59 research outputs found
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On Automorphisms and Focal Subgroups of Blocks
Given a p-block B of a finite group with defect group P and fusion system on P, we show that the rank of the group is invariant under stable equivalences of Morita type. The main ingredients are the construction, due to Broué and Puig, a theorem of Weiss on linear source modules, arguments of Hertweck and Kimmerle applying Weiss’ theorem to blocks, and connections with integrable derivations in the Hochschild cohomology of block algebras
Backprojection for Training Feedforward Neural Networks in the Input and Feature Spaces
After the tremendous development of neural networks trained by
backpropagation, it is a good time to develop other algorithms for training
neural networks to gain more insights into networks. In this paper, we propose
a new algorithm for training feedforward neural networks which is fairly faster
than backpropagation. This method is based on projection and reconstruction
where, at every layer, the projected data and reconstructed labels are forced
to be similar and the weights are tuned accordingly layer by layer. The
proposed algorithm can be used for both input and feature spaces, named as
backprojection and kernel backprojection, respectively. This algorithm gives an
insight to networks with a projection-based perspective. The experiments on
synthetic datasets show the effectiveness of the proposed method.Comment: Accepted (to appear) in International Conference on Image Analysis
and Recognition (ICIAR) 2020, Springe
Principal Component Analysis Using Structural Similarity Index for Images
Despite the advances of deep learning in specific tasks using images, the
principled assessment of image fidelity and similarity is still a critical
ability to develop. As it has been shown that Mean Squared Error (MSE) is
insufficient for this task, other measures have been developed with one of the
most effective being Structural Similarity Index (SSIM). Such measures can be
used for subspace learning but existing methods in machine learning, such as
Principal Component Analysis (PCA), are based on Euclidean distance or MSE and
thus cannot properly capture the structural features of images. In this paper,
we define an image structure subspace which discriminates different types of
image distortions. We propose Image Structural Component Analysis (ISCA) and
also kernel ISCA by using SSIM, rather than Euclidean distance, in the
formulation of PCA. This paper provides a bridge between image quality
assessment and manifold learning opening a broad new area for future research.Comment: Paper for the methods named "Image Structural Component Analysis
(ISCA)" and "Kernel Image Structural Component Analysis (Kernel ISCA)
Weighted Fisher Discriminant Analysis in the Input and Feature Spaces
Fisher Discriminant Analysis (FDA) is a subspace learning method which
minimizes and maximizes the intra- and inter-class scatters of data,
respectively. Although, in FDA, all the pairs of classes are treated the same
way, some classes are closer than the others. Weighted FDA assigns weights to
the pairs of classes to address this shortcoming of FDA. In this paper, we
propose a cosine-weighted FDA as well as an automatically weighted FDA in which
weights are found automatically. We also propose a weighted FDA in the feature
space to establish a weighted kernel FDA for both existing and newly proposed
weights. Our experiments on the ORL face recognition dataset show the
effectiveness of the proposed weighting schemes.Comment: Accepted (to appear) in International Conference on Image Analysis
and Recognition (ICIAR) 2020, Springe
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