A Survey on Potential of the Support Vector Machines in Solving Classification and Regression Problems

Kernel methods and support vector machines have become the most popular learning from examples paradigms. Several areas of application research make use of SVM approaches as for instance hand written character recognition, text categorization, face detection, pharmaceutical data analysis and drug design. Also, adapted SVM’s have been proposed for time series forecasting and in computational neuroscience as a tool for detection of symmetry when eye movement is connected with attention and visual perception. The aim of the paper is to investigate the potential of SVM’s in solving classification and regression tasks as well as to analyze the computational complexity corresponding to different methodologies aiming to solve a series of afferent arising sub-problems.Support Vector Machines, Kernel-Based Methods, Supervised Learning, Regression, Classification

Kernel methods for time series data

Kernel methods are powerful learning techniques with excellent generalization capability. This thesis develops three advanced approaches within the generic SVM framework in the application domain of time series data. The first contribution presents a new methodology for incorporating privileged information about the future evolution of time series, which is only available in the training phase. The task is prediction of the ordered categories of future time series movements. This is implemented by directly extending support vector ordinal regression with implicit constraints to leaning using privileged information paradigm. The second contribution demonstrates a novel methodology of constructing efficient kernels for time series classification problems. These kernels are constructed by representing each time series through a linear readout model from a high dimensional state space model with a fixed deterministically constructed dynamic part. Learning is then performed in the linear readout model space. Finally, in the same context, we introduce yet another novel time series kernel by co-learning the dynamic part and a global metric in the linear readout model space, encouraging time series from the same class to be represented by close model representations, while model representations of time series from different classes to be well-separated

High-Dimensional Feature Selection by Feature-Wise Kernelized Lasso

The goal of supervised feature selection is to find a subset of input features that are responsible for predicting output values. The least absolute shrinkage and selection operator (Lasso) allows computationally efficient feature selection based on linear dependency between input features and output values. In this paper, we consider a feature-wise kernelized Lasso for capturing non-linear input-output dependency. We first show that, with particular choices of kernel functions, non-redundant features with strong statistical dependence on output values can be found in terms of kernel-based independence measures. We then show that the globally optimal solution can be efficiently computed; this makes the approach scalable to high-dimensional problems. The effectiveness of the proposed method is demonstrated through feature selection experiments with thousands of features.Comment: 18 page

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