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arXiv 2502.08098cs.LGcs.NE

相似性度量的无监督分类

Unsupervised categorization of similarity measures

The University of Tokyo(东京大学)

Yoshiyuki Ohmura, Wataru Shimaya, Yasuo Kuniyoshi

AI总结:

针对对象特征对应度量空间的无监督分类机制未知问题,提出通过表示学习使神经网络满足代数独立性、仅约束空间独立而非轴独立的方法,为独立度量空间无监督分类提供一般条件,推动神经网络功能分化数学理论发展。

摘要:

通常,对象可基于颜色或形状等特征进行区分。特别地,假设此类特征的相似性判断可在不同度量空间中独立处理。然而,对应对象特征的度量空间的无监督分类机制仍未知。本文表明,人工神经网络系统可通过表示学习自主分类度量空间,以满足神经网络间的代数独立性,并将感官信息投影到多个高维度量空间,独立评估特征间的差异与相似性。传统方法常约束潜在空间的轴相互独立或正交,但独立轴不适用于度量空间分类:相互独立的高维度量空间并非由独立轴唯一确定,因独立轴的任意组合可形成相互独立的空间,即独立轴无法自然分类颜色空间、形状空间等不同特征空间,故约束轴独立会使高维度量空间分类困难。为解决该问题,我们提出仅约束空间相互独立、而非约束组成轴独立的方法。我们的理论为独立度量空间的无监督分类提供一般条件,推动了神经网络功能分化的数学理论发展。

英文摘要:

In general, objects can be distinguished on the basis of their features, such as color or shape. In particular, it is assumed that similarity judgments about such features can be processed independently in different metric spaces. However, the unsupervised categorization mechanism of metric spaces corresponding to object features remains unknown. Here, we show that the artificial neural network system can autonomously categorize metric spaces through representation learning to satisfy the algebraic independence between neural networks, and project sensory information onto multiple high-dimensional metric spaces to independently evaluate the differences and similarities between features. Conventional methods often constrain the axes of the latent space to be mutually independent or orthogonal. However, the independent axes are not suitable for categorizing metric spaces. High-dimensional metric spaces that are independent of each other are not uniquely determined by the mutually independent axes, because any combination of independent axes can form mutually independent spaces. In other words, the mutually independent axes cannot be used to naturally categorize different feature spaces, such as color space and shape space. Therefore, constraining the axes to be mutually independent makes it difficult to categorize high-dimensional metric spaces. To overcome this problem, we developed a method to constrain only the spaces to be mutually independent and not the composed axes to be independent. Our theory provides general conditions for the unsupervised categorization of independent metric spaces, thus advancing the mathematical theory of functional differentiation of neural networks.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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