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.
Different from the alternating optimization approaches in @cite_22 @cite_17 @cite_16 , we estimate the weights directly by solving a single optimization problem. Moreover, we iteratively discard the irrelevant graphs based on a simulated annealing approach guided by the cross-validation performance to prevent them from deteriorating the results. Through weeding out the intrusive graphs and learning globally optimal graph weights we produce the most robust results.
@cite_16 @cite_22 @cite_17
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The paradigm of simulated annealing is applied to the problem of drawing graphs “nicely.” Our algorithm deals with general undirected graphs with straight-line edges, and employs several simple criteria for the aesthetic quality of the result. The algorithm is flexible, in that the relative weights of the criteria can be changed. For graphs of modest size it produces good results, competitive with those produced by other methods, notably, the “spring method” and its variants. We present a Multiple-Instance Learning (MIL) algorithm for determining the salience of each item in each bag with respect to the bag’s real-valued label. We use an alternating-projections constrained optimization approach to simultaneously learn a regression model and estimate all salience values. We evaluate this algorithm on a significant real-world problem, crop yield modeling, and demonstrate that it provides more extensive, intuitive, and stable salience models than Primary-Instance Regression, which selects a single relevant item from each bag. Many graph-based semi-supervised learning methods for large datasets have been proposed to cope with the rapidly increasing size of data, such as Anchor Graph Regularization (AGR). This model builds a regularization framework by exploring the underlying structure of the whole dataset with both datapoints and anchors. Nevertheless, AGR still has limitations in its two components: (1) in anchor graph construction, the estimation of the local weights between each datapoint and its neighboring anchors could be biased and relatively slow; and (2) in anchor graph regularization, the adjacency matrix that estimates the relationship between datapoints, is not sufficiently effective. In this paper, we develop an Efficient Anchor Graph Regularization (EAGR) by tackling these issues. First, we propose a fast local anchor embedding method, which reformulates the optimization of local weights and obtains an analytical solution. We show that this method better reconstructs datapoints with anchors and speeds up the optimizing process. Second, we propose a new adjacency matrix among anchors by considering the commonly linked datapoints, which leads to a more effective normalized graph Laplacian over anchors. We show that, with the novel local weight estimation and normalized graph Laplacian, EAGR is able to achieve better classification accuracy with much less computational costs. Experimental results on several publicly available datasets demonstrate the effectiveness of our approach. We consider scheduling on an unreliable machine that may experience unexpected changes in processing speed or even full breakdowns. We aim for a universal solution that performs well without adaptation for any possible machine behavior. For the objective of minimizing the total weighted completion time, we design a polynomial time deterministic algorithm that finds a universal scheduling sequence with a solution value within 4 times the value of an optimal clairvoyant algorithm that knows the disruptions in advance. A randomized version of this algorithm attains in expectation a ratio of e. We also show that both results are best possible among all universal solutions. As a direct consequence of our results, we answer affirmatively the question of whether a constant approximation algorithm exists for the offline version of the problem when machine unavailability periods are known in advance. When jobs have individual release dates, the situation changes drastically. Even if all weights are equal, there are instances for which any universal solution is a factor of Ω(logn loglogn) worse than an optimal sequence. Motivated by this hardness, we study the special case when the processing time of each job is proportional to its weight. We present a non-trivial algorithm with a small constant performance guarantee.