Mutual coherence is a measure of similarity between two opinions. Although
the notion comes from philosophy, it is essential for a wide range of
technologies, e.g., the Wahl-O-Mat system. In Germany, this system helps voters
to find candidates that are the closest to their political preferences. The
exact computation of mutual coherence is highly time-consuming due to the
iteration over all subsets of an opinion. Moreover, for every subset, an
instance of the SAT model counting problem has to be solved which is known to
be a hard problem in computer science. This work is the first study to
accelerate this computation. We model the distribution of the so-called
confirmation values as a mixture of three Gaussians and present efficient
heuristics to estimate its model parameters. The mutual coherence is then
approximated with the expected value of the distribution. Some of the presented
algorithms are fully polynomial-time, others only require solving a small
number of instances of the SAT model counting problem. The average squared
error of our best algorithm lies below 0.0035 which is insignificant if the
efficiency is taken into account. Furthermore, the accuracy is precise enough
to be used in Wahl-O-Mat-like systems.

本文提出了一种使用高斯混合模型和启发式算法来加速计算 Mutual coherence，达到高效精准的指标估算，可以用在 Wahl-O-Mat 等系统中的新方法。

逼近互相一致性的启发式算法

Heuristic Algorithms for the Approximation of Mutual Coherence

This paper seeks to answer the question: as the (near-) orthogonality of
weights is found to be a favorable property for training deep convolutional
neural networks, how can we enforce it in more effective and easy-to-use ways?
We develop novel orthogonality regularizations on training deep CNNs, utilizing
various advanced analytical tools such as mutual coherence and restricted
isometry property. These plug-and-play regularizations can be conveniently
incorporated into training almost any CNN without extra hassle. We then
benchmark their effects on state-of-the-art models: ResNet, WideResNet, and
ResNeXt, on several most popular computer vision datasets: CIFAR-10, CIFAR-100,
SVHN and ImageNet. We observe consistent performance gains after applying those
proposed regularizations, in terms of both the final accuracies achieved, and
faster and more stable convergences. We have made our codes and pre-trained
models publicly available:
this https URL

本文旨在探讨如何在训练深度卷积神经网络时实现更有效和易于使用的（近）正交性权重。我们利用各种先进的分析工具，如相互相干性和受限等距性质，开发新型正交性正则化方法，可方便地应用于训练几乎任何卷积神经网络。通过在几个流行的计算机视觉数据集上使用 ResNet、WideResNet 和 ResNeXt 等最先进模型的基准测试，我们观察到使用这些提议的正则化方法后，模型的准确率和收敛速度都有更稳定的提高。我们已经将我们的代码和预训练模型公开。

深度卷积神经网络训练中正交正则化是否有更多优势？

Can We Gain More from Orthogonality Regularizations in Training Deep  CNNs?

Compressed Sensing (CS) is a novel technique for simultaneous signal sampling
and compression based on the existence of a sparse representation of signal and
a projected dictionary $PD$, where $P\in\mathbb{R}^{m\times d}$ is the
projection matrix and $D\in\mathbb{R}^{d\times n}$ is the dictionary. To
exactly recover the signal with a small number of measurements $m$, the
projected dictionary $PD$ is expected to be of low mutual coherence. Several
previous methods attempt to find the projection $P$ such that the mutual
coherence of $PD$ can be as low as possible. However, they do not minimize the
mutual coherence directly and thus their methods are far from optimal. Also the
solvers they used lack of the convergence guarantee and thus there has no
guarantee on the quality of their obtained solutions. This work aims to address
these issues. We propose to find an optimal projection by minimizing the mutual
coherence of $PD$ directly. This leads to a nonconvex nonsmooth minimization
problem. We then approximate it by smoothing and solve it by alternate
minimization. We further prove the convergence of our algorithm. To the best of
our knowledge, this is the first work which directly minimizes the mutual
coherence of the projected dictionary with a convergence guarantee. Numerical
experiments demonstrate that the proposed method can recover sparse signals
better than existing methods.

本研究提出通过直接最小化投影词典的互不一致性来找到最优投影，并证明了算法的收敛性。该算法在实验中表现优于现有方法，能更好地恢复稀疏信号。

通过直接相互相干最小化优化压缩感知的投影

Optimized Projections for Compressed Sensing via Direct Mutual Coherence  Minimization

Given a dictionary that consists of multiple blocks and a signal that lives
in the range space of only a few blocks, we study the problem of finding a
block-sparse representation of the signal, i.e., a representation that uses the
minimum number of blocks. Motivated by signal/image processing and computer
vision applications, such as face recognition, we consider the block-sparse
recovery problem in the case where the number of atoms in each block is
arbitrary, possibly much larger than the dimension of the underlying subspace.
To find a block-sparse representation of a signal, we propose two classes of
non-convex optimization programs, which aim to minimize the number of nonzero
coefficient blocks and the number of nonzero reconstructed vectors from the
blocks, respectively. Since both classes of problems are NP-hard, we propose
convex relaxations and derive conditions under which each class of the convex
programs is equivalent to the original non-convex formulation. Our conditions
depend on the notions of mutual and cumulative subspace coherence of a
dictionary, which are natural generalizations of existing notions of mutual and
cumulative coherence. We evaluate the performance of the proposed convex
programs through simulations as well as real experiments on face recognition.
We show that treating the face recognition problem as a block-sparse recovery
problem improves the state-of-the-art results by 10% with only 25% of the
training data.

该论文提出了两类非凸优化方案，旨在寻找最小块数的块稀疏表示，其中互补和累积子空间相干的概念被引入以得到等价的凸松弛，在人脸识别实验中取得了与现有最佳结果相比提高了 10% 的性能。