In this paper, we define and study a new notion of stability for the k-means clustering scheme building upon the field of quantization of a probability measure. We connect this definition of stability to a geometric feature of the underlying distribution of the data, named absolute margin condition, inspired by recent works on the subject.

Abstract—This paper investigates the problem of absolute stability and robust stability of a class of Lur’e systems with neutral type and time-varying delays. By using Lyapunov direct method and linear matrix inequality technique, new delay-dependent stability criteria are obtained and formulated in terms of linear matrix inequalities (LMIs) which are easy to check the stability of the consider...

This paper investigates the mean stability of a class of discrete-time stochastic switched linear systems using the Lp-norm joint spectral radius of the probability distributions governing the switched systems. First we prove a converse Lyapunov theorem that shows the equivalence between the mean stability and the existence of a homogeneous Lyapunov function. Then we show that, when p goes to ∞...

Appendix A: Nonlinear regression model and nonlinear approximation methods In this section, we extend the approximation approaches that we developed in Sections 4.2 and 4.3 to the case of the nonlinear regression model y = Ψ (kk a; b) + εε (A.1) where b ∈ R n+1 , k ≡ (k 0 k T −1) ∈ R T , a ≡ (a 0 a T −1) ∈ R T , and Ψ (kk a; β) ≡ (Ψ (k 0 a 0 ; β) Ψ (k T −1 a T −1 ; β)) ∈ R T. 1 We first conside...