示例代码

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示例代码

SPD 流形即为由 SPD 矩阵所张成的空间，那么对于任意两个SPD矩阵 X, Y ，它们之间的距离通常可以由如下四种方式来计算：

1.仿射不变黎曼度量 (Affine Invariant Riemannian Metric):

d A 2 ( X , Y ) = ∣ ∣ log ⁡ ( X − 1 2 Y X − 1 2 ) ∣ ∣ F 2 d_A^2(X,Y)=|| \log(X^{-\frac{1}{2}}Y X^{-\frac{1}{2}}) ||_F^2 dA2​(X,Y)=∣∣log(X−21​YX−21​)∣∣F2​

2. Stein散度 (Stein divergence):

d S 2 ( X , Y ) = log ⁡ det ⁡ ( X + Y 2 ) − 1 2 log ⁡ det ⁡ ( X Y ) d_S^2(X,Y)= \log \det(\frac{X+Y}{2})-\frac{1}{2}\log \det(XY) dS2​(X,Y)=logdet(2X+Y​)−21​logdet(XY)

3. Jeffrey散度 (Jeffrey divergence):

d J 2 ( X , Y ) = 1 2 T r ( X − 1 Y ) + 1 2 T r ( Y − 1 X ) − n {d{_J^2}}(X,Y) = \frac{1}{2}Tr(X^{-1}Y) + \frac{1}{2}Tr(Y^{-1}X) - n dJ2​(X,Y)=21​Tr(X−1Y)+21​Tr(Y−1X)−n

4.对数欧氏度量 (Log-Euclidean Metric):

d L 2 ( X , Y ) = ∥ log ⁡ ( X ) − log ⁡ ( Y ) ∥ F 2 {{d}{_{L}^2}}(X,Y) = {\parallel{\log\left(X\right)-\log\left(Y\right)}\parallel}{_F^2} dL2​(X,Y)=∥log(X)−log(Y)∥F2​

 
示例代码：
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如果这个内容对于您的研究工作有帮助，我们将非常感激您可以引用我们的文章：[1,2].

[1]. Chen K X, Ren J Y, Wu X J, et al. Covariance Descriptors on a Gaussian Manifold and their Application to Image Set Classification[J]. Pattern Recognition, 2020, 107: 107463. [link]
[2]. Chen K X, Wu X J, Wang R, et al. Riemannian kernel based Nyström method for approximate infinite-dimensional covariance descriptors with application to image set classification[C]//International conference on pattern recognition (ICPR). 2018, 651-656. [link]
 

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