A Metric-learning based framework for Support Vector Machines and Multiple Kernel Learning

Most metric learning algorithms, as well as Fisher's Discriminant Analysis (FDA), optimize some cost function of different measures of within-and between-class distances. On the other hand, Support Vector Machines(SVMs) and several Multiple Kernel Learning (MKL) algorithms are based on the SVM large margin theory. Recently, SVMs have been analyzed from SVM and metric learning, and to develop new algorithms that build on the strengths of each. Inspired by the metric learning interpretation of SVM, we develop here a new metric-learning based SVM framework in which we incorporate metric learning concepts within SVM. We extend the optimization problem of SVM to include some measure of the within-class distance and along the way we develop a new within-class distance measure which is appropriate for SVM. In addition, we adopt the same approach for MKL and show that it can be also formulated as a Mahalanobis metric learning problem. Our end result is a number of SVM/MKL algorithms that incorporate metric learning concepts. We experiment with them on a set of benchmark datasets and observe important predictive performance improvements

Reproducing Kernel Hilbert Space, Mercer's Theorem, Eigenfunctions, Nystr\"om Method, and Use of Kernels in Machine Learning: Tutorial and Survey

This is a tutorial and survey paper on kernels, kernel methods, and related fields. We start with reviewing the history of kernels in functional analysis and machine learning. Then, Mercer kernel, Hilbert and Banach spaces, Reproducing Kernel Hilbert Space (RKHS), Mercer's theorem and its proof, frequently used kernels, kernel construction from distance metric, important classes of kernels (including bounded, integrally positive definite, universal, stationary, and characteristic kernels), kernel centering and normalization, and eigenfunctions are explained in detail. Then, we introduce types of use of kernels in machine learning including kernel methods (such as kernel support vector machines), kernel learning by semi-definite programming, Hilbert-Schmidt independence criterion, maximum mean discrepancy, kernel mean embedding, and kernel dimensionality reduction. We also cover rank and factorization of kernel matrix as well as the approximation of eigenfunctions and kernels using the Nystr{\"o}m method. This paper can be useful for various fields of science including machine learning, dimensionality reduction, functional analysis in mathematics, and mathematical physics in quantum mechanics.Comment: To appear as a part of an upcoming textbook on dimensionality reduction and manifold learnin

A Kernel Classification Framework for Metric Learning

Learning a distance metric from the given training samples plays a crucial role in many machine learning tasks, and various models and optimization algorithms have been proposed in the past decade. In this paper, we generalize several state-of-the-art metric learning methods, such as large margin nearest neighbor (LMNN) and information theoretic metric learning (ITML), into a kernel classification framework. First, doublets and triplets are constructed from the training samples, and a family of degree-2 polynomial kernel functions are proposed for pairs of doublets or triplets. Then, a kernel classification framework is established, which can not only generalize many popular metric learning methods such as LMNN and ITML, but also suggest new metric learning methods, which can be efficiently implemented, interestingly, by using the standard support vector machine (SVM) solvers. Two novel metric learning methods, namely doublet-SVM and triplet-SVM, are then developed under the proposed framework. Experimental results show that doublet-SVM and triplet-SVM achieve competitive classification accuracies with state-of-the-art metric learning methods such as ITML and LMNN but with significantly less training time.Comment: 11 pages, 7 figure

Parametic Classification of Handvein Patterns Based on Texture Features

In this paper, we have developed Biometric recognition system adopting hand based modality Handvein, which has the unique pattern for each individual and it is impossible to counterfeit and fabricate as it is an internal feature. We have opted in choosing feature extraction algorithms such as LBP-visual descriptor ,LPQ-blur insensitive texture operator, Log-Gabor-Texture descriptor. We have chosen well known classifiers such as KNN and SVM for classification. We have experimented and tabulated results of single algorithm recognition rate for Handvein under different distance measures and kernel options. The feature level fusion is carried out which increased the performance level.Comment: 8 pages, International Conference on Electrical, Electronics, Materials and Applied Science (ICEEMAS). AIP: Proceedings International Conference on Electrical, Electronics, Materials and Applied Science (ICEEMAS),22nd and 23rd December 201

Classifying Network Data with Deep Kernel Machines

Inspired by a growing interest in analyzing network data, we study the problem of node classification on graphs, focusing on approaches based on kernel machines. Conventionally, kernel machines are linear classifiers in the implicit feature space. We argue that linear classification in the feature space of kernels commonly used for graphs is often not enough to produce good results. When this is the case, one naturally considers nonlinear classifiers in the feature space. We show that repeating this process produces something we call "deep kernel machines." We provide some examples where deep kernel machines can make a big difference in classification performance, and point out some connections to various recent literature on deep architectures in artificial intelligence and machine learning

