Preprint Article Version 1 This version is not peer-reviewed

Unsupervised Metric Learning Using Low Dimensional Embedding

Version 1 : Received: 7 September 2018 / Approved: 11 September 2018 / Online: 11 September 2018 (12:13:18 CEST)
Version 2 : Received: 19 September 2018 / Approved: 19 September 2018 / Online: 19 September 2018 (13:53:42 CEST)

How to cite: Jain, P. Unsupervised Metric Learning Using Low Dimensional Embedding. Preprints 2018, 2018090197 (doi: 10.20944/preprints201809.0197.v1). Jain, P. Unsupervised Metric Learning Using Low Dimensional Embedding. Preprints 2018, 2018090197 (doi: 10.20944/preprints201809.0197.v1).

Abstract

Unsupervised metric learning has been generally studied as a byproduct of dimensionality reduction or manifold learning techniques. Manifold learning techniques like Di usion maps, Laplacian eigenmaps has a special property that embedded space is Euclidean. Although laplacian eigenmaps can provide us with some (dis)similarity information it does not provide with a metric which can further be used on out-of-sample data. On other hand supervised metric learning technique like ITML which can learn a metric needs labeled data for learning. In this work propose methods for incremental unsupervised metric learning. In rst approach Laplacian eigenmaps is used along with Information Theoretic Metric Learning(ITML) to form an unsupervised metric learning method. We rst project data into a low dimensional manifold using Laplacian eigenmaps, in embedded space we use euclidean distance to get an idea of similarity between points. If euclidean distance between points in embedded space is below a threshold t1 value we consider them as similar points and if it is greater than a certain threshold t2 we consider them as dissimilar points. Using this we collect a batch of similar and dissimilar points which are then used as a constraints for ITML algorithm and learn a metric. To prove this concept we have tested our approach on various UCI machine learning datasets. In second approach we propose Incremental Di usion Maps by updating SVD in a batch-wise manner.

Subject Areas

unsupervised, metric learning, embedding learning, laplacian, information theoretic, diffusion maps

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