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.
A foundational problem in semi-supervised learning is the construction of a graph underlying the data. We propose to use a method which optimally combines a number of differently constructed graphs. For each of these graphs we associate a basic graph kernel. We then compute an optimal combined kernel. This kernel solves an extended regularization problem which requires a joint minimization over both the data and the set of graph kernels. We present encouraging results on different OCR tasks where the optimal combined kernel is computed from graphs constructed with a variety of distances functions and the 'k' in nearest neighbors. Motivation: During the past decade, the new focus on genomics has highlighted a particular challenge: to integrate the different views of the genome that are provided by various types of experimental data. Results: This paper describes a computational framework for integrating and drawing inferences from a collection of genome-wide measurements. Each dataset is represented via a kernel function, which defines generalized similarity relationships between pairs of entities, such as genes or proteins. The kernel representation is both flexible and efficient, and can be applied to many different types of data. Furthermore, kernel functions derived from different types of data can be combined in a straightforward fashion. Recent advances in the theory of kernel methods have provided efficient algorithms to perform such combinations in a way that minimizes a statistical loss function. These methods exploit semidefinite programming techniques to reduce the problem of finding optimizing kernel combinations to a convex optimization problem. Computational experiments performed using yeast genome-wide datasets, including amino acid sequences, hydropathy profiles, gene expression data and known protein--protein interactions, demonstrate the utility of this approach. A statistical learning algorithm trained from all of these data to recognize particular classes of proteins---membrane proteins and ribosomal proteins---performs significantly better than the same algorithm trained on any single type of data. Availability: Supplementary data at http: noble.gs.washington.edu proj sdp-svm Determining protein function constitutes an exercise in integrating information derived from several heterogeneous high-throughput experiments. To utilize the information spread across multiple sources in a combined fashion, these data sources are transformed into kernels. Several protein function prediction methods follow a two-phased approach: they first optimize the weights on individual kernels to produce a composite kernel, and then train a classifier on the composite kernel. As such, these methods result in an optimal composite kernel, but not necessarily in an optimal classifier. On the other hand, some methods optimize the loss of binary classifiers, and learn weights for the different kernels iteratively. A protein has multiple functions, and each function can be viewed as a label. These methods solve the problem of optimizing weights on the input kernels for each of the labels. This is computationally expensive and ignores inter-label correlations. In this paper, we propose a method called Protein Function Prediction by Integrating Multiple Kernels (ProMK). ProMK iteratively optimizes the phases of learning optimal weights and reducing the empirical loss of a multi-label classifier for each of the labels simultaneously, using a combined objective function. ProMK can assign larger weights to smooth kernels and downgrade the weights on noisy kernels. We evaluate the ability of ProMK to predict the function of proteins using several standard benchmarks. We show that our approach performs better than previously proposed protein function prediction approaches that integrate data from multiple networks, and multi-label multiple kernel learning methods. For large scale image data mining, a challenging problem is to design a method that could work efficiently under the situation of little ground-truth annotation and a mass of unlabeled or noisy data. As one of the major solutions, semi-supervised learning (SSL) has been deeply investigated and widely used in image classification, ranking and retrieval. However, most SSL approaches are not able to incorporate multiple information sources. Furthermore, no sample selection is done on unlabeled data, leading to the unpredictable risk brought by uncontrolled unlabeled data and heavy computational burden that is not suitable for learning on real world dataset. In this paper, we propose a scalable semi-supervised multiple kernel learning method (S3MKL) to deal with the first problem. Our method imposes group LASSO regularization on the kernel coefficients to avoid over-fitting and conditional expectation consensus for regularizing the behaviors of different kernel on the unlabeled data. To reduce the risk of using unlabeled data, we also design a hashing system where multiple kernel locality sensitive hashing (MKLSH) are constructed with respect to different kernels to identify a set of "informative" and "compact" unlabeled training subset from a large unlabeled data corpus. Combining S3MKL with MKLSH, the method is suitable for real world image classification and personalized web image re-ranking with very little user interaction. Comprehensive experiments are conducted to test the performance of our method, and the results show that our method provides promising powers for large scale real world image classification and retrieval.