Grassmann Learning for Recognition and Classification

Computational performance associated with high-dimensional data is a common challenge for real-world classification and recognition systems. Subspace learning has received considerable attention as a means of finding an efficient low-dimensional representation that leads to better classification and efficient processing. A Grassmann manifold is a space that promotes smooth surfaces, where points represent subspaces and the relationship between points is defined by a mapping of an orthogonal matrix. Grassmann learning involves embedding high dimensional subspaces and kernelizing the embedding onto a projection space where distance computations can be effectively performed. In this dissertation, Grassmann learning and its benefits towards action classification and face recognition in terms of accuracy and performance are investigated and evaluated. Grassmannian Sparse Representation (GSR) and Grassmannian Spectral Regression (GRASP) are proposed as Grassmann inspired subspace learning algorithms. GSR is a novel subspace learning algorithm that combines the benefits of Grassmann manifolds with sparse representations using least squares loss §¤1-norm minimization for improved classification. GRASP is a novel subspace learning algorithm that leverages the benefits of Grassmann manifolds and Spectral Regression in a framework that supports high discrimination between classes and achieves computational benefits by using manifold modeling and avoiding eigen-decomposition. The effectiveness of GSR and GRASP is demonstrated for computationally intensive classification problems: (a) multi-view action classification using the IXMAS Multi-View dataset, the i3DPost Multi-View dataset, and the WVU Multi-View dataset, (b) 3D action classification using the MSRAction3D dataset and MSRGesture3D dataset, and (c) face recognition using the ATT Face Database, Labeled Faces in the Wild (LFW), and the Extended Yale Face Database B (YALE). Additional contributions include the definition of Motion History Surfaces (MHS) and Motion Depth Surfaces (MDS) as descriptors suitable for activity representations in video sequences and 3D depth sequences. An in-depth analysis of Grassmann metrics is applied on high dimensional data with different levels of noise and data distributions which reveals that standardized Grassmann kernels are favorable over geodesic metrics on a Grassmann manifold. Finally, an extensive performance analysis is made that supports Grassmann subspace learning as an effective approach for classification and recognition

