5,278 research outputs found
Classification of geometrical objects by integrating currents and functional data analysis. An application to a 3D database of Spanish child population
This paper focuses on the application of Discriminant Analysis to a set of
geometrical objects (bodies) characterized by currents. A current is a relevant
mathematical object to model geometrical data, like hypersurfaces, through
integration of vector fields along them. As a consequence of the choice of a
vector-valued Reproducing Kernel Hilbert Space (RKHS) as a test space to
integrate hypersurfaces, it is possible to consider that hypersurfaces are
embedded in this Hilbert space. This embedding enables us to consider
classification algorithms of geometrical objects. A method to apply Functional
Discriminant Analysis in the obtained vector-valued RKHS is given. This method
is based on the eigenfunction decomposition of the kernel. So, the novelty of
this paper is the reformulation of a size and shape classification problem in
Functional Data Analysis terms using the theory of currents and vector-valued
RKHS. This approach is applied to a 3D database obtained from an anthropometric
survey of the Spanish child population with a potential application to online
sales of children's wear
Kernel Cross-Correlator
Cross-correlator plays a significant role in many visual perception tasks,
such as object detection and tracking. Beyond the linear cross-correlator, this
paper proposes a kernel cross-correlator (KCC) that breaks traditional
limitations. First, by introducing the kernel trick, the KCC extends the linear
cross-correlation to non-linear space, which is more robust to signal noises
and distortions. Second, the connection to the existing works shows that KCC
provides a unified solution for correlation filters. Third, KCC is applicable
to any kernel function and is not limited to circulant structure on training
data, thus it is able to predict affine transformations with customized
properties. Last, by leveraging the fast Fourier transform (FFT), KCC
eliminates direct calculation of kernel vectors, thus achieves better
performance yet still with a reasonable computational cost. Comprehensive
experiments on visual tracking and human activity recognition using wearable
devices demonstrate its robustness, flexibility, and efficiency. The source
codes of both experiments are released at https://github.com/wang-chen/KCCComment: The Thirty-Second AAAI Conference on Artificial Intelligence
(AAAI-18
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
A Stable Multi-Scale Kernel for Topological Machine Learning
Topological data analysis offers a rich source of valuable information to
study vision problems. Yet, so far we lack a theoretically sound connection to
popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In
this work, we establish such a connection by designing a multi-scale kernel for
persistence diagrams, a stable summary representation of topological features
in data. We show that this kernel is positive definite and prove its stability
with respect to the 1-Wasserstein distance. Experiments on two benchmark
datasets for 3D shape classification/retrieval and texture recognition show
considerable performance gains of the proposed method compared to an
alternative approach that is based on the recently introduced persistence
landscapes
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