Learning Smooth Pattern Transformation Manifolds

Download

index.pdf

Date

2013-04-01

Author

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

62
views

0
downloads

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 and classification. For the approximation problem, we propose a greedy method that constructs a representative pattern by selecting analytic atoms from a continuous dictionary manifold. We present a dc optimization scheme that is applicable to a wide range of transformation and dictionary models, and demonstrate its application to the transformation manifolds generated by the rotation, translation, and anisotropic scaling of a reference pattern. Then, we generalize this approach to a setting with multiple transformation manifolds, where each manifold represents a different class of signals. We present an iterative multiple-manifold-building algorithm such that the classification accuracy is promoted in the learning of the representative patterns. The experimental results suggest that the proposed methods yield high accuracy in the approximation and classification of data compared with some reference methods, while the invariance to geometric transformations is achieved because of the transformation manifold model.

Subject Keywords

Manifold learning, Pattern transformation manifolds, Pattern classification, Transformation-invariance, Sparse approximations

URI

https://hdl.handle.net/11511/35066

Journal

IEEE TRANSACTIONS ON IMAGE PROCESSING

DOI

https://doi.org/10.1109/tip.2012.2227768

Collections

Department of Electrical and Electronics Engineering, Article

Suggestions

OpenMETU
Core

Learning pattern transformation manifolds for classification Vural, Elif (2013-02-21) Manifold models provide low-dimensional representations that are useful for analyzing and classifying data in a transformation-invariant way. In this paper we study the problem of jointly building multiple pattern transformation manifolds from a collection of image sets, where each set consists of observations from a class of geometrically transformed signals. We build the manifolds such that each manifold approximates a different signal class. Each manifold is characterized by a representative pattern that...
Distance-based discretization of parametric signal manifolds Vural, Elif (2010-06-28) The characterization of signals and images in manifolds often lead to efficient dimensionality reduction algorithms based on manifold distance computation for analysis or classification tasks. We propose in this paper a method for the discretization of signal manifolds given in a parametric form. We present an iterative algorithm for the selection of samples on the manifold that permits to minimize the average error in the manifold distance computation. Experimental results with image appearance manifolds d...
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...
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 semi-supervised nonlinear embeddings for domain-adaptive pattern recognition Vural, Elif (null; 2019-05-20) We study the problem of learning nonlinear data embeddings in order to obtain representations for efficient and domain-invariant recognition of visual patterns. Given observations of a training set of patterns from different classes in two different domains, we propose a method to learn a nonlinear mapping of the data samples from different domains into a common domain. The nonlinear mapping is learnt such that the class means of different domains are mapped to nearby points in the common domain in order to...

Citation Formats

E. Vural, “Learning Smooth Pattern Transformation Manifolds,” IEEE TRANSACTIONS ON IMAGE PROCESSING, pp. 1311–1325, 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/35066.