Robert M. Freund

Bio: Robert M. Freund is an academic researcher from Massachusetts Institute of Technology. The author has contributed to research in topics: Convex optimization & Linear programming. The author has an hindex of 33, co-authored 129 publications receiving 8056 citations. Previous affiliations of Robert M. Freund include Stanford University & University of Michigan.

Training support vector machines: an application to face detection

Abstract: We investigate the application of Support Vector Machines (SVMs) in computer vision. SVM is a learning technique developed by V. Vapnik and his team (AT&T Bell Labs., 1985) that can be seen as a new method for training polynomial, neural network, or Radial Basis Functions classifiers. The decision surfaces are found by solving a linearly constrained quadratic programming problem. This optimization problem is challenging because the quadratic form is completely dense and the memory requirements grow with the square of the number of data points. We present a decomposition algorithm that guarantees global optimality, and can be used to train SVM's over very large data sets. The main idea behind the decomposition is the iterative solution of sub-problems and the evaluation of optimality conditions which are used both to generate improved iterative values, and also establish the stopping criteria for the algorithm. We present experimental results of our implementation of SVM, and demonstrate the feasibility of our approach on a face detection problem that involves a data set of 50,000 data points.

An improved training algorithm for support vector machines

Abstract: We investigate the problem of training a support vector machine (SVM) on a very large database in the case in which the number of support vectors is also very large. Training a SVM is equivalent to solving a linearly constrained quadratic programming (QP) problem in a number of variables equal to the number of data points. This optimization problem is known to be challenging when the number of data points exceeds few thousands. In previous work done by us as well as by other researchers, the strategy used to solve the large scale QP problem takes advantage of the fact that the expected number of support vectors is small (<3,000). Therefore, the existing algorithms cannot deal with more than a few thousand support vectors. In this paper we present a decomposition algorithm that is guaranteed to solve the QP problem and that does not make assumptions on the expected number of support vectors. In order to present the feasibility of our approach we consider a foreign exchange rate time series database with 110,000 data points that generates 100,000 support vectors.

Support Vector Machines: Training and Applications

Abstract: 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.

Optimal investment in product-flexible manufacturing capacity

Abstract: This paper presents a model and an analysis of the cost-flexibility tradeoffs involved in investing in product-flexible manufacturing capacity. Flexible capacity provides a firm with the ability to...

Relatively Smooth Convex Optimization by First-Order Methods, and Applications

Abstract: The usual approach to developing and analyzing first-order methods for smooth convex optimization assumes that the gradient of the objective function is uniformly smooth with some Lipschitz constant $L$. However, in many settings the differentiable convex function $f(\cdot)$ is not uniformly smooth---for example, in $D$-optimal design where $f(x):=-\ln \det(HXH^T)$ and $X:= \mbox{{\bf D}iag} (x)$, or even the univariate setting with $f(x) := -\ln(x) + x^2$. In this paper we develop a notion of “relative smoothness” and relative strong convexity that is determined relative to a user-specified “reference function” $h(\cdot)$ (that should be computationally tractable for algorithms), and we show that many differentiable convex functions are relatively smooth with respect to a correspondingly fairly simple reference function $h(\cdot)$. We extend two standard algorithms---the primal gradient scheme and the dual averaging scheme---to our new setting, with associated computational guarantees. We apply our new a...

Gradient-based learning applied to document recognition

Abstract: Multilayer neural networks trained with the back-propagation algorithm constitute the best example of a successful gradient based learning technique. Given an appropriate network architecture, gradient-based learning algorithms can be used to synthesize a complex decision surface that can classify high-dimensional patterns, such as handwritten characters, with minimal preprocessing. This paper reviews various methods applied to handwritten character recognition and compares them on a standard handwritten digit recognition task. Convolutional neural networks, which are specifically designed to deal with the variability of 2D shapes, are shown to outperform all other techniques. Real-life document recognition systems are composed of multiple modules including field extraction, segmentation recognition, and language modeling. A new learning paradigm, called graph transformer networks (GTN), allows such multimodule systems to be trained globally using gradient-based methods so as to minimize an overall performance measure. Two systems for online handwriting recognition are described. Experiments demonstrate the advantage of global training, and the flexibility of graph transformer networks. A graph transformer network for reading a bank cheque is also described. It uses convolutional neural network character recognizers combined with global training techniques to provide record accuracy on business and personal cheques. It is deployed commercially and reads several million cheques per day.

