In this article we investigate the L1–norm of certain functions on groups called divisibility functions. Using these functions, their connection to residual finiteness, and integration theory on profinite groups, we define the residual average of a finitely generated group. One of the main results in this article is the finiteness of residual averages on finitely generated linear groups. Whethe...

It has recently been shown that the performance of multivariate exponentially weighted mean square (MEWMS) and multivariate exponentially weighted moving variance (MEWMV) charts of Huwang et al. (2007) in monitoring the variability of a multivariate process for individual observations is better than existing schemes. Both of these control charts monitor a distinct matrix which is an estimator o...

In this paper, we apply Sequential Unconstrained Minimization Techniques (SUMTs) to the classical formulations of both the classical L1 norm SVM and the least squares SVM. We show that each can be solved as a sequence of unconstrained optimization problems with only box constraints. We propose relaxed SVM and relaxed LSSVM formulations that correspond to a single problem in the corresponding up...

In this paper we study a version of the Multidimensional Arrangement Problem (MAP) that embeds a graph into a multidimensional array minimizing the aggregated (Manhattan) distance of the embedded edges. This problem includes the minimum Linear Arrangement Problem (minLA) as a special case, among others. We propose JAM, a tabu-based two-stage simulated annealing heuristic for this problem. Our a...

Targeting at sparse learning, we construct Banach spaces B of functions on an input space X with the following properties: (1) B possesses an l norm in the sense that B is isometrically isomorphic to the Banach space of integrable functions on X with respect to the counting measure; (2) point evaluations are continuous linear functionals on B and are representable through a bilinear form with a...

In this paper, we consider the rectilinear one-center problem on uncertain points in the plane. In this problem, we are given a set P of n (weighted) uncertain points in the plane and each uncertain point has m possible locations each associated with a probability for the point appearing at that location. The goal is to find a point q∗ in the plane which minimizes the maximum expected rectiline...

As a common problem in data clustering applications, how to identify a suitable proximity measure between data instances is still an open problem. Especially when interval-valued data is becoming more and more popular, it is expected to have a suitable distance for intervals. Existing distance measures only consider the lower and upper bounds of intervals, but overlook the overlapped area betwe...

We consider the problem of estimating change in the dependency structure between two p-dimensional Ising models, based on respectively n1 and n2 samples drawn from the models. The change is assumed to be structured, e.g., sparse, block sparse, node-perturbed sparse, etc., such that it can be characterized by a suitable (atomic) norm. We present and analyze a norm-regularized estimator for direc...

The paper presents a novel feature extraction technique for face recognition which uses sparse projection axes to compute a lowdimensional representation of face images. The proposed technique derives the sparse axes by first recasting the problem of face recognition as a regression problem and then solving the new (under-determined) regression problem by computing the solution with minimum L1 ...

Let D be a finite set and g : D × D → R a symmetric function satisfying g(x, x) = 0 and g(x, y) = g(y, x) for all x, y ∈ D. A switch gσ is obtained from g by using a local valuation σ : D → R: gσ(x, y) = σ(x) + g(x, y) + σ(y) for x 6= y. It is shown that every symmetric function g has a unique minimal pseudometric switch, and, moreover, there is a switch gσ of g that is isometric to a finite Ma...