (MCE) discriminative training algorithm to include stream relevance weights. For the continuous HMM, we introduce a. new approach that integrates the stream relevance weights in the objective function. Our approach is based on the linearization of the probability density function. Two variations are proposed: the mixture and state level variations. As in the discrete case, we generalize the continuous Baum-Welch learning algorithm to accommodate these changes, and we derive the necessary conditions for updating the model parameters. We also generalize the MCE learning algorithm to derive the necessary conditions for the model parameters\u27 update. The proposed discrete and continuous HMM are tested on synthetic data sets. They are also validated on various applications including Australian Sign Language, audio classification, face classification, and more extensively on the problem of landmine detection using ground penetrating radar data. For all applications, we show that considerable improvement can be achieved compared to the baseline HMM and the existing multi-stream HMM algorithms

PREDICTION OF RESPIRATORY MOTION

Radiation therapy is a cancer treatment method that employs high-energy radiation beams to destroy cancer cells by damaging the ability of these cells to reproduce. Thoracic and abdominal tumors may change their positions during respiration by as much as three centimeters during radiation treatment. The prediction of respiratory motion has become an important research area because respiratory motion severely affects precise radiation dose delivery. This study describes recent radiotherapy technologies including tools for measuring target position during radiotherapy and tracking-based delivery systems. In the first part of our study we review three prediction approaches of respiratory motion, i.e., model-based methods, model-free heuristic learning algorithms, and hybrid methods. In the second part of our work we propose respiratory motion estimation with hybrid implementation of extended Kalman filter. The proposed method uses the recurrent neural network as the role of the predictor and the extended Kalman filter as the role of the corrector. In the third part of our work we further extend our research work to present customized prediction of respiratory motion with clustering from multiple patient interactions. For the customized prediction we construct the clustering based on breathing patterns of multiple patients using the feature selection metrics that are composed of a variety of breathing features. In the fourth part of our work we retrospectively categorize breathing data into several classes and propose a new approach to detect irregular breathing patterns using neural networks. We have evaluated the proposed new algorithm by comparing the prediction overshoot and the tracking estimation value. The experimental results of 448 patients’ breathing patterns validated the proposed irregular breathing classifier

Speech Recognition

Chapters in the first part of the book cover all the essential speech processing techniques for building robust, automatic speech recognition systems: the representation for speech signals and the methods for speech-features extraction, acoustic and language modeling, efficient algorithms for searching the hypothesis space, and multimodal approaches to speech recognition. The last part of the book is devoted to other speech processing applications that can use the information from automatic speech recognition for speaker identification and tracking, for prosody modeling in emotion-detection systems and in other speech processing applications that are able to operate in real-world environments, like mobile communication services and smart homes