LIBSVM: A library for support vector machines

Abstract: LIBSVM is a library for Support Vector Machines (SVMs). We have been actively developing this package since the year 2000. The goal is to help users to easily apply SVM to their applications. LIBSVM has gained wide popularity in machine learning and many other areas. In this article, we present all implementation details of LIBSVM. Issues such as solving SVM optimization problems theoretical convergence multiclass classification probability estimates and parameter selection are discussed in detail.

Data Mining: Concepts and Techniques

Abstract: The increasing volume of data in modern business and science calls for more complex and sophisticated tools. Although advances in data mining technology have made extensive data collection much easier, it's still always evolving and there is a constant need for new techniques and tools that can help us transform this data into useful information and knowledge. Since the previous edition's publication, great advances have been made in the field of data mining. Not only does the third of edition of Data Mining: Concepts and Techniques continue the tradition of equipping you with an understanding and application of the theory and practice of discovering patterns hidden in large data sets, it also focuses on new, important topics in the field: data warehouses and data cube technology, mining stream, mining social networks, and mining spatial, multimedia and other complex data. Each chapter is a stand-alone guide to a critical topic, presenting proven algorithms and sound implementations ready to be used directly or with strategic modification against live data. This is the resource you need if you want to apply today's most powerful data mining techniques to meet real business challenges. * Presents dozens of algorithms and implementation examples, all in pseudo-code and suitable for use in real-world, large-scale data mining projects. * Addresses advanced topics such as mining object-relational databases, spatial databases, multimedia databases, time-series databases, text databases, the World Wide Web, and applications in several fields. *Provides a comprehensive, practical look at the concepts and techniques you need to get the most out of real business data

Rapid object detection using a boosted cascade of simple features

Abstract: This paper describes a machine learning approach for visual object detection which is capable of processing images extremely rapidly and achieving high detection rates. This work is distinguished by three key contributions. The first is the introduction of a new image representation called the "integral image" which allows the features used by our detector to be computed very quickly. The second is a learning algorithm, based on AdaBoost, which selects a small number of critical visual features from a larger set and yields extremely efficient classifiers. The third contribution is a method for combining increasingly more complex classifiers in a "cascade" which allows background regions of the image to be quickly discarded while spending more computation on promising object-like regions. The cascade can be viewed as an object specific focus-of-attention mechanism which unlike previous approaches provides statistical guarantees that discarded regions are unlikely to contain the object of interest. In the domain of face detection the system yields detection rates comparable to the best previous systems. Used in real-time applications, the detector runs at 15 frames per second without resorting to image differencing or skin color detection.

A Tutorial on Support Vector Machines for Pattern Recognition

Abstract: The tutorial starts with an overview of the concepts of VC dimension and structural risk minimization. We then describe linear Support Vector Machines (SVMs) for separable and non-separable data, working through a non-trivial example in detail. We describe a mechanical analogy, and discuss when SVM solutions are unique and when they are global. We describe how support vector training can be practically implemented, and discuss in detail the kernel mapping technique which is used to construct SVM solutions which are nonlinear in the data. We show how Support Vector machines can have very large (even infinite) VC dimension by computing the VC dimension for homogeneous polynomial and Gaussian radial basis function kernels. While very high VC dimension would normally bode ill for generalization performance, and while at present there exists no theory which shows that good generalization performance is guaranteed for SVMs, there are several arguments which support the observed high accuracy of SVMs, which we review. Results of some experiments which were inspired by these arguments are also presented. We give numerous examples and proofs of most of the key theorems. There is new material, and I hope that the reader will find that even old material is cast in a fresh light.