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Covariance & Gram Matrices

https://cbmm.mit.edu/video/nonlinear-dimensionality-reduction 

What are "Covariance Matrix" and "Gram Matrix"?

Let you understand them with example.
Suppose you have 3 data of (ID, age, height, weight, heart rate) as 
(1, 25, 183, 70, 60) 
(2, 30, 160, 63, 70) 
(3, 40, 172, 80, 75)
The dimension of data is 5, number of data is 3.
You can form a 5x3 data matrix, we call it X as:
1    2    3
25  30  40
183 160 172
70  63  80
60  70  75
The covariance matrix C is defined as C=XX^T with dimension 5x5 (dimension over "parameters" of data)
The gram matrix K is defined as K=X^TX with dimension 3x3  (dimension over "number" of data)
#video  #online  #Matrix  #example  #heart 
分類:學習

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