CBCL Memos (1993 - 2004)
http://hdl.handle.net/1721.1/5462
Thu, 25 May 2017 01:05:41 GMT2017-05-25T01:05:41ZObject Detection in Images by Components
http://hdl.handle.net/1721.1/7293
Object Detection in Images by Components
Mohan, Anuj
In this paper we present a component based person detection system that is capable of detecting frontal, rear and near side views of people, and partially occluded persons in cluttered scenes. The framework that is described here for people is easily applied to other objects as well. The motivation for developing a component based approach is two fold: first, to enhance the performance of person detection systems on frontal and rear views of people and second, to develop a framework that directly addresses the problem of detecting people who are partially occluded or whose body parts blend in with the background. The data classification is handled by several support vector machine classifiers arranged in two layers. This architecture is known as Adaptive Combination of Classifiers (ACC). The system performs very well and is capable of detecting people even when all components of a person are not found. The performance of the system is significantly better than a full body person detector designed along similar lines. This suggests that the improved performance is due to the components based approach and the ACC data classification structure.
Wed, 11 Aug 1999 00:00:00 GMThttp://hdl.handle.net/1721.1/72931999-08-11T00:00:00ZA Note on Support Vector Machines Degeneracy
http://hdl.handle.net/1721.1/7291
A Note on Support Vector Machines Degeneracy
Rifkin, Ryan; Pontil, Massimiliano; Verri, Alessandro
When training Support Vector Machines (SVMs) over non-separable data sets, one sets the threshold $b$ using any dual cost coefficient that is strictly between the bounds of $0$ and $C$. We show that there exist SVM training problems with dual optimal solutions with all coefficients at bounds, but that all such problems are degenerate in the sense that the "optimal separating hyperplane" is given by ${f w} = {f 0}$, and the resulting (degenerate) SVM will classify all future points identically (to the class that supplies more training data). We also derive necessary and sufficient conditions on the input data for this to occur. Finally, we show that an SVM training problem can always be made degenerate by the addition of a single data point belonging to a certain unboundedspolyhedron, which we characterize in terms of its extreme points and rays.
Wed, 11 Aug 1999 00:00:00 GMThttp://hdl.handle.net/1721.1/72911999-08-11T00:00:00ZSupport Vector Machines: Training and Applications
http://hdl.handle.net/1721.1/7290
Support Vector Machines: Training and Applications
Osuna, Edgar; Freund, Robert; Girosi, Federico
The Support Vector Machine (SVM) is a new and very promising classification technique developed by Vapnik and his group at AT&T Bell Labs. This new learning algorithm can be seen as an alternative training technique for Polynomial, Radial Basis Function and Multi-Layer Perceptron classifiers. An interesting property of this approach is that it is an approximate implementation of the Structural Risk Minimization (SRM) induction principle. The derivation of Support Vector Machines, its relationship with SRM, and its geometrical insight, are discussed in this paper. Training a SVM is equivalent to solve a quadratic programming problem with linear and box constraints in a number of variables equal to the number of data points. When the number of data points exceeds few thousands the problem is very challenging, because the quadratic form is completely dense, so the memory needed to store the problem grows with the square of the number of data points. Therefore, training problems arising in some real applications with large data sets are impossible to load into memory, and cannot be solved using standard non-linear constrained optimization algorithms. We present a decomposition algorithm that can be used to train SVM's over large data sets. The main idea behind the decomposition is the iterative solution of sub-problems and the evaluation of, and also establish the stopping criteria for the algorithm. We present previous approaches, as well as results and important details of our implementation of the algorithm using a second-order variant of the Reduced Gradient Method as the solver of the sub-problems. As an application of SVM's, we present preliminary results we obtained applying SVM to the problem of detecting frontal human faces in real images.
Sat, 01 Mar 1997 00:00:00 GMThttp://hdl.handle.net/1721.1/72901997-03-01T00:00:00ZAn Equivalence Between Sparse Approximation and Support Vector Machines
http://hdl.handle.net/1721.1/7289
An Equivalence Between Sparse Approximation and Support Vector Machines
Girosi, Federico
In the first part of this paper we show a similarity between the principle of Structural Risk Minimization Principle (SRM) (Vapnik, 1982) and the idea of Sparse Approximation, as defined in (Chen, Donoho and Saunders, 1995) and Olshausen and Field (1996). Then we focus on two specific (approximate) implementations of SRM and Sparse Approximation, which have been used to solve the problem of function approximation. For SRM we consider the Support Vector Machine technique proposed by V. Vapnik and his team at AT&T Bell Labs, and for Sparse Approximation we consider a modification of the Basis Pursuit De-Noising algorithm proposed by Chen, Donoho and Saunders (1995). We show that, under certain conditions, these two techniques are equivalent: they give the same solution and they require the solution of the same quadratic programming problem.
Thu, 01 May 1997 00:00:00 GMThttp://hdl.handle.net/1721.1/72891997-05-01T00:00:00Z