Ranking with large margin principle: Two approaches

We discuss the problem of ranking instances with the use of a “large margin ” principle. We introduce two main approaches: the first is the “fixed margin ” policy in which the margin of the closest neighboring classes is being maximized — which turns out to be a direct generalization of SVM to ranking learning. The second approach allows for different margins where the sum of margins is maximized. This approach is shown to reduce to-SVM when the number of classes. Both approaches are optimal in size of where is the total number of training examples. Experiments performed on visual classification and “collaborative filtering ” show that both approaches outperform existing ordinal regression algorithms applied for ranking and multi-class SVM applied to general multi-class classification.

Abstract

We discuss the problem of ranking ¡ instances with the use of a “large margin ” principle. We introduce two main approaches: the first is the “fixed margin ” policy in which the margin of the closest neighboring classes is being maximized — which turns out to be a direct generalization of SVM to ranking learning. The second approach allows for ¡£¢¥¤ different margins where the sum of margins is maximized. This approach is shown to reduce ¦ to-SVM when the number of classes ¡¨§� ©. Both approaches are optimal in size of ©� � where � is the total number of training examples. Experiments performed on visual classification and “collaborative filtering ” show that both approaches outperform existing ordinal regression algorithms applied for ranking and multi-class SVM applied to general multi-class classification.

Revisiting Single-view Shape Tensors: Theory and Applications

Given the projection of asuffi tnumber of points it is possible to algebraically eliminate the camera parameters and obtain viewinvariant functions of image coordinates and space coordinates. These single view invariants havebeenintroduced in the past, however, they are not as well understood as their dual multi-view tensors. In this paper we revisit the dual tensors (bilinear, trilinear and quadlinear), both the general and the reference-plane reduced version, and describe the complete set of synthetic constraints, properties of the tensor slices, reprojection equations, non-linear constraints and reconstruction formulas. We then apply some of the new results, such as the dual reprojection equations, for multi-view pointtracking under occlusions

Manifold Pursuit: A New Approach to Appearance Based Recognition

Manifold Pursuit (MP) extends Principal Component Analysis to be invariant to a desired group of image-plane transformations of an ensemble of un-aligned images. We derive

On Representation Theory in Computer Vision Problems

We introduce the following general question: Let V be a complex n-dimensional space and for m k consider the GL(V )-module V (n# m# k)=f v 1 \Omega \Delta\Delta\Delta \Omega vm 2 V We would like to determine dim V (n# m# k) for any choice of n# m k

STarT back tool retained its predicting abilities in patients with acute and sub-acute low back pain patients after a transcultural adaptation and validation to Hebrew

Background The STarT Back Screening Tool (SBT) distributes low back pain (LBP) patients into three prognostic groups for stratified care. This approach has demonstrated beneficial clinical and cost-effectiveness. Objectives To translate and validate the SBT by investigating its psychometric properties among Israelis with acute and sub-acute LBP, and to evaluate its ability to predict disability after three months. Design Prospective study. Method The SBT was transcultural adapted into Hebrew using published guidelines. A total of 150 patients receiving physical therapy for acute or subacute LBP were administered the SBT. Clinical outcomes included the Roland-Morris Disability Questionnaire (RMDQ), the Hospital Anxiety and Depression Scale (HADS), the Fear-Avoidance Beliefs Questionnaire (FABQ) and a numerical pain rating scale (NPRS), collected by an independent interviewer by phone at the start of the physical therapy treatment and after three months. Results The test-retest reliability of the SBT total score and psychosocial subscale were excellent (intraclass correlation coefficient 0.89 and 0.82). Spearman’s correlation coefficient between SBT total score and RMDQ was 0.82, HADS (Anxiety 0.66, Depression 0.76), FABQ (exercise 0.53), NPRS (severe pain 0.48, average pain 0.53). The SBT baseline score showed excellent predictive abilities in discriminating poor disability after three months (ROC curve = 0.825, P < 0.001, 95% CI 0.756–0.894). Conclusion The Israeli translation and cross-cultural adaptation of the SBT is a valid and reliable instrument. The SBT discriminated low, medium and high-risk groups, and predicts disability after three months