You can think of your data as a matrix, where the rows represent the instances and the columns represent the features. Let's call this matrix $A$. Now $A^TA$ represents feature $\times$ feature, or as it is commonly called: the co-variance matrix. On the other hand, $AA^T$ represents instance $\times$ instance, i.e. the similarity! This matrix is called the gram matrix.
This is useful in computing SVD. SVD is a method to decompose a matrix $A$ into 3 components:
$A=U\Sigma V^T$
U is obtained from the eigenvectors of the gram matrix ( $AA^T$), while V is obtained from the eigenvectors of the co-variance matrix ( $A^TA$).
This is useful in computing SVD. SVD is a method to decompose a matrix $A$ into 3 components:
$A=U\Sigma V^T$
U is obtained from the eigenvectors of the gram matrix ( $AA^T$), while V is obtained from the eigenvectors of the co-variance matrix ( $A^TA$).
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ReplyDeleteI will try to update it more frequently! Thanks for the comment.
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