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

Ensemble learning method for hidden markov models.

For complex classification systems, data are gathered from various sources and potentially have different representations. Thus, data may have large intra-class variations. In fact, modeling each data class with a single model might lead to poor generalization. The classification error can be more severe for temporal data where each sample is represented by a sequence of observations. Thus, there is a need for building a classification system that takes into account the variations within each class in the data. This dissertation introduces an ensemble learning method for temporal data that uses a mixture of Hidden Markov Model (HMM) classifiers. We hypothesize that the data are generated by K models, each of which reacts a particular trend in the data. Model identification could be achieved through clustering in the feature space or in the parameters space. However, this approach is inappropriate in the context of sequential data. The proposed approach is based on clustering in the log-likelihood space, and has two main steps. First, one HMM is fit to each of the N individual sequences. For each fitted model, we evaluate the log-likelihood of each sequence. This will result in an N-by-N log-likelihood distance matrix that will be partitioned into K groups using a relational clustering algorithm. In the second step, we learn the parameters of one HMM per group. We propose using and optimizing various training approaches for the different K groups depending on their size and homogeneity. In particular, we investigate the maximum likelihood (ML), the minimum classification error (MCE) based discriminative, and the Variational Bayesian (VB) training approaches. Finally, to test a new sequence, its likelihood is computed in all the models and a final confidence value is assigned by combining the multiple models outputs using a decision level fusion method such as an artificial neural network or a hierarchical mixture of experts. Our approach was evaluated on two real-world applications: (1) identification of Cardio-Pulmonary Resuscitation (CPR) scenes in video simulating medical crises; and (2) landmine detection using Ground Penetrating Radar (GPR). Results on both applications show that the proposed method can identify meaningful and coherent HMM mixture components that describe different properties of the data. Each HMM mixture component models a group of data that share common attributes. The results indicate that the proposed method outperforms the baseline HMM that uses one model for each class in the data

Structural and statistical properties of the collocation technique for error characterization

The validation of geophysical data sets (e.g. derived from models, exploration techniques or remote sensing) presents a formidable challenge as all products are inherently different and subject to errors. The collocation technique permits the retrieval of the error variances of different data sources without the need to specify one data set as a reference. In addition calibration constants can be determined to account for biases and different dynamic ranges. The method is frequently applied to the study and comparison of remote sensing, in-situ and modelled data, particularly in hydrology and oceanography. Previous studies have almost exclusively focussed on the validation of three data sources; in this paper it is shown how the technique generalizes to an arbitrary number of data sets. It turns out that only parts of the covariance structure can be resolved by the collocation technique, thus emphasizing the necessity of expert knowledge for the correct validation of geophysical products. Furthermore the bias and error variance of the estimators are derived with particular emphasis on the assumptions necessary for establishing those characteristics. Important properties of the method, such as the structural deficiencies, dependence of the accuracy on the number of measurements and the impact of violated assumptions, are illustrated by application to simulated data

Multiple instance fuzzy inference.

A novel fuzzy learning framework that employs fuzzy inference to solve the problem of multiple instance learning (MIL) is presented. The framework introduces a new class of fuzzy inference systems called Multiple Instance Fuzzy Inference Systems (MI-FIS). Fuzzy inference is a powerful modeling framework that can handle computing with knowledge uncertainty and measurement imprecision effectively. Fuzzy Inference performs a non-linear mapping from an input space to an output space by deriving conclusions from a set of fuzzy if-then rules and known facts. Rules can be identified from expert knowledge, or learned from data. In multiple instance problems, the training data is ambiguously labeled. Instances are grouped into bags, labels of bags are known but not those of individual instances. MIL deals with learning a classifier at the bag level. Over the years, many solutions to this problem have been proposed. However, no MIL formulation employing fuzzy inference exists in the literature. In this dissertation, we introduce multiple instance fuzzy logic that enables fuzzy reasoning with bags of instances. Accordingly, different multiple instance fuzzy inference styles are proposed. The Multiple Instance Mamdani style fuzzy inference (MI-Mamdani) extends the standard Mamdani style inference to compute with multiple instances. The Multiple Instance Sugeno style fuzzy inference (MI-Sugeno) is an extension of the standard Sugeno style inference to handle reasoning with multiple instances. In addition to the MI-FIS inference styles, one of the main contributions of this work is an adaptive neuro-fuzzy architecture designed to handle bags of instances as input and capable of learning from ambiguously labeled data. The proposed architecture, called Multiple Instance-ANFIS (MI-ANFIS), extends the standard Adaptive Neuro Fuzzy Inference System (ANFIS). We also propose different methods to identify and learn fuzzy if-then rules in the context of MIL. In particular, a novel learning algorithm for MI-ANFIS is derived. The learning is achieved by using the backpropagation algorithm to identify the premise parameters and consequent parameters of the network. The proposed framework is tested and validated using synthetic and benchmark datasets suitable for MIL problems. Additionally, we apply the proposed Multiple Instance Inference to the problem of region-based image categorization as well as to fuse the output of multiple discrimination algorithms for the purpose of landmine detection using Ground Penetrating Radar

