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

Spatial Filtering Pipeline Evaluation of Cortically Coupled Computer Vision System for Rapid Serial Visual Presentation

Rapid Serial Visual Presentation (RSVP) is a paradigm that supports the application of cortically coupled computer vision to rapid image search. In RSVP, images are presented to participants in a rapid serial sequence which can evoke Event-related Potentials (ERPs) detectable in their Electroencephalogram (EEG). The contemporary approach to this problem involves supervised spatial filtering techniques which are applied for the purposes of enhancing the discriminative information in the EEG data. In this paper we make two primary contributions to that field: 1) We propose a novel spatial filtering method which we call the Multiple Time Window LDA Beamformer (MTWLB) method; 2) we provide a comprehensive comparison of nine spatial filtering pipelines using three spatial filtering schemes namely, MTWLB, xDAWN, Common Spatial Pattern (CSP) and three linear classification methods Linear Discriminant Analysis (LDA), Bayesian Linear Regression (BLR) and Logistic Regression (LR). Three pipelines without spatial filtering are used as baseline comparison. The Area Under Curve (AUC) is used as an evaluation metric in this paper. The results reveal that MTWLB and xDAWN spatial filtering techniques enhance the classification performance of the pipeline but CSP does not. The results also support the conclusion that LR can be effective for RSVP based BCI if discriminative features are available

An Open Source C++ Implementation of Multi-Threaded Gaussian Mixture Models, k-Means and Expectation Maximisation

Modelling of multivariate densities is a core component in many signal processing, pattern recognition and machine learning applications. The modelling is often done via Gaussian mixture models (GMMs), which use computationally expensive and potentially unstable training algorithms. We provide an overview of a fast and robust implementation of GMMs in the C++ language, employing multi-threaded versions of the Expectation Maximisation (EM) and k-means training algorithms. Multi-threading is achieved through reformulation of the EM and k-means algorithms into a MapReduce-like framework. Furthermore, the implementation uses several techniques to improve numerical stability and modelling accuracy. We demonstrate that the multi-threaded implementation achieves a speedup of an order of magnitude on a recent 16 core machine, and that it can achieve higher modelling accuracy than a previously well-established publically accessible implementation. The multi-threaded implementation is included as a user-friendly class in recent releases of the open source Armadillo C++ linear algebra library. The library is provided under the permissive Apache~2.0 license, allowing unencumbered use in commercial products

How to Solve Classification and Regression Problems on High-Dimensional Data with a Supervised Extension of Slow Feature Analysis

Supervised learning from high-dimensional data, e.g., multimedia data, is a challenging task. We propose an extension of slow feature analysis (SFA) for supervised dimensionality reduction called graph-based SFA (GSFA). The algorithm extracts a label-predictive low-dimensional set of features that can be post-processed by typical supervised algorithms to generate the final label or class estimation. GSFA is trained with a so-called training graph, in which the vertices are the samples and the edges represent similarities of the corresponding labels. A new weighted SFA optimization problem is introduced, generalizing the notion of slowness from sequences of samples to such training graphs. We show that GSFA computes an optimal solution to this problem in the considered function space, and propose several types of training graphs. For classification, the most straightforward graph yields features equivalent to those of (nonlinear) Fisher discriminant analysis. Emphasis is on regression, where four different graphs were evaluated experimentally with a subproblem of face detection on photographs. The method proposed is promising particularly when linear models are insufficient, as well as when feature selection is difficult

Graph Laplacian for Image Anomaly Detection

Reed-Xiaoli detector (RXD) is recognized as the benchmark algorithm for image anomaly detection; however, it presents known limitations, namely the dependence over the image following a multivariate Gaussian model, the estimation and inversion of a high-dimensional covariance matrix, and the inability to effectively include spatial awareness in its evaluation. In this work, a novel graph-based solution to the image anomaly detection problem is proposed; leveraging the graph Fourier transform, we are able to overcome some of RXD's limitations while reducing computational cost at the same time. Tests over both hyperspectral and medical images, using both synthetic and real anomalies, prove the proposed technique is able to obtain significant gains over performance by other algorithms in the state of the art.Comment: Published in Machine Vision and Applications (Springer

Masking Strategies for Image Manifolds

We consider the problem of selecting an optimal mask for an image manifold, i.e., choosing a subset of the pixels of the image that preserves the manifold's geometric structure present in the original data. Such masking implements a form of compressive sensing through emerging imaging sensor platforms for which the power expense grows with the number of pixels acquired. Our goal is for the manifold learned from masked images to resemble its full image counterpart as closely as possible. More precisely, we show that one can indeed accurately learn an image manifold without having to consider a large majority of the image pixels. In doing so, we consider two masking methods that preserve the local and global geometric structure of the manifold, respectively. In each case, the process of finding the optimal masking pattern can be cast as a binary integer program, which is computationally expensive but can be approximated by a fast greedy algorithm. Numerical experiments show that the relevant manifold structure is preserved through the data-dependent masking process, even for modest mask sizes