Training Support Vector Machines Using Frank-Wolfe Optimization Methods

Training a Support Vector Machine (SVM) requires the solution of a quadratic programming problem (QP) whose computational complexity becomes prohibitively expensive for large scale datasets. Traditional optimization methods cannot be directly applied in these cases, mainly due to memory restrictions. By adopting a slightly different objective function and under mild conditions on the kernel used within the model, efficient algorithms to train SVMs have been devised under the name of Core Vector Machines (CVMs). This framework exploits the equivalence of the resulting learning problem with the task of building a Minimal Enclosing Ball (MEB) problem in a feature space, where data is implicitly embedded by a kernel function. In this paper, we improve on the CVM approach by proposing two novel methods to build SVMs based on the Frank-Wolfe algorithm, recently revisited as a fast method to approximate the solution of a MEB problem. In contrast to CVMs, our algorithms do not require to compute the solutions of a sequence of increasingly complex QPs and are defined by using only analytic optimization steps. Experiments on a large collection of datasets show that our methods scale better than CVMs in most cases, sometimes at the price of a slightly lower accuracy. As CVMs, the proposed methods can be easily extended to machine learning problems other than binary classification. However, effective classifiers are also obtained using kernels which do not satisfy the condition required by CVMs and can thus be used for a wider set of problems

Multi-View Region Adaptive Multi-temporal DMM and RGB Action Recognition

Human action recognition remains an important yet challenging task. This work proposes a novel action recognition system. It uses a novel Multiple View Region Adaptive Multi-resolution in time Depth Motion Map (MV-RAMDMM) formulation combined with appearance information. Multiple stream 3D Convolutional Neural Networks (CNNs) are trained on the different views and time resolutions of the region adaptive Depth Motion Maps. Multiple views are synthesised to enhance the view invariance. The region adaptive weights, based on localised motion, accentuate and differentiate parts of actions possessing faster motion. Dedicated 3D CNN streams for multi-time resolution appearance information (RGB) are also included. These help to identify and differentiate between small object interactions. A pre-trained 3D-CNN is used here with fine-tuning for each stream along with multiple class Support Vector Machines (SVM)s. Average score fusion is used on the output. The developed approach is capable of recognising both human action and human-object interaction. Three public domain datasets including: MSR 3D Action,Northwestern UCLA multi-view actions and MSR 3D daily activity are used to evaluate the proposed solution. The experimental results demonstrate the robustness of this approach compared with state-of-the-art algorithms.Comment: 14 pages, 6 figures, 13 tables. Submitte