4,219 research outputs found
Nonlinear Supervised Dimensionality Reduction via Smooth Regular Embeddings
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 algorithms.
Motivated by these performance bounds, we propose a supervised manifold
learning method that computes a nonlinear embedding while constructing a smooth
and regular interpolation function that extends the embedding to the whole data
space in order to achieve satisfactory generalization. The embedding and the
interpolator are jointly learnt such that the Lipschitz regularity of the
interpolator is imposed while ensuring the separation between different
classes. Experimental results on several image data sets show that the proposed
method outperforms traditional classifiers and the supervised dimensionality
reduction algorithms in comparison in terms of classification accuracy in most
settings
Robust Image Recognition Based on a New Supervised Kernel Subspace Learning Method
Fecha de lectura de Tesis Doctoral: 13 de septiembre 2019Image recognition is a term for computer technologies that can recognize certain people, objects or other targeted subjects through the use of algorithms and machine learning concepts. Face recognition is one of the most popular techniques to achieve the goal of figuring out the identity of a person. This study has been conducted to develop a new non-linear subspace learning method named “supervised kernel locality-based discriminant neighborhood embedding,” which performs data classification by learning an optimum embedded subspace from a principal high dimensional space. In this approach, not only is a nonlinear and complex variation of face images effectively represented using nonlinear kernel mapping, but local structure information of data from the same class and discriminant information from distinct classes are also simultaneously preserved to further improve final classification performance. Moreover, to evaluate the robustness of the proposed method, it was compared with several well-known pattern recognition methods through comprehensive experiments with six publicly accessible datasets. In this research, we particularly focus on face recognition however, two other types of databases rather than face databases are also applied to well investigate the implementation of our algorithm. Experimental results reveal that our method consistently outperforms its competitors across a wide range of dimensionality on all the datasets. SKLDNE method has reached 100 percent of recognition rate for Tn=17 on the Sheffield, 9 on the Yale, 8 on the ORL, 7 on the Finger vein and 11on the Finger Knuckle respectively, while the results are much lower for other methods. This demonstrates the robustness and effectiveness of the proposed method
Extrinsic Methods for Coding and Dictionary Learning on Grassmann Manifolds
Sparsity-based representations have recently led to notable results in
various visual recognition tasks. In a separate line of research, Riemannian
manifolds have been shown useful for dealing with features and models that do
not lie in Euclidean spaces. With the aim of building a bridge between the two
realms, we address the problem of sparse coding and dictionary learning over
the space of linear subspaces, which form Riemannian structures known as
Grassmann manifolds. To this end, we propose to embed Grassmann manifolds into
the space of symmetric matrices by an isometric mapping. This in turn enables
us to extend two sparse coding schemes to Grassmann manifolds. Furthermore, we
propose closed-form solutions for learning a Grassmann dictionary, atom by
atom. Lastly, to handle non-linearity in data, we extend the proposed Grassmann
sparse coding and dictionary learning algorithms through embedding into Hilbert
spaces.
Experiments on several classification tasks (gender recognition, gesture
classification, scene analysis, face recognition, action recognition and
dynamic texture classification) show that the proposed approaches achieve
considerable improvements in discrimination accuracy, in comparison to
state-of-the-art methods such as kernelized Affine Hull Method and
graph-embedding Grassmann discriminant analysis.Comment: Appearing in International Journal of Computer Visio
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