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Multiclass Learning with Simplex Coding     Multiclass  Simplex  Coding       2012/11/22
In this paper we discuss a novel framework for multiclass learning, defined by a suitable coding/decoding strategy, namely the simplex coding, that allows to generalize to multiple classes a relaxatio...
The cluster complex $\Delta (\Phi)$ is an abstract simplicial complex, introduced by Fomin and Zelevinsky for a finite root system $\Phi$. The positive part of $\Delta (\Phi)$ naturally defines a simp...
Abstract: We determine the mixing time of a simple Gibbs sampler on the unit simplex, confirming a conjecture of D. Aldous. The upper bound is based on a two-step coupling, where the first step is a s...
The A-hypergeometric system was introduced by Gel’fand, Kapranov and Zelevinsky in the 1980’s. Among several classes of A-hypergeometric functions, those for 1-simplex × (n − 1)-simplex are know...
Uniform probability distributions on $\ell_p$ balls and spheres have been studied extensively and are known to behave like product measures in high dimensions. In this note we consider the uniform di...
We study states, measures, and signed measures on pseudo effect algebras with some kind of the Riesz Decomposition Property, (RDP). We show that the set of all Jordan signed measures is always an Abel...
Improved inclusion-exclusion inequalities for unions of sets are available wherein terms usually included in the alternating sum formula can be left out. This is the case when a key abstract tube con...
In this paper, we study a problem of geometric inequalities for an n-simplex. Some new geometric inequalities for a simplex are established. As special cases, some known inequalities are deduced.
In this paper, we study the problem of geometric inequalities for the inscribed simplex of an n-dimensional simplex. An inequality for the inscribed simplex of a simplex is established. Applying it we...
In this paper, a modification of the bisection simplex method$^{[7]}$ is made for more general purpose use. Organized in an alternative simpler form, the modified version exploits information of the...
In this paper, we introduce simplex linear codes over the ring \sumn=0n=sun F2 of types a and b, where us+1=0. And we determine their properties. These codes are an extension and generalization of sim...

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