We analyse optimal rejection strategies for classifiers with input space partitioning, e.g. prototype-based classifiers, support vector machines or decision trees using certainty measures such as the distance to the closest decision border. We provide new theoretical results: we link this problem to the multiple choice knapsack problem and devise an exact polynomial-time dynamic programming (DP...

For least squares support vector machine (LSSVM) the lack of sparse, while the standard sparse algorithm exist a problem that it need to mark all of training data. We propose an active learning algorithm based on LSSVM to solve sparse problem. This method first construct a minimum classification LSSVM, and then calculate the uncertainty of the sample, select the closest category to mark the sam...

The discrete Gaussian DL−t,s is the distribution that assigns to each vector x in a shifted lattice L − t probability proportional to e−π‖x‖ 2/s2 . It has long been an important tool in the study of lattices. More recently, algorithms for discrete Gaussian sampling (DGS) have found many applications in computer science. In particular, polynomial-time algorithms for DGS with very high parameters...

In this paper a new efficient public key cryptosystem usable for both encryption and digital signatures is presented. Due to its simple structure this public key cipher can be implemented easily in every software or hardware device, making the cryptosystem available for circumstances where the implementation of an alternative like RSA, El Gamal / Diffie Hellmann, etc. is too complicated. Furthe...

The problem of finding a center string that is ‘close’ to every given string arises and has many applications in computational molecular biology and coding theory. This problem has two versions: the Closest String problem and the Closest Substring problem. Assume that we are given a set of strings S = {s1, s2, . . . , sn} of strings, say, each of length m. The Closest String problem [1, 2, 4, 5...

The security of most public-key encryption schemes relies on the hardness of the learning with errors (LWE) problem – an average-case hard lattice problem introduced by Regev ([Reg05]). While LWE has been proved to be as hard as quantumly approximating the so-called Short Independent Vectors Problem, the parameters used in the proof are not suitable for practical reasons. It makes difficult to ...

Given a query location Q in multi-dimensional space, the classical KNN problem is to return the K spatially closest answers in the database with respect to Q. The KNDN (K-Nearest Diverse Neighbor) problem is a semantic extension where the objective is to return the spatially closest result set such that each answer is sufficiently different, or diverse, from the rest of the answers. We review h...

Diierent alignments of multi-dimensional arrays on a mesh-connected SIMD architecture result in diierent communication patterns during parallel program execution. In this paper a compile-time selection of data alignment that minimizes communication cost is discussed. First, it is shown that the selection is computationally as hard as a sub-class of the well-known problem of nding the closest ve...

A given six dimensional vector represents a 3D straight line in Plücker coordinates if its coordinates satisfy the Klein quadric constraint. In many problems aiming to find the Plücker coordinates of lines, noise in the data and other type of errors contribute for obtaining 6D vectors that do not correspond to lines, because of that constraint. A common procedure to overcome this drawback is to...

In this paper, a numerical method is proposed for solving optimal control problem of Volterra integral equations using radial basis functions (RBFs) for approximating unknown function. Actually, the method is based on interpolation by radial basis functions including multiquadrics (MQs), to determine the control vector and the corresponding state vector in linear dynamic system while minimizing...