Learning pattern transformation manifolds for classification

Download

index.pdf

Date

2013-02-21

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

192
views

110
downloads

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 consists of a linear combination of analytic atoms selected from a continuous dictionary manifold. We propose an iterative algorithm for jointly building multiple manifolds such that the classification accuracy is promoted in the learning of the representative patterns. We present a DC (Difference-of-Convex) optimization scheme that is applicable to a wide range of transformation and dictionary models, and demonstrate its application to transformation manifolds generated by the rotation, translation and scaling of a reference image. Experimental results suggest that the proposed method yields a high classification accuracy compared to reference methods based on individual manifold building or locally linear manifold approximations.

Subject Keywords

Manifold Learning, Pattern Transformation Manifolds, Pattern Classification, Transformation-Invariance, Sparse Approximations

URI

https://hdl.handle.net/11511/48029

DOI

https://doi.org/10.1109/icip.2012.6467072

Collections

Department of Electrical and Electronics Engineering, Conference / Seminar

Suggestions

OpenMETU
Core

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...
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...
Curvature analysis of pattern transformation manifolds Vural, Elif (2010-12-03) Transformation manifolds are quite attractive for image analysis applications that require transformation invariance properties. The geometric structure of a transformation manifold has a profound influence on the design of processing algorithm, and the curvature is a major parameter in the characterization of the manifold geometry. We propose here a procedure for the computation of an upper bound for the maximum principal curvature of a pattern transformation manifold. We provide an analytical formulation ...

Citation Formats

E. Vural, “Learning pattern transformation manifolds for classification,” 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48029.