Microwave NDT&E using open-ended waveguide probe for multilayered structures

Ph. D. Thesis.Microwave NDT&E has been proved to be suitable for inspecting of dielectric structures due to low attenuation in dielectric materials and free-space. However, the microwave responses from multilayered structures are complex as an interrogation of scattering electromagnetic waves among the layers and defects. In many practical applications, electromagnetic analysis based on analytic- and forward structural models cannot be generalised since the defect shape and properties are usually unknown and hidden beneath the surface layer. This research proposes the design and implementation of microwave NDT&E system for inspection of multilayered structures. Standard microwave open-ended rectangular waveguides in X, Ku and K bands (frequency range between 8-26.5 GHz) and vector network analyser (VNA) generating sweep frequency of wideband monochromatic waves have been used to obtain reflection coefficient responses over three types of challenging multilayered samples: (1) corrosion progression under coating, (2) woven carbon fibre reinforced polymer (CFRP) with impact damages, and (3) thermal coated glass fibre reinforced polymer (GFRP) pipe with inner flat-bottom holes. The obtained data are analysed by the selected feature extraction method extracting informative features and verify with the sample parameters (defect parameters). In addition, visualisation methods are utilised to improve the presentation of the defects and material structures resulting in a better interpretation for quantitative evaluation. The contributions of this project are summarised as follows: (1) implementation of microwave NDT&E scanning system using open-ended waveguide with the highest resolution of 0.1mm x 0.1 mm, based on the NDT applications for the three aforementioned samples; (2) corrosion stages of steel corrosion under coating have been successfully characterised by the principal component analysis (PCA) method; (3) A frequency selective based PCA feature has been used to visualise the impact damage at different impact energies with elimination of woven texture influences; (4) PCA and SAR (synthetic aperture radar) tomography together with time-offlight extraction, have been used for detection and quantitative evaluation of flat-bottom hole defects (i.e., location, size and depth). The results conclude that the proposed microwave NDT&E system can be used for detection and evaluation of multilayered structures, which its major contributions are follows. (1) The early stages (0-12month) of steel corrosion undercoating has been successfully characterised by mean of spectral responses from microwave opened rectangular waveguide probe and PCA. (2) The detection of low energy impact damages on CFRP as low as 4 Joules has been archived with microwave opened rectangular waveguide probe raster scan together with SAR imaging and PCA for feature extraction methods. (3) The inner flat-bottom holes beneath the thermal coated GFRP up to 11.5 mm depth has been successfully quantitative evaluated by open-ended waveguide raster scan using PCA and 3-D reconstruction based on SAR tomography techniques. The evaluation includes location, sizing and depth. Nevertheless, the major downside of feature quantities extracted from statistically based methods such as PCA, is it intensely relies on the correlation of the input dataset, and thus hardly link them with the physical parameters of the test sample, in particular, the complex composite architectures. Therefore, there are still challenges of feature extraction and quantitative evaluation to accurately determine the essential parameters from the samples. This can be achieved by a future investigation of multiple features fusion and complementary features.Ministry of Science and Technology of Royal Thai Government and Office of Educational Affairs, the Royal Thai Embass

Problems in Signal Processing and Inference on Graphs

Modern datasets are often massive due to the sharp decrease in the cost of collecting and storing data. Many are endowed with relational structure modeled by a graph, an object comprising a set of points and a set of pairwise connections between them. A ``signal on a graph'' has elements related to each other through a graph---it could model, for example, measurements from a sensor network. In this dissertation we study several problems in signal processing and inference on graphs. We begin by introducing an analogue to Heisenberg's time-frequency uncertainty principle for signals on graphs. We use spectral graph theory and the standard extension of Fourier analysis to graphs. Our spectral graph uncertainty principle makes precise the notion that a highly localized signal on a graph must have a broad spectrum, and vice versa. Next, we consider the problem of detecting a random walk on a graph from noisy observations. We characterize the performance of the optimal detector through the (type-II) error exponent, borrowing techniques from statistical physics to develop a lower bound exhibiting a phase transition. Strong performance is only guaranteed when the signal to noise ratio exceeds twice the random walk's entropy rate. Monte Carlo simulations show that the lower bound is quite close to the true exponent. Next, we introduce a technique for inferring the source of an epidemic from observations at a few nodes. We develop a Monte Carlo technique to simulate the infection process, and use statistics computed from these simulations to approximate the likelihood, which we then maximize to locate the source. We further introduce a logistic autoregressive model (ALARM), a simple model for binary processes on graphs that can still capture a variety of behavior. We demonstrate its simplicity by showing how to easily infer the underlying graph structure from measurements; a technique versatile enough that it can work under model mismatch. Finally, we introduce the exact formula for the error of the randomized Kaczmarz algorithm, a linear system solver for sparse systems, which often arise in graph theory. This is important because, as we show, existing performance bounds are quite loose.Engineering and Applied Sciences - Engineering Science