Multiclass latent locally linear support vector machines

Kernelized Support Vector Machines (SVM) have gained the status of off-the-shelf classifiers, able to deliver state of the art performance on almost any problem. Still, their practical use is constrained by their computational and memory complexity, which grows super-linearly with the number of training samples. In order to retain the low training and testing complexity of linear classifiers and the exibility of non linear ones, a growing, promising alternative is represented by methods that learn non-linear classifiers through local combinations of linear ones. In this paper we propose a new multi class local classifier, based on a latent SVM formulation. The proposed classifier makes use of a set of linear models that are linearly combined using sample and class specific weights. Thanks to the latent formulation, the combination coefficients are modeled as latent variables. We allow soft combinations and we provide a closed-form solution for their estimation, resulting in an efficient prediction rule. This novel formulation allows to learn in a principled way the sample specific weights and the linear classifiers, in a unique optimization problem, using a CCCP optimization procedure. Extensive experiments on ten standard UCI machine learning datasets, one large binary dataset, three character and digit recognition databases, and a visual place categorization dataset show the power of the proposed approach

Principal Boundary on Riemannian Manifolds

We consider the classification problem and focus on nonlinear methods for classification on manifolds. For multivariate datasets lying on an embedded nonlinear Riemannian manifold within the higher-dimensional ambient space, we aim to acquire a classification boundary for the classes with labels, using the intrinsic metric on the manifolds. Motivated by finding an optimal boundary between the two classes, we invent a novel approach -- the principal boundary. From the perspective of classification, the principal boundary is defined as an optimal curve that moves in between the principal flows traced out from two classes of data, and at any point on the boundary, it maximizes the margin between the two classes. We estimate the boundary in quality with its direction, supervised by the two principal flows. We show that the principal boundary yields the usual decision boundary found by the support vector machine in the sense that locally, the two boundaries coincide. Some optimality and convergence properties of the random principal boundary and its population counterpart are also shown. We illustrate how to find, use and interpret the principal boundary with an application in real data.Comment: 31 pages,10 figure

Targeted Local Support Vector Machine for Age-Dependent Classification

We develop methods to accurately predict whether pre-symptomatic individuals are at risk of a disease based on their various marker profiles, which offers an opportunity for early intervention well before definitive clinical diagnosis. For many diseases, existing clinical literature may suggest the risk of disease varies with some markers of biological and etiological importance, for example age. To identify effective prediction rules using nonparametric decision functions, standard statistical learning approaches treat markers with clear biological importance (e.g., age) and other markers without prior knowledge on disease etiology interchangeably as input variables. Therefore, these approaches may be inadequate in singling out and preserving the effects from the biologically important variables, especially in the presence of potential noise markers. Using age as an example of a salient marker to receive special care in the analysis, we propose a local smoothing large margin classifier implemented with support vector machine (SVM) to construct effective age-dependent classification rules. The method adaptively adjusts age effect and separately tunes age and other markers to achieve optimal performance. We derive the asymptotic risk bound of the local smoothing SVM, and perform extensive simulation studies to compare with standard approaches. We apply the proposed method to two studies of premanifest Huntington’s disease (HD) subjects and controls to construct age-sensitive predictive scores for the risk of HD and risk of receiving HD diagnosis during the study period

Efficient object detection via structured learning and local classifiers

Object detection has made great strides recently. However, it is still facing two big challenges: detection accuracy and computational efficiency. In this thesis, we present an automatic efficient object detection frarnework to detect object instances ·in images using bounding boxes, which can be trained and tested easily on current personal computers. Our framework is a sliding-window based approach, and consists of two major components: (1) efficient object proposal generation, predicting possible object bounding boxes, and (2) efficient object proposal verification, classifying each bounding box in a multiclass manner. For object proposal generation, we formulate this problem as a structured learning problem and investigate structural support vector machines (SSVMs) with our proposed scale/aspect-ratio quantization scheme and ranking constraints. A general ranking-order decomposition algorithm is developed for solving the formulation efficiently, and applied to generate proposals using a two-stage cascade. Using image gradients as features, our object proposal generation method achieves state-of-the-art results in terms Df object recall at a low cost in computation. For object proposal verification, we propose two locally linear and one locally nonlinear classifiers to approximate the nonlinear decision boundaries in the feature space efficiently. Inspired by the kernel trick, these classifiers map the original features into another feature space explicitly where linear classifiers are employed for classification, and thus have linear computational complexity in both training and testing, similar to that of linear classifiers. Therefore, in general, our classifiers can achieve comparable accuracy to kernel based classifiers at the cost of lower computational time. To demonstrate its efficiency and generality, our framework is applied to four different object detection tasks: VOC detection challenges, traffic sign detection, pedestrian detection, and face detection. In each task, it can perform reasonably well with acceptable detection accuracy and good computational efficiency. For instance, on VOC datasets with 20 object classes, our method achieved about 0.1 mean average precision (AP) within 2 hours of training and 0.05 second of testing a 500 x 300 pixel image using a mixture of MATLAB and C++ code on a current personal computer