PROGRESSIVE CLUSTERING OF MANIFOLD-MODELED DATA BASED ON TANGENT SPACE VARIATIONS

Date

2017-09-28

Author

Gokdogan, Gokhan
Vural, Elif

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

236
views

0
downloads

An important research topic of the recent years has been to understand and analyze manifold-modeled data for clustering and classification applications. Most clustering methods developed for data of non-linear and low-dimensional structure are based on local linearity assumptions. However, clustering algorithms based on locally linear representations can tolerate difficult sampling conditions only to some extent, and may fail for scarcely sampled data manifolds or at high-curvature regions. In this paper, we consider a setting where each cluster is concentrated around a manifold and propose a manifold clustering algorithm that relies on the observation that the variation of the tangent space must be consistent along curves over the same data manifold. In order to achieve robustness against challenges due to noise, manifold intersections, and high curvature, we propose a progressive clustering approach: Observing the variation of the tangent space, we first detect the non-problematic manifold regions and form pre-clusters with the data samples belonging to such reliable regions. Next, these pre-clusters are merged together to form larger clusters with respect to constraints on both the distance and the tangent space variations. Finally, the samples identified as problematic are also assigned to the computed clusters to finalize the clustering. Experiments with synthetic and real datasets show that the proposed method outperforms the manifold clustering algorithms in comparison based on Euclidean distance and sparse representations.

Subject Keywords

Unsupervised classification, Tangent space, Dimensionality reduction, Manifold clustering

URI

https://hdl.handle.net/11511/53474

Conference Name

27th IEEE International Workshop on Machine Learning for Signal Processing (MLSP)

Collections

Department of Electrical and Electronics Engineering, Conference / Seminar

Suggestions

OpenMETU
Core

Clustering of manifold-modeled data based on tangent space variations Gökdoğan, Gökhan; Vural, Elif; Department of Electrical and Electronics Engineering (2017) An important research topic of the recent years has been to understand and analyze data collections for clustering and classification applications. In many data analysis problems, the data sets at hand have an intrinsically low-dimensional structure and admit a manifold model. Most state-of-the-art clustering methods developed for data of non-linear and low-dimensional structure are based on local linearity assumptions. However, clustering algorithms based on locally linear representations can tolerate diff...
Approximation of pattern transformation manifolds with parametric dictionaries Vural, Elif (2011-07-12) The construction of low-dimensional models explaining high-dimensional signal observations provides concise and efficient data representations. In this paper, we focus on pattern transformation manifold models generated by in-plane geometric transformations of 2D visual patterns. We propose a method for computing a manifold by building a representative pattern such that its transformation manifold accurately fits a set of given observations. We present a solution for the progressive construction of the repr...
Nonlinear supervised dimensionality reduction via smooth regular embeddings Ornek, Cem; Vural, Elif (2019-03-01) The recovery of the intrinsic geometric structures of data collections is an important problem in data analysis. Supervised extensions of several manifold learning approaches have been proposed in the recent years. Meanwhile, existing methods primarily focus on the embedding of the training data, and the generalization of the embedding to initially unseen test data is rather ignored. In this work, we build on recent theoretical results on the generalization performance of supervised manifold learning algori...
Out-of-Sample Generalizations for Supervised Manifold Learning for Classification Vural, Elif (2016-03-01) Supervised manifold learning methods for data classification map high-dimensional data samples to a lower dimensional domain in a structure-preserving way while increasing the separation between different classes. Most manifold learning methods compute the embedding only of the initially available data; however, the generalization of the embedding to novel points, i.e., the out-of-sample extension problem, becomes especially important in classification applications. In this paper, we propose a semi-supervis...
Learning Smooth Pattern Transformation Manifolds Vural, Elif (2013-04-01) Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image sets that represent observations of geometrically transformed signals. To construct a manifold, we build a representative pattern whose transformations accurately fit various input images. We examine two objectives of the manifold-building problem, namely, approximation a...

Citation Formats

G. Gokdogan and E. Vural, “PROGRESSIVE CLUSTERING OF MANIFOLD-MODELED DATA BASED ON TANGENT SPACE VARIATIONS,” presented at the 27th IEEE International Workshop on Machine Learning for Signal Processing (MLSP), Int House Japan, Tokyo, JAPAN, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/53474.