Graph-regularized semi-supervised learning has been used effectively for classification when (i) instances are connected through a graph, and (ii) labeled data is scarce. If available, using multiple relations (or graphs) between the instances can improve the prediction performance. On the other hand, when these relations have varying levels of veracity and exhibit varying relevance for the task, very noisy and or irrelevant relations may deteriorate the performance. As a result, an effective weighing scheme needs to be put in place. In this work, we propose a robust and scalable approach for multi-relational graph-regularized semi-supervised classification. Under a convex optimization scheme, we simultaneously infer weights for the multiple graphs as well as a solution. We provide a careful analysis of the inferred weights, based on which we devise an algorithm that filters out irrelevant and noisy graphs and produces weights proportional to the informativeness of the remaining graphs. Moreover, the proposed method is linearly scalable w.r.t. the number of edges in the union of the multiple graphs. Through extensive experiments we show that our method yields superior results under different noise models, and under increasing number of noisy graphs and intensity of noise, as compared to a list of baselines and state-of-the-art approaches.
While most transductive methods consider a single given graph, there also exist methods that aim to predict the node labels by leveraging multiple graphs @cite_26 @cite_18 @cite_25 @cite_33 @cite_22 @cite_17 . The problem is sometimes referred as multiple kernel learning @cite_11 , where data is represented by means of kernel matrices defined by similarities between data pairs.
@cite_18 @cite_26 @cite_11 @cite_33 @cite_22 @cite_25 @cite_17
1552297528 1495400410 2136294701 2160569988
We propose a new graph-based label propagation algorithm for transductive learning. Each example is associated with a vertex in an undirected graph and a weighted edge between two vertices represents similarity between the two corresponding example. We build on Adsorption, a recently proposed algorithm and analyze its properties. We then state our learning algorithm as a convex optimization problem over multi-label assignments and derive an efficient algorithm to solve this problem. We state the conditions under which our algorithm is guaranteed to converge. We provide experimental evidence on various real-world datasets demonstrating the effectiveness of our algorithm over other algorithms for such problems. We also show that our algorithm can be extended to incorporate additional prior information, and demonstrate it with classifying data where the labels are not mutually exclusive. Typical graph-theoretic approaches for semi-supervised classification infer labels of unlabeled instances with the help of graph Laplacians. Founded on the spectral decomposition of the graph Laplacian, this paper learns a kernel matrix via minimizing the leave-one-out classification error on the labeled instances. To this end, an efficient algorithm is presented based on linear programming, resulting in a transductive spectral kernel. The idea of our algorithm stems from regularization methodology and also has a nice interpretation in terms of spectral clustering. A simple classifier can be readily built upon the learned kernel, which suffices to give prediction for any data point aside from those in the available dataset. Besides this usage, the spectral kernel can be effectively used in tandem with conventional kernel machines such as SVMs. We demonstrate the efficacy of the proposed algorithm through experiments carried out on challenging classification tasks. We consider spectral clustering and transductive inference for data with multiple views. A typical example is the web, which can be described by either the hyperlinks between web pages or the words occurring in web pages. When each view is represented as a graph, one may convexly combine the weight matrices or the discrete Laplacians for each graph, and then proceed with existing clustering or classification techniques. Such a solution might sound natural, but its underlying principle is not clear. Unlike this kind of methodology, we develop multiview spectral clustering via generalizing the normalized cut from a single view to multiple views. We further build multiview transductive inference on the basis of multiview spectral clustering. Our framework leads to a mixture of Markov chains defined on every graph. The experimental evaluation on real-world web classification demonstrates promising results that validate our method. We pose transductive classification as a matrix completion problem. By assuming the underlying matrix has a low rank, our formulation is able to handle three problems simultaneously: i) multi-label learning, where each item has more than one label, ii) transduction, where most of these labels are unspecified, and iii) missing data, where a large number of features are missing. We obtained satisfactory results on several real-world tasks, suggesting that the low rank assumption may not be as restrictive as it seems. Our method allows for different loss functions to apply on the feature and label entries of the matrix. The resulting nuclear norm minimization problem is solved with a modified fixed-point continuation method that is guaranteed to find the global optimum.