Probabilistic classifiers with low rank indefinite kernels

Indefinite similarity measures can be frequently found in bio-informatics by means of alignment scores, but are also common in other fields like shape measures in image retrieval. Lacking an underlying vector space, the data are given as pairwise similarities only. The few algorithms available for such data do not scale to larger datasets. Focusing on probabilistic batch classifiers, the Indefinite Kernel Fisher Discriminant (iKFD) and the Probabilistic Classification Vector Machine (PCVM) are both effective algorithms for this type of data but, with cubic complexity. Here we propose an extension of iKFD and PCVM such that linear runtime and memory complexity is achieved for low rank indefinite kernels. Employing the Nystr\"om approximation for indefinite kernels, we also propose a new almost parameter free approach to identify the landmarks, restricted to a supervised learning problem. Evaluations at several larger similarity data from various domains show that the proposed methods provides similar generalization capabilities while being easier to parametrize and substantially faster for large scale data

Blindfold learning of an accurate neural metric

The brain has no direct access to physical stimuli, but only to the spiking activity evoked in sensory organs. It is unclear how the brain can structure its representation of the world based on differences between those noisy, correlated responses alone. Here we show how to build a distance map of responses from the structure of the population activity of retinal ganglion cells, allowing for the accurate discrimination of distinct visual stimuli from the retinal response. We introduce the Temporal Restricted Boltzmann Machine to learn the spatiotemporal structure of the population activity, and use this model to define a distance between spike trains. We show that this metric outperforms existing neural distances at discriminating pairs of stimuli that are barely distinguishable. The proposed method provides a generic and biologically plausible way to learn to associate similar stimuli based on their spiking responses, without any other knowledge of these stimuli

Learning Local Invariant Mahalanobis Distances

For many tasks and data types, there are natural transformations to which the data should be invariant or insensitive. For instance, in visual recognition, natural images should be insensitive to rotation and translation. This requirement and its implications have been important in many machine learning applications, and tolerance for image transformations was primarily achieved by using robust feature vectors. In this paper we propose a novel and computationally efficient way to learn a local Mahalanobis metric per datum, and show how we can learn a local invariant metric to any transformation in order to improve performance

Deep Transductive Semi-supervised Maximum Margin Clustering

Semi-supervised clustering is an very important topic in machine learning and computer vision. The key challenge of this problem is how to learn a metric, such that the instances sharing the same label are more likely close to each other on the embedded space. However, little attention has been paid to learn better representations when the data lie on non-linear manifold. Fortunately, deep learning has led to great success on feature learning recently. Inspired by the advances of deep learning, we propose a deep transductive semi-supervised maximum margin clustering approach. More specifically, given pairwise constraints, we exploit both labeled and unlabeled data to learn a non-linear mapping under maximum margin framework for clustering analysis. Thus, our model unifies transductive learning, feature learning and maximum margin techniques in the semi-supervised clustering framework. We pretrain the deep network structure with restricted Boltzmann machines (RBMs) layer by layer greedily, and optimize our objective function with gradient descent. By checking the most violated constraints, our approach updates the model parameters through error backpropagation, in which deep features are learned automatically. The experimental results shows that our model is significantly better than the state of the art on semi-supervised clustering.Comment: 1

Multiscale CNN based Deep Metric Learning for Bioacoustic Classification: Overcoming Training Data Scarcity Using Dynamic Triplet Loss

This paper proposes multiscale convolutional neural network (CNN)-based deep metric learning for bioacoustic classification, under low training data conditions. The proposed CNN is characterized by the utilization of four different filter sizes at each level to analyze input feature maps. This multiscale nature helps in describing different bioacoustic events effectively: smaller filters help in learning the finer details of bioacoustic events, whereas, larger filters help in analyzing a larger context leading to global details. A dynamic triplet loss is employed in the proposed CNN architecture to learn a transformation from the input space to the embedding space, where classification is performed. The triplet loss helps in learning this transformation by analyzing three examples, referred to as triplets, at a time where intra-class distance is minimized while maximizing the inter-class separation by a dynamically increasing margin. The number of possible triplets increases cubically with the dataset size, making triplet loss more suitable than the softmax cross-entropy loss in low training data conditions. Experiments on three different publicly available datasets show that the proposed framework performs better than existing bioacoustic classification frameworks. Experimental results also confirm the superiority of the triplet loss over the cross-entropy loss in low training data conditionsComment: Under Review at JASA. Primitive version of paper. We are still working on getting better performances out of the comparative method