Graph-based semi-supervised learning methods are based on some smoothness assumption about the data. As a discrete approximation of the data manifold, the graph plays a crucial role in the success of such graphbased methods. In most existing methods, graph construction makes use of a predefined weighting function without utilizing label information even when it is available. In this work, by in...

‎Let $G$ be a graph without an isolated vertex‎, ‎the normalized Laplacian matrix $tilde{mathcal{L}}(G)$‎ ‎is defined as $tilde{mathcal{L}}(G)=mathcal{D}^{-frac{1}{2}}mathcal{L}(G)mathcal{D}^{-frac{1}{2}}$‎, where ‎$mathcal{D}$ ‎is a‎ diagonal matrix whose entries are degree of ‎vertices ‎‎of ‎$‎G‎$‎‎. ‎The eigenvalues of‎ $tilde{mathcal{L}}(G)$ are ‎called as ‎the ‎normalized Laplacian eigenva...

In multi-label learning problems, the class labels are correlated and label correlations can be leveraged to improve predictive performance of a classifier. Methods that consider high-order in space, usually do not utilize pairwise correlations. most these methods, considered as prior knowledge, which misleading problems with noisy or missing labels. such cases, correlation part model training ...

let $g$ be a simple graph with vertex set $v(g) = {v_1, v_2,ldots, v_n}$ and $d_i$ the degree of its vertex $v_i$, $i = 1, 2,cdots, n$. inspired by the randi'c matrix and the general randi'cindex of a graph, we introduce the concept of general randi'cmatrix $textbf{r}_alpha$ of $g$, which is defined by$(textbf{r}_alpha)_{i,j}=(d_id_j)^alpha$ if $v_i$ and $v_j$ areadjacent, and zero otherwise. s...

We propose a method for domain adaptation on graphs. Given sufficiently many observations of the label function on a source graph, we study the problem of transferring the label information from the source graph to a target graph for estimating the target label function. Our assumption about the relation between the two domains is that the frequency content of the label function, regarded as a ...

Computer vision is full of problems that are elegantly expressed in terms of mathematical optimization, or energy minimization. This is particularly true of “low-level” inference problems such as cleaning up noisy signals, clustering and classifying data, or estimating 3D points from images. Energies let us state each problem as a clear, precise objective function. Minimizing the correct energy...

Recent years have seen a growing number of graph-based semisupervised learning methods. While the literature currently contains several of these methods, their relationships with one another and with other graph-based data analysis algorithms remain unclear. In this paper, we present a unified view of graph-based semi-supervised learning. Our framework unifies three important and seemingly unre...

The results of aerial scene classification can provide valuable information for urban planning and land monitoring. In this specific field, there are always a number object-level semantic classes in big remote-sensing pictures. Complex label-space makes it hard to detect all the targets perceive corresponding semantics typical scene, thereby weakening sensing ability. Even worse, preparation la...

given a non-abelian finite group $g$, let $pi(g)$ denote the set of prime divisors of the order of $g$ and denote by $z(g)$ the center of $g$. thetextit{ prime graph} of $g$ is the graph with vertex set $pi(g)$ where two distinct primes $p$ and $q$ are joined by an edge if and only if $g$ contains an element of order $pq$ and the textit{non-commuting graph} of $g$ is the graph with the vertex s...

We present a machine learning task, which we call bidirectional semi-supervised learning, where label-only samples are given as well as labeled and unlabeled samples. A label-only sample contains the label information of the sample but not the feature information. Then, we propose a simple and effective graph-based method for bidirectional semisupervised learning in multi-label classification. ...