Machine learning for automatic analysis of affective behaviour

The automated analysis of affect has been gaining rapidly increasing attention by researchers over the past two decades, as it constitutes a fundamental step towards achieving next-generation computing technologies and integrating them into everyday life (e.g. via affect-aware, user-adaptive interfaces, medical imaging, health assessment, ambient intelligence etc.). The work presented in this thesis focuses on several fundamental problems manifesting in the course towards the achievement of reliable, accurate and robust affect sensing systems. In more detail, the motivation behind this work lies in recent developments in the field, namely (i) the creation of large, audiovisual databases for affect analysis in the so-called ''Big-Data`` era, along with (ii) the need to deploy systems under demanding, real-world conditions. These developments led to the requirement for the analysis of emotion expressions continuously in time, instead of merely processing static images, thus unveiling the wide range of temporal dynamics related to human behaviour to researchers. The latter entails another deviation from the traditional line of research in the field: instead of focusing on predicting posed, discrete basic emotions (happiness, surprise etc.), it became necessary to focus on spontaneous, naturalistic expressions captured under settings more proximal to real-world conditions, utilising more expressive emotion descriptions than a set of discrete labels. To this end, the main motivation of this thesis is to deal with challenges arising from the adoption of continuous dimensional emotion descriptions under naturalistic scenarios, considered to capture a much wider spectrum of expressive variability than basic emotions, and most importantly model emotional states which are commonly expressed by humans in their everyday life. In the first part of this thesis, we attempt to demystify the quite unexplored problem of predicting continuous emotional dimensions. This work is amongst the first to explore the problem of predicting emotion dimensions via multi-modal fusion, utilising facial expressions, auditory cues and shoulder gestures. A major contribution of the work presented in this thesis lies in proposing the utilisation of various relationships exhibited by emotion dimensions in order to improve the prediction accuracy of machine learning methods - an idea which has been taken on by other researchers in the field since. In order to experimentally evaluate this, we extend methods such as the Long Short-Term Memory Neural Networks (LSTM), the Relevance Vector Machine (RVM) and Canonical Correlation Analysis (CCA) in order to exploit output relationships in learning. As it is shown, this increases the accuracy of machine learning models applied to this task. The annotation of continuous dimensional emotions is a tedious task, highly prone to the influence of various types of noise. Performed real-time by several annotators (usually experts), the annotation process can be heavily biased by factors such as subjective interpretations of the emotional states observed, the inherent ambiguity of labels related to human behaviour, the varying reaction lags exhibited by each annotator as well as other factors such as input device noise and annotation errors. In effect, the annotations manifest a strong spatio-temporal annotator-specific bias. Failing to properly deal with annotation bias and noise leads to an inaccurate ground truth, and therefore to ill-generalisable machine learning models. This deems the proper fusion of multiple annotations, and the inference of a clean, corrected version of the ``ground truth'' as one of the most significant challenges in the area. A highly important contribution of this thesis lies in the introduction of Dynamic Probabilistic Canonical Correlation Analysis (DPCCA), a method aimed at fusing noisy continuous annotations. By adopting a private-shared space model, we isolate the individual characteristics that are annotator-specific and not shared, while most importantly we model the common, underlying annotation which is shared by annotators (i.e., the derived ground truth). By further learning temporal dynamics and incorporating a time-warping process, we are able to derive a clean version of the ground truth given multiple annotations, eliminating temporal discrepancies and other nuisances. The integration of the temporal alignment process within the proposed private-shared space model deems DPCCA suitable for the problem of temporally aligning human behaviour; that is, given temporally unsynchronised sequences (e.g., videos of two persons smiling), the goal is to generate the temporally synchronised sequences (e.g., the smile apex should co-occur in the videos). Temporal alignment is an important problem for many applications where multiple datasets need to be aligned in time. Furthermore, it is particularly suitable for the analysis of facial expressions, where the activation of facial muscles (Action Units) typically follows a set of predefined temporal phases. A highly challenging scenario is when the observations are perturbed by gross, non-Gaussian noise (e.g., occlusions), as is often the case when analysing data acquired under real-world conditions. To account for non-Gaussian noise, a robust variant of Canonical Correlation Analysis (RCCA) for robust fusion and temporal alignment is proposed. The model captures the shared, low-rank subspace of the observations, isolating the gross noise in a sparse noise term. RCCA is amongst the first robust variants of CCA proposed in literature, and as we show in related experiments outperforms other, state-of-the-art methods for related tasks such as the fusion of multiple modalities under gross noise. Beyond private-shared space models, Component Analysis (CA) is an integral component of most computer vision systems, particularly in terms of reducing the usually high-dimensional input spaces in a meaningful manner pertaining to the task-at-hand (e.g., prediction, clustering). A final, significant contribution of this thesis lies in proposing the first unifying framework for probabilistic component analysis. The proposed framework covers most well-known CA methods, such as Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), Locality Preserving Projections (LPP) and Slow Feature Analysis (SFA), providing further theoretical insights into the workings of CA. Moreover, the proposed framework is highly flexible, enabling novel CA methods to be generated by simply manipulating the connectivity of latent variables (i.e. the latent neighbourhood). As shown experimentally, methods derived via the proposed framework outperform other equivalents in several problems related to affect sensing and facial expression analysis, while providing advantages such as reduced complexity and explicit variance modelling.Open Acces

