Active Semi-Supervised Learning Using Sampling Theory for Graph Signals

We consider the problem of offline, pool-based active semi-supervised learning on graphs. This problem is important when the labeled data is scarce and expensive whereas unlabeled data is easily available. The data points are represented by the vertices of an undirected graph with the similarity between them captured by the edge weights. Given a target number of nodes to label, the goal is to choose those nodes that are most informative and then predict the unknown labels. We propose a novel framework for this problem based on our recent results on sampling theory for graph signals. A graph signal is a real-valued function defined on each node of the graph. A notion of frequency for such signals can be defined using the spectrum of the graph Laplacian matrix. The sampling theory for graph signals aims to extend the traditional Nyquist-Shannon sampling theory by allowing us to identify the class of graph signals that can be reconstructed from their values on a subset of vertices. This approach allows us to define a criterion for active learning based on sampling set selection which aims at maximizing the frequency of the signals that can be reconstructed from their samples on the set. Experiments show the effectiveness of our method.Comment: 10 pages, 6 figures, To appear in KDD'1

A submodular optimization framework for never-ending learning : semi-supervised, online, and active learning.

The revolution in information technology and the explosion in the use of computing devices in people\u27s everyday activities has forever changed the perspective of the data mining and machine learning fields. The enormous amounts of easily accessible, information rich data is pushing the data analysis community in general towards a shift of paradigm. In the new paradigm, data comes in the form a stream of billions of records received everyday. The dynamic nature of the data and its sheer size makes it impossible to use the traditional notion of offline learning where the whole data is accessible at any time point. Moreover, no amount of human resources is enough to get expert feedback on the data. In this work we have developed a unified optimization based learning framework that approaches many of the challenges mentioned earlier. Specifically, we developed a Never-Ending Learning framework which combines incremental/online, semi-supervised, and active learning under a unified optimization framework. The established framework is based on the class of submodular optimization methods. At the core of this work we provide a novel formulation of the Semi-Supervised Support Vector Machines (S3VM) in terms of submodular set functions. The new formulation overcomes the non-convexity issues of the S3VM and provides a state of the art solution that is orders of magnitude faster than the cutting edge algorithms in the literature. Next, we provide a stream summarization technique via exemplar selection. This technique makes it possible to keep a fixed size exemplar representation of a data stream that can be used by any label propagation based semi-supervised learning technique. The compact data steam representation allows a wide range of algorithms to be extended to incremental/online learning scenario. Under the same optimization framework, we provide an active learning algorithm that constitute the feedback between the learning machine and an oracle. Finally, the developed Never-Ending Learning framework is essentially transductive in nature. Therefore, our last contribution is an inductive incremental learning technique for incremental training of SVM using the properties of local kernels. We demonstrated through this work the importance and wide applicability of the proposed methodologies