Improving Graph Construction for Semi-supervised Learning in Computer Vision Applications

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Mahdieh, Mostafa | 2013

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 44559 (19)
University: Sharif University of Technology
Department: Computer Engineering
Advisor(s): Rabiee, Hamid Reza
Abstract:
Semi-supervised Learning (SSL) is an extremely useful approach in many applications where unlabeled data can be easily obtained. Graph based methods are among the most studied branches in SSL. Since neighborhood graph is a key component in these methods, we focus on methods of graph construction in this project. Graph construction methods based on Euclidean distance have the common problem of creating shortcut edges. Shortcut edges refer to the edges which connect two nearby points that are far apart on the manifold. Specifically, we show both in theory and practice that using geodesic distance for selecting and weighting edges results in more appropriate neighborhood graphs. We propose an algorithm, called Isograph, that estimates the geodesic distance between pairs of neighboring points based on an arbitrary initial graph (such as k-NN) to improve it. Moreover, theoretical bounds are provided stating that the estimated values of geodesic distances are reasonable and will approach the real values after each iteration. The experimental results on synthetic and real world data, support our claims
Keywords:
Machine Learning ; Semi-Supervised Learning ; Machine Vision ; Graph Construction ; Manifold Assumption