preprints.org > mathematics & computer science > artificial intelligence & robotics > doi: 10.20944/preprints201809.0197.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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)

Unsupervised metric learning has been generally studied as a byproduct of dimensionality reduction or manifold learning techniques. Manifold learning techniques like Diusion 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 Diusion Maps by updating SVD in a batch-wise manner.

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

MATHEMATICS & COMPUTER SCIENCE, Artificial Intelligence & Robotics