将高斯混合模型嵌入对称正定矩阵流形，构建新距离度量。
Distance Measure Based on an Embedding of the Manifold of K-Component Gaussian Mixture Models into the Manifold of Symmetric Positive Definite Matrices
- 通过流形嵌入将多分量GMM映射到对称正定矩阵空间。
- 提出下界距离度量，在3个纹理数据集上准确率达92%以上。
- 适合需要高效相似性度量的模式识别与机器学习任务。
本文提出一种基于将K分量高斯混合模型（GMM）嵌入对称正定矩阵流形的方法，构建其距离度量。证明了K分量GMM可嵌入该流形并构成子流形，且在拉回度量下与诱导度量保持等距。由此获得费舍尔-罗信息度量的通用下界，作为GMM流形上的距离度量，并用于衡量GMM相似性。在标准机器学习基准测试中验证了该框架的有效性：在UIUC、KTH-TIPS和UMD纹理识别数据集上分别达到98%、92%和93.33%的准确率。
原文摘要 · Abstract (English)
In this paper, a distance between the Gaussian Mixture Models(GMMs) is obtained based on an embedding of the K-component Gaussian Mixture Model into the manifold of the symmetric positive definite matrices. Proof of embedding of K-component GMMs into the manifold of symmetric positive definite matrices is given and shown that it is a submanifold. Then, proved that the manifold of GMMs with the pullback of induced metric is isometric to the submanifold with the induced metric. Through this embedding we obtain a general lower bound for the Fisher-Rao metric. This lower bound is a distance measure on the manifold of GMMs and we employ it for the similarity measure of GMMs. The effectiveness of this framework is demonstrated through an experiment on standard machine learning benchmarks, achieving accuracy of 98%, 92%, and 93.33% on the UIUC, KTH-TIPS, and UMD texture recognition datasets respectively.
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