Fast SVM training using approximate extreme points

Applications of non-linear kernel Support Vector Machines (SVMs) to large datasets is seriously hampered by its excessive training time. We propose a modification, called the approximate extreme points support vector machine (AESVM), that is aimed at overcoming this burden. Our approach relies on conducting the SVM optimization over a carefully selected subset, called the representative set, of the training dataset. We present analytical results that indicate the similarity of AESVM and SVM solutions. A linear time algorithm based on convex hulls and extreme points is used to compute the representative set in kernel space. Extensive computational experiments on nine datasets compared AESVM to LIBSVM \citep{LIBSVM}, CVM \citep{Tsang05}, BVM \citep{Tsang07}, LASVM \citep{Bordes05}, $\text{SVM}^{\text{perf}}$ \citep{Joachims09}, and the random features method \citep{rahimi07}. Our AESVM implementation was found to train much faster than the other methods, while its classification accuracy was similar to that of LIBSVM in all cases. In particular, for a seizure detection dataset, AESVM training was almost $10^3$ times faster than LIBSVM and LASVM and more than forty times faster than CVM and BVM. Additionally, AESVM also gave competitively fast classification times.Comment: The manuscript in revised form has been submitted to J. Machine Learning Researc

Similarity Learning for High-Dimensional Sparse Data

A good measure of similarity between data points is crucial to many tasks in machine learning. Similarity and metric learning methods learn such measures automatically from data, but they do not scale well respect to the dimensionality of the data. In this paper, we propose a method that can learn efficiently similarity measure from high-dimensional sparse data. The core idea is to parameterize the similarity measure as a convex combination of rank-one matrices with specific sparsity structures. The parameters are then optimized with an approximate Frank-Wolfe procedure to maximally satisfy relative similarity constraints on the training data. Our algorithm greedily incorporates one pair of features at a time into the similarity measure, providing an efficient way to control the number of active features and thus reduce overfitting. It enjoys very appealing convergence guarantees and its time and memory complexity depends on the sparsity of the data instead of the dimension of the feature space. Our experiments on real-world high-dimensional datasets demonstrate its potential for classification, dimensionality reduction and data exploration.Comment: 14 pages. Proceedings of the 18th International Conference on Artificial Intelligence and Statistics (AISTATS 2015). Matlab code: https://github.com/bellet/HDS