27,280 research outputs found
A global approach to the refinement of manifold data
A refinement of manifold data is a computational process, which produces a
denser set of discrete data from a given one. Such refinements are closely
related to multiresolution representations of manifold data by pyramid
transforms, and approximation of manifold-valued functions by repeated
refinements schemes. Most refinement methods compute each refined element
separately, independently of the computations of the other elements. Here we
propose a global method which computes all the refined elements simultaneously,
using geodesic averages. We analyse repeated refinements schemes based on this
global approach, and derive conditions guaranteeing strong convergence.Comment: arXiv admin note: text overlap with arXiv:1407.836
Idempotent Generative Network
We propose a new approach for generative modeling based on training a neural
network to be idempotent. An idempotent operator is one that can be applied
sequentially without changing the result beyond the initial application, namely
. The proposed model is trained to map a source distribution
(e.g, Gaussian noise) to a target distribution (e.g. realistic images) using
the following objectives: (1) Instances from the target distribution should map
to themselves, namely . We define the target manifold as the set of all
instances that maps to themselves. (2) Instances that form the source
distribution should map onto the defined target manifold. This is achieved by
optimizing the idempotence term, which encourages the range of
to be on the target manifold. Under ideal assumptions such a process
provably converges to the target distribution. This strategy results in a model
capable of generating an output in one step, maintaining a consistent latent
space, while also allowing sequential applications for refinement.
Additionally, we find that by processing inputs from both target and source
distributions, the model adeptly projects corrupted or modified data back to
the target manifold. This work is a first step towards a ``global projector''
that enables projecting any input into a target data distribution
Image classification by visual bag-of-words refinement and reduction
This paper presents a new framework for visual bag-of-words (BOW) refinement
and reduction to overcome the drawbacks associated with the visual BOW model
which has been widely used for image classification. Although very influential
in the literature, the traditional visual BOW model has two distinct drawbacks.
Firstly, for efficiency purposes, the visual vocabulary is commonly constructed
by directly clustering the low-level visual feature vectors extracted from
local keypoints, without considering the high-level semantics of images. That
is, the visual BOW model still suffers from the semantic gap, and thus may lead
to significant performance degradation in more challenging tasks (e.g. social
image classification). Secondly, typically thousands of visual words are
generated to obtain better performance on a relatively large image dataset. Due
to such large vocabulary size, the subsequent image classification may take
sheer amount of time. To overcome the first drawback, we develop a graph-based
method for visual BOW refinement by exploiting the tags (easy to access
although noisy) of social images. More notably, for efficient image
classification, we further reduce the refined visual BOW model to a much
smaller size through semantic spectral clustering. Extensive experimental
results show the promising performance of the proposed framework for visual BOW
refinement and reduction
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