We investigate inverse limits with set-valued bonding functions. We generalize theorems of W. T. Ingram and William S. Mahavier, and of Van Nall, on the connectedness of the inverse limit space. We establish a fixed point theorem and show that under certain conditions, inverse limits with set-valued bonding functions can be realized as ordinary inverse limits. We also obtain some results that a...

Following a discussion on the general form of regularization for semi-supervised learning, we propose a semi-supervised regression algorithm. It is based on the assumption that we have certain order preferences on unlabeled data (e.g., point x1 has a larger target value than x2). Semi-supervised learning consists of enforcing the order preferences as regularization in a risk minimization framew...

Constructing an informative and discriminative graph plays an important role in various pattern recognition tasks such as clustering and classification. Among the existing graph-based learning models, low-rank representation (LRR) is a very competitive one, which has been extensively employed in spectral clustering and semi-supervised learning (SSL). In SSL, the graph is composed of both labele...

A multiple-valued transformation T from a space X to a space Y is a function assigning to each point x o f X a nonempty closed subset T(x) of F. The graph of T comprises those points (x, y) in the topological product X Y for which y belongs to T(x). All spaces to be considered shall be compact metric and all transformations T shall be upper semi-continuous, meaning that their graphs are closed,...

In this paper, we introduce the (G-$psi$) contraction in a metric space by using a graph. Let $F,T$ be two multivalued mappings on $X.$ Among other things, we obtain a common fixed point of the mappings $F,T$ in the metric space $X$ endowed with a graph $G.$

Graph-based semi-supervised learning (GSSL) is an important paradigm among approaches and includes the two processes of graph construction label inference. In most traditional GSSL methods, are completed independently. Once constructed, result inference cannot be changed. Therefore, quality directly determines GSSL’s performance. Most methods make certain assumptions about data distribution, re...

Wiring schemes which exploit the potential of modern integrated circuit technology are likely to exhibit a high degree of "periodicity," as well as various other attributes. The first contribution of this paper is to formulate a precise definition of periodicity in terms of a graph-theoretic model originated by Yoeli. Roughly speaking, an infinite graph is said to be periodic if it can be gener...

LetN be a point placed directed graph andG be a sub-graph of N . We study the point placement problem of optimally re-placing the nodes in G assuming that the remaining nodes in N are fixed. The goal is to minimize the total “wiring” cost i.e. the cost of the internal nets of G plus the external nets connecting G to other other nodes of N . The cost of a net is the semi-perimeter of the smalles...

Graph neural networks (GNNs) have emerged as effective approaches for graph analysis, especially in the scenario of semi-supervised learning. Despite its success, GNN often suffers from over-smoothing and over-fitting problems, which affects performance on node classification tasks. We analyze that an alternative method, label propagation algorithm (LPA), avoids aforementioned problems thus it ...