3,891 research outputs found
KCRC-LCD: Discriminative Kernel Collaborative Representation with Locality Constrained Dictionary for Visual Categorization
We consider the image classification problem via kernel collaborative
representation classification with locality constrained dictionary (KCRC-LCD).
Specifically, we propose a kernel collaborative representation classification
(KCRC) approach in which kernel method is used to improve the discrimination
ability of collaborative representation classification (CRC). We then measure
the similarities between the query and atoms in the global dictionary in order
to construct a locality constrained dictionary (LCD) for KCRC. In addition, we
discuss several similarity measure approaches in LCD and further present a
simple yet effective unified similarity measure whose superiority is validated
in experiments. There are several appealing aspects associated with LCD. First,
LCD can be nicely incorporated under the framework of KCRC. The LCD similarity
measure can be kernelized under KCRC, which theoretically links CRC and LCD
under the kernel method. Second, KCRC-LCD becomes more scalable to both the
training set size and the feature dimension. Example shows that KCRC is able to
perfectly classify data with certain distribution, while conventional CRC fails
completely. Comprehensive experiments on many public datasets also show that
KCRC-LCD is a robust discriminative classifier with both excellent performance
and good scalability, being comparable or outperforming many other
state-of-the-art approaches
Peacock Bundles: Bundle Coloring for Graphs with Globality-Locality Trade-off
Bundling of graph edges (node-to-node connections) is a common technique to
enhance visibility of overall trends in the edge structure of a large graph
layout, and a large variety of bundling algorithms have been proposed. However,
with strong bundling, it becomes hard to identify origins and destinations of
individual edges. We propose a solution: we optimize edge coloring to
differentiate bundled edges. We quantify strength of bundling in a flexible
pairwise fashion between edges, and among bundled edges, we quantify how
dissimilar their colors should be by dissimilarity of their origins and
destinations. We solve the resulting nonlinear optimization, which is also
interpretable as a novel dimensionality reduction task. In large graphs the
necessary compromise is whether to differentiate colors sharply between locally
occurring strongly bundled edges ("local bundles"), or also between the weakly
bundled edges occurring globally over the graph ("global bundles"); we allow a
user-set global-local tradeoff. We call the technique "peacock bundles".
Experiments show the coloring clearly enhances comprehensibility of graph
layouts with edge bundling.Comment: Appears in the Proceedings of the 24th International Symposium on
Graph Drawing and Network Visualization (GD 2016
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
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