Learning pattern transformation manifolds for classification

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.


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...
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...
Software metamaterials: Transformation media based multi-scale techniques for computational electromagnetics
Ozgun, Ozlem; Kuzuoğlu, Mustafa (2013-03-01)
This paper presents computational models employing special transformation-based media-which we call software metamaterials-for the purpose of enhancing the ability of numerical modeling methods for solving multi-scale electromagnetic boundary value problems involving features with multiple length or frequency scales or both. The multi-scale problems, in general, suffer from difficulties in mesh generation and the number of unknowns due to certain meshing requirements dictated by the fine features of the pro...
Citation Formats
E. Vural, “Learning pattern transformation manifolds for classification,” 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48029.