Kernel Multivariate Analysis Framework for Supervised Subspace Learning: A Tutorial on Linear and Kernel Multivariate Methods

Feature extraction and dimensionality reduction are important tasks in many fields of science dealing with signal processing and analysis. The relevance of these techniques is increasing as current sensory devices are developed with ever higher resolution, and problems involving multimodal data sources become more common. A plethora of feature extraction methods are available in the literature collectively grouped under the field of Multivariate Analysis (MVA). This paper provides a uniform treatment of several methods: Principal Component Analysis (PCA), Partial Least Squares (PLS), Canonical Correlation Analysis (CCA) and Orthonormalized PLS (OPLS), as well as their non-linear extensions derived by means of the theory of reproducing kernel Hilbert spaces. We also review their connections to other methods for classification and statistical dependence estimation, and introduce some recent developments to deal with the extreme cases of large-scale and low-sized problems. To illustrate the wide applicability of these methods in both classification and regression problems, we analyze their performance in a benchmark of publicly available data sets, and pay special attention to specific real applications involving audio processing for music genre prediction and hyperspectral satellite images for Earth and climate monitoring

Loughborough University Spontaneous Expression Database and baseline results for automatic emotion recognition

The study of facial expressions in humans dates back to the 19th century and the study of the emotions that these facial expressions portray dates back even further. It is a natural part of non-verbal communication for humans to pass across messages using facial expressions either consciously or subconsciously, it is also routine for other humans to recognize these facial expressions and understand or deduce the underlying emotions which they represent. Over two decades ago and following technological advances, particularly in the area of image processing, research began into the use of machines for the recognition of facial expressions from images with the aim of inferring the corresponding emotion. Given a previously unknown test sample, the supervised learning problem is to accurately determine the facial expression class to which the test sample belongs using the knowledge of the known class memberships of each image from a set of training images. The solution to this problem building an effective classifier to recognize the facial expression is hinged on the availability of representative training data. To date, much of the research in the area of Facial Expression Recognition (FER) is still based on posed (acted) facial expression databases, which are often exaggerated and therefore not representative of real life affective displays, as such there is a need for more publically accessible spontaneous databases that are well labelled. This thesis therefore reports on the development of the newly collected Loughborough University Spontaneous Expression Database (LUSED); designed to bolster the development of new recognition systems and to provide a benchmark for researchers to compare results with more natural expression classes than most existing databases. To collect the database, an experiment was set up where volunteers were discretely videotaped while they watched a selection of emotion inducing video clips. The utility of the new LUSED dataset is validated using both traditional and more recent pattern recognition techniques; (1) baseline results are presented using the combination of Principal Component Analysis (PCA), Fisher Linear Discriminant Analysis (FLDA) and their kernel variants Kernel Principal Component Analysis (KPCA), Kernel Fisher Discriminant Analysis (KFDA) with a Nearest Neighbour-based classifier. These results are compared to the performance of an existing natural expression database Natural Visible and Infrared Expression (NVIE) database. A scheme for the recognition of encrypted facial expression images is also presented. (2) Benchmark results are presented by combining PCA, FLDA, KPCA and KFDA with a Sparse Representation-based Classifier (SRC). A maximum accuracy of 68% was obtained recognizing five expression classes, which is comparatively better than the known maximum for a natural database; around 70% (from recognizing only three classes) obtained from NVIE

Using Stacked Sparse Auto-Encoder and Superpixel CRF for Long-Term Visual Scene Understanding of UGVs

Multiple images have been widely used for scene understanding and navigation of unmanned ground vehicles in long term operations. However, as the amount of visual data in multiple images is huge, the cumulative error in many cases becomes untenable. This paper proposes a novel method that can extract features from a large dataset of multiple images efficiently. Then the membership K-means clustering is used for high dimensional features, and the large dataset is divided into N subdatasets to train N conditional random field (CRF) models based on superpixel. A Softmax subdataset selector is used to decide which one of the N CRF models is chosen as the prediction model for labeling images. Furthermore, some experiments are conducted to evaluate the feasibility and performance of the proposed approach

Robust PCA as Bilinear Decomposition with Outlier-Sparsity Regularization

Principal component analysis (PCA) is widely used for dimensionality reduction, with well-documented merits in various applications involving high-dimensional data, including computer vision, preference measurement, and bioinformatics. In this context, the fresh look advocated here permeates benefits from variable selection and compressive sampling, to robustify PCA against outliers. A least-trimmed squares estimator of a low-rank bilinear factor analysis model is shown closely related to that obtained from an $\ell_0$-(pseudo)norm-regularized criterion encouraging sparsity in a matrix explicitly modeling the outliers. This connection suggests robust PCA schemes based on convex relaxation, which lead naturally to a family of robust estimators encompassing Huber's optimal M-class as a special case. Outliers are identified by tuning a regularization parameter, which amounts to controlling sparsity of the outlier matrix along the whole robustification path of (group) least-absolute shrinkage and selection operator (Lasso) solutions. Beyond its neat ties to robust statistics, the developed outlier-aware PCA framework is versatile to accommodate novel and scalable algorithms to: i) track the low-rank signal subspace robustly, as new data are acquired in real time; and ii) determine principal components robustly in (possibly) infinite-dimensional feature spaces. Synthetic and real data tests corroborate the effectiveness of the proposed robust PCA schemes, when used to identify aberrant responses in personality assessment surveys, as well as unveil communities in social networks, and intruders from video surveillance data.Comment: 30 pages, submitted to IEEE Transactions on Signal Processin