This paper describes an improved algorithm for the numerical solution to the Support Vector Machine (SVM) classification problem for all values of the regularization parameter, C. The algorithm is motivated by the work of Hastie \emph{et. al.} and follows the main idea of tracking the optimality conditions of the SVM solution for descending value of … Read more
The affine rank minimization problem, which consists of finding a matrix of minimum rank subject to linear equality constraints, has been proposed in many areas of engineering and science. A specific rank minimization problem is the matrix completion problem, in which we wish to recover a (low-rank) data matrix from incomplete samples of its entries. … Read more
We introduce a general-purpose learning machine that we call the “Guaranteed Error Machine”, or GEM, and two learning algorithms, a “real GEM algorithm” and an “ideal GEM algorithm”. The real GEM algorithm is for use in real applications, while the ideal GEM algorithm is introduced as a theoretical tool; however, these two algorithms have identical … Read more
Support Vector Machines are a powerful machine learning technology, but the training process involves a dense quadratic optimization problem and is computationally challenging. A parallel implementation of Support Vector Machine training has been developed, using a combination of MPI and OpenMP. Using an interior point method for the optimization and a reformulation that avoids the … Read more
In the interest of deriving classifiers that are robust to outlier observations, we present integer programming formulations of Vapnik’s support vector machine (SVM) with the ramp loss and hard margin loss. The ramp loss allows a maximum error of 2 for each training observation, while the hard margin loss calculates error by counting the number … Read more
this paper I present several novel, efficient, algorithmic techniques for solving some multidimensional geometric data management and analysis problems. The techniques are based on several data structures from computational geometry (e.g. segment tree and range tree) and on the well-known sweep-line method. Citation Proceedings of the 3rd International Conference “Knowledge Management – Projects, Systems and … Read more
Citation This paper is published in Proceedings of KDIR 2009
Citation This paper is published in Lecture Notes in Artificial Intelligence 5139, p411-418, Springer
Revenue management (RM) enhances the revenues of a company by means of demand-management decisions. An RM system must take into account the possibility that a booking may be canceled, or that a booked customer may fail to show up at the time of service (no-show). We review the Passenger Name Record data mining based cancellation … Read more
Given a non empty polyhedral set, we consider the problem of finding a vector belonging to it and having the minimum number of nonzero components, i.e., a feasible vector with minimum zero-norm. This nonsmooth combinatorial optimization problem is NP-Hard and arises in various fields such as machine learning, pattern recognition, signal processing. We propose two … Read more