Learning Pattern Transformation Manifolds with Parametric Atom Selection

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2011-05-02

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Vural, Elif

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https://hdl.handle.net/11511/76770

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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...
Learning Parametric Time-Vertex Graph Processes from Incomplete Realizations Guneyi, Eylem Tugce; Canbolat, Abdullah; Vural, Elif (2021-01-01) © 2021 IEEE.We consider the problem of estimating time-varying graph signals with missing observations, which is of interest in many applications involving data acquisition on irregular topologies. We model time-varying graph signals as jointly stationary time-vertex ARMA graph processes. We formulate the learning of ARMA process parameters as an optimization problem where the joint power spectral density of the model is fit to a rough empirical estimate of the process covariance matrix. We propose a convex...
Learning Graph Signal Representations with Narrowband Spectral Kernels Kar, Osman Furkan; Turhan, Gülce; Vural, Elif (2022-01-01) © 2022 IEEE.In this work, we study the problem of learning graph dictionary models from partially observed graph signals. We represent graph signals in terms of atoms generated by narrowband graph kernels. We formulate an optimization problem where the kernel parameters are learnt jointly with the signal representations under a triple regularization scheme: While the first regularization term aims to control the spectrum of the narrowband kernels, the second term encourages the reconstructed graph signals t...
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...
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 Pattern Transformation Manifolds with Parametric Atom Selection,” 2011, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/76770.