Graph-based semi-supervised classification uses a graph to capture the relationship between samples and exploits label propagation techniques on the graph to predict the labels of unlabeled samples. However, it is difficult to construct a graph that faithfully describes the relationship between high-dimensional samples. Recently, low-rank representation has been introduced to construct a graph,...

The on-line nearest-neighbour graph on a sequence of n uniform random points in (0, 1)d (d ∈ N) joins each point after the first to its nearest neighbour amongst its predecessors. For the total power-weighted edge-length of this graph, with weight exponent α ∈ (0, d/2], we prove O(max{n1−(2α/d), log n}) upper bounds on the variance. On the other hand, we give an n → ∞ large-sample convergence r...

The Universum data, defined as a collection of ”nonexamples” that do not belong to any class of interest, have been shown to encode some prior knowledge by representing meaningful concepts in the same domain as the problem at hand. In this paper, we address a novel semi-supervised classification problem, called semi-supervised Universum, that can simultaneously utilize the labeled data, unlabel...

let $g$ be a simple graph of order $n$‎. ‎we consider the‎ ‎independence polynomial and the domination polynomial of a graph‎ ‎$g$‎. ‎the value of a graph polynomial at a specific point can give‎ ‎sometimes a very surprising information about the structure of the‎ ‎graph‎. ‎in this paper we investigate independence and domination‎ ‎polynomial at $-1$ and $1$‎.

we study umbilic (space-like) submanifolds of pseudo-riemannian space forms, then define totally semi-umbilic space-like submanifold of pseudo euclidean space and relate this notion to umbilicity. finally we give characterization of total semi-umbilicity for space-like submanifolds contained in pseudo sphere or pseudo hyperbolic space or the light cone.a pseudo-riemannian submanifold m in (a ps...