Feature Selection Based on Sequential Orthogonal Search Strategy

This thesis introduces three new feature selection methods based on sequential orthogonal search strategy that addresses three different contexts of feature selection problem being considered. The first method is a supervised feature selection called the maximum relevance–minimum multicollinearity (MRmMC), which can overcome some shortcomings associated with existing methods that apply the same form of feature selection criterion, especially those that are based on mutual information. In the proposed method, relevant features are measured by correlation characteristics based on conditional variance while redundancy elimination is achieved according to multiple correlation assessment using an orthogonal projection scheme. The second method is an unsupervised feature selection based on Locality Preserving Projection (LPP), which is incorporated in a sequential orthogonal search (SOS) strategy. Locality preserving criterion has been proved a successful measure to evaluate feature importance in many feature selection methods but most of which ignore feature correlation and this means these methods ignore redundant features. This problem has motivated the introduction of the second method that evaluates feature importance jointly rather than individually. In the method, the first LPP component which contains the information of local largest structure (LLS) is utilized as a reference variable to guide the search for significant features. This method is referred to as sequential orthogonal search for local largest structure (SOS-LLS). The third method is also an unsupervised feature selection with essentially the same SOS strategy but it is specifically designed to be robust on noisy data. As limited work has been reported concerning feature selection in the presence of attribute noise, the third method is thus attempts to make an effort towards this scarcity by further exploring the second proposed method. The third method is designed to deal with attribute noise in the search for significant features, and kernel pre-images (KPI) based on kernel PCA are used in the third method to replace the role of the first LPP component as the reference variable used in the second method. This feature selection scheme is referred to as sequential orthogonal search for kernel pre-images (SOS-KPI) method. The performance of these three feature selection methods are demonstrated based on some comprehensive analysis on public real datasets of different characteristics and comparative studies with a number of state-of-the-art methods. Results show that each of the proposed methods has the capacity to select more efficient feature subsets than the other feature selection methods in the comparative studies

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Graph enabled cross-domain knowledge transfer

The world has never been more connected, led by the information technology revolution in the past decades that has fundamentally changed the way people interact with each other using social networks. Consequently, enormous human activity data are collected from the business world and machine learning techniques are widely adopted to aid our decision processes. Despite of the success of machine learning in various application scenarios, there are still many questions that need to be well answered, such as optimizing machine learning outcomes when desired knowledge cannot be extracted from the available data. This naturally drives us to ponder if one can leverage some side information to populate the knowledge domain of their interest, such that the problems within that knowledge domain can be better tackled. In this work, such problems are investigated and practical solutions are proposed. To leverage machine learning in any decision-making process, one must convert the given knowledge (for example, natural language, unstructured text) into representation vectors that can be understood and processed by machine learning model in their compatible language and data format. The frequently encountered difficulty is, however, the given knowledge is not rich or reliable enough in the first place. In such cases, one seeks to fuse side information from a separate domain to mitigate the gap between good representation learning and the scarce knowledge in the domain of interest. This approach is named Cross-Domain Knowledge Transfer. It is crucial to study the problem because of the commonality of scarce knowledge in many scenarios, from online healthcare platform analyses to financial market risk quantification, leaving an obstacle in front of us benefiting from automated decision making. From the machine learning perspective, the paradigm of semi-supervised learning takes advantage of large amount of data without ground truth and achieves impressive learning performance improvement. It is adopted in this dissertation for cross-domain knowledge transfer. Furthermore, graph learning techniques are indispensable given that networks commonly exist in real word, such as taxonomy networks and scholarly article citation networks. These networks contain additional useful knowledge and are ought to be incorporated in the learning process, which serve as an important lever in solving the problem of cross-domain knowledge transfer. This dissertation proposes graph-based learning solutions and demonstrates their practical usage via empirical studies on real-world applications. Another line of effort in this work lies in leveraging the rich capacity of neural networks to improve the learning outcomes, as we are in the era of big data. In contrast to many Graph Neural Networks that directly iterate on the graph adjacency to approximate graph convolution filters, this work also proposes an efficient Eigenvalue learning method that directly optimizes the graph convolution in the spectral space. This work articulates the importance of network spectrum and provides detailed analyses on the spectral properties in the proposed EigenLearn method, which well aligns with a series of CNN models that attempt to have meaningful spectral interpretation in designing graph neural networks. The disser-tation also addresses the efficiency, which can be categorized in two folds. First, by adopting approximate solutions it mitigates the complexity concerns for graph related algorithms, which are naturally quadratic in most cases and do not scale to large datasets. Second, it mitigates the storage and computation overhead in deep neural network, such that they can be deployed on many light-weight devices and significantly broaden the applicability. Finally, the dissertation is concluded by future endeavors