合并树的瓦斯斯坦自动编码器 (和持久图)
IEEE transactions on visualization and computer graphics
|November 28, 2023
概括
本研究介绍了Wasserstein自动编码合并树 (MT-WAE),这是一个用于准确编码复杂数据结构的新型神经网络. MT-WAE为数据分析提供高效的合并树压缩和维度减小.
科学领域:
- 计算拓学的计算拓.
- 机器学习 机器学习
- 数据分析数据分析
背景情况:
- 经典的自动编码器运行在向量化数据上,限制其应用到复杂的拓结构,如合并树.
- 以前用于合并树编码的线性方法已经显示出希望,但缺乏非线性方法的灵活性.
研究的目的:
- 为了介绍一个新的计算框架,Wasserstein自动编码合并树 (MT-WAE),用于合并树的度量空间.
- 扩展自编码神经网络的功能,以更高的准确性和可解释性处理拓数据结构.
- 证明框架在数据压缩和维度减少方面的效率和适用性.
主要方法:
- 开发了一种Wasserstein自动编码器 (MT-WAE),该自动编码器直接运行在合并树的度量空间上.
- 扩展了框架以处理持久性图.
- 引入了惩罚术语,以保护潜空间中的瓦瑟斯坦距离和集群.
主要成果:
- 与传统的自动编码器相比,MT-WAE实现了更高的准确性和可解释性.
- 证明了有效的合并树压缩和维度减小,用于集成数据的视觉分析.
- MT-WAE计算是高效的,在公共合奏中平均分钟.
结论:
- MT-WAE为合并树编码提供了强大的非线性概括,扩展了以前的线性方法.
- 该框架具有多功能性,适用于压缩,缩小维度和分析拓数据.
- 一个C++实现确保了可重现性,并促进了进一步的研究.
更多相关视频
14:38Creating Objects and Object Categories for Studying Perception and Perceptual Learning
Published on: November 2, 2012
11.9K
09:38Generalized Psychophysiological Interaction PPI Analysis of Memory Related Connectivity in Individuals at Genetic Risk for Alzheimer's Disease
Published on: November 14, 2017
14.9K
相关概念视频
Woodward–Hoffmann Selection Rules and Microscopic Reversibility
3.1K
Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
3.1K
pV-Diagrams
4.2K
The pV diagram, which is a graph of pressure versus volume of the gas under study, is helpful in describing certain aspects of the substance. When the substance behaves like an ideal gas, the ideal gas equation describes the relationship between its pressure and volume. On a pV diagram, it is common to plot an isotherm, which is a curve showing p as a function of V with the number of molecules and the temperature fixed. Then, for an ideal gas, the product of the pressure of the gas and its...
4.2K
Sequence Networks of Rotating Machines
103
A Y-connected synchronous generator, grounded through a neutral impedance, is designed to produce balanced internal phase voltages with only positive-sequence components. The generator's sequence networks include a source voltage that is exclusively in the positive-sequence network. The sequence components of line-to-ground voltages at the generator terminals illustrate this configuration.
Zero-sequence current induces a voltage drop across the generator's neutral impedance and other...
Zero-sequence current induces a voltage drop across the generator's neutral impedance and other...
103
Divergence and Stokes' Theorems
1.6K
The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write...
1.6K
Divergence and Curl
1.7K
The divergence of a vector field at a point is the net outward flow of the flux out of a small volume through a closed surface enclosing the volume, as the volume tends to zero. More practically, divergence measures how much a vector field spreads out or diverges from a given point. For an outgoing flux, conventionally, the divergence is positive. The diverging point is often called the "source" of the field. Meanwhile, the negative divergence of a vector field at a point means that the...
1.7K
Wald-Wolfowitz Runs Test II
245
The Wald-Wolfowitz runs test, commonly referred to as the runs test, is a nonparametric test used to assess the randomness of ordered data. The test evaluates the number of runs, which are consecutive sequences of similar elements within the data. If the number of runs is significantly higher or lower than expected, the data is considered non-random, indicating a detectable pattern or structure.
For binary data, runs are identified using symbols such as + and −, or equivalently, 1s and...
For binary data, runs are identified using symbols such as + and −, or equivalently, 1s and...
245
