Generalized multiple kernel learning with data-dependent priors

One-Class Classification Using ℓp-Norm Multiple Kernel Fisher Null Approach

We address the one-class classification (OCC) problem and advocate a one-class MKL (multiple kernel learning) approach for this purpose. To this aim, based on the Fisher null-space OCC principle, we present a multiple kernel learning algorithm where an $\ell _{p}$ -norm regularisation ( $p \geq 1$ ) is considered for kernel weight learning. We cast the proposed one-class MKL problem as a min-max saddle point Lagrangian optimisation task and propose an efficient approach to optimise it. An extension of the proposed approach is also considered where several related one-class MKL tasks are learned concurrently by constraining them to share common weights for kernels. An extensive evaluation of the proposed MKL approach on a range of data sets from different application domains confirms its merits against the baseline and several other algorithms.

Scaling Up Kernel SVM on Limited Resources: A Low-Rank Linearization Approach

Kernel support vector machines (SVMs) deliver state-of-the-art results in many real-world nonlinear classification problems, but the computational cost can be quite demanding in order to maintain a large number of support vectors. Linear SVM, on the other hand, is highly scalable to large data but only suited for linearly separable problems. In this paper, we propose a novel approach called low-rank linearized SVM to scale up kernel SVM on limited resources. Our approach transforms a nonlinear SVM to a linear one via an approximate empirical kernel map computed from efficient kernel low-rank decompositions. We theoretically analyze the gap between the solutions of the approximate and optimal rank- k kernel map, which in turn provides guidance on the sampling scheme of the Nyström approximation. Furthermore, we extend it to a semisupervised metric learning scenario in which partially labeled samples can be exploited to further improve the quality of the low-rank embedding. Our approach inherits rich representability of kernel SVM and high efficiency of linear SVM. Experimental results demonstrate that our approach is more robust and achieves a better tradeoff between model representability and scalability against state-of-the-art algorithms for large-scale SVMs.

Probabilistic Dimensionality Reduction via Structure Learning

We propose an alternative probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a set of embedding points in a low-dimensional space by retaining the inherent structure from high-dimensional data. The objective function of this new model can be equivalently interpreted as two coupled learning problems, i.e., structure learning and the learning of projection matrix. Inspired by this interesting interpretation, we propose another model, which finds a set of embedding points that can directly form an explicit graph structure. We proved that the model by learning explicit graphs generalizes the reversed graph embedding method, but leads to a natural interpretation from Bayesian perspective. This can greatly facilitate data visualization and scientific discovery in downstream analysis. Extensive experiments are performed that demonstrate that the proposed framework is able to retain the inherent structure of datasets and achieve competitive quantitative results in terms of various performance evaluation criteria.

Multiview Privileged Support Vector Machines

Multiview learning (MVL), by exploiting the complementary information among multiple feature sets, can improve the performance of many existing learning tasks. Support vector machine (SVM)-based models have been frequently used for MVL. A typical SVM-based MVL model is SVM-2K, which extends SVM for MVL by using the distance minimization version of kernel canonical correlation analysis. However, SVM-2K cannot fully unleash the power of the complementary information among different feature views. Recently, a framework of learning using privileged information (LUPI) has been proposed to model data with complementary information. Motivated by LUPI, we propose a new multiview privileged SVM model, multi-view privileged SVM model (PSVM-2V), for MVL. This brings a new perspective that extends LUPI to MVL. The optimization of PSVM-2V can be solved by the classical quadratic programming solver. We theoretically analyze the performance of PSVM-2V from the viewpoints of the consensus principle, the generalization error bound, and the SVM-2K learning model. Experimental results on 95 binary data sets demonstrate the effectiveness of the proposed method.

Feature Combination via Clustering

In image classification, feature combination is often used to combine the merits of multiple complementary features and improve the classification accuracy compared with one single feature. Existing feature combination algorithms, e.g., multiple kernel learning, usually determine the weights of features based on the optimization with respect to some classifier-dependent objective function. These algorithms are often computationally expensive, and in some cases are found to perform no better than simple baselines. In this paper, we solve the feature combination problem from a totally different perspective. Our algorithm is based on the simple idea of combining only base kernels suitable to be combined. Since the very aim of feature combination is to obtain the highest possible classification accuracy, we measure the combination suitableness of two base kernels by the maximum possible cross-validation accuracy of their combined kernel. By regarding the pairwise suitableness as the kernel adjacency, we obtain a weighted graph of all base kernels and find that the base kernels suitable to be combined correspond to a cluster in the graph. We then use the dominant sets algorithm to find the cluster and determine the weights of base kernels automatically. In this way, we transform the kernel combination problem into a clustering one. Our algorithm can be implemented in parallel easily and the running time can be adjusted based on available memory to a large extent. In experiments on several data sets, our algorithm generates comparable classification accuracy with the state of the art.