In this thesis, we perform object recognition using (i) maximum similarity based feature matching, and (ii) adaptive multiple kernel learning. Images are likely more similar if they contain objects within the same categories, so how to measure image similarities correctly and efficiently is one of the critical issues for object recognition. We first propose to match features between two images so that their similarity is maximized, and employ support vector machines (SVMs) for recognition based on the maximum similarity matrix. Secondly, given several similarity matrices (kernels) created by different visual information in images, we propose a novel adaptive multiple kernel learning technique to generate an optimal kernel from all the kernels based on biconvex optimization. These two new approaches are tested on the most recent image benchmark datasets and their results are impressive, equalling or bettering the state-of-the-art results.

methods

Linear complementarity, linear and nonlinear programming

Maximum similarity based feature matching and adaptive multiple kernel learning for object recognition

Intersection computation of convex sets is a typical problem in distributed optimization. In this paper, a multi-agent network is considered for continuous-time dynamics with the fixed topology, in which each agent is associated with a convex set. The objective is for all the agents to achieve an agreement within the intersection of the associated convex sets. A distributed “projected consensus algorithm” is introduced, and the computation of the projection term is converted to a constrained optimization problem. The solution of the optimization problem is determined by Karush-Kuhn-Tucker (KKT) conditions. Particularly, when the associated set of each agent is a polyhedral set, the projection computation is converted to solving a quadratic programming problem, in which an extension algorithm of the simplex method can be used. A numerical example is given to illustrate the effectiveness of the algorithms.

background or methods

A distributed algorithm based on KKT conditions for convex intersection computation

The aim of this thesis is to consider the mathematical treatment of mechanical systems in the presence of constraints which are energetically dissipative. Constraints may be energetically dissipative due to impacts and friction. In the frictionless setting, we generalize Hamilton’s principle of stationary action, central to the Lagrangian formulation of classical mechanics, to reflect optimality conditions in constrained spaces. We show that this generalization leads to the standard measure-theoretic equations for shocks in the presence of unilateral constraints. Previously, these equations were simply postulated; we derive them from a fundamental variational principle. We also present results in the frictional setting. We survey the extensive literature on the subject, which focusses on existence results and numerical schemes known as timestepping algorithms. We consider a novel model of friction (which is more dissipative than standard Coulomb friction) for which we can give better well-posedness results than what is currently available for the Coulomb theory. To this end, we study multi-valued maps, differential inclusions, and optimization theory. We construct a differential inclusion we call the feedback problem, for which the multi-valued map is the solution set of a convex program. We give existence and uniqueness results regarding this feedback problem. We cast the persistent contact evolution problem of our novel model of friction into the form of a feedback problem to derive an existence result.

Linear complementarity, linear and nonlinear programming

Citations

Maximum similarity based feature matching and adaptive multiple kernel learning for object recognition

A distributed algorithm based on KKT conditions for convex intersection computation

Classical mechanics with dissipative constraints

With unilateral contacts

Linear complementarity representation of piecewise linear functions

Related Papers (5)

The Linear Complementarity Problem

Bimatrix Equilibrium Points and Mathematical Programming

Complementary pivot theory of mathematical programming

Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications

Engineering and Economic Applications of Complementarity Problems