Here is a term co-occurrence matrix, given three documents and two terms: A = 100 0 1 1 0 0 1 and here is its singular value decomposition: A = USVT 0 1 0 U = 0.85 0 -0.53 0.53 0 0.85 1.62 0 0 1 0 S = VT = 0 0 0 0.62 0 1 0 0.53 0 -0.85 0.85 0 0.53 Perform a dimensionality reduction on this by removing one singular value, and reconstructing the matrix, Â.
Here is a term co-occurrence matrix, given three documents and two terms: A = 100 0 1 1 0 0 1 and here is its singular value decomposition: A = USVT 0 1 0 U = 0.85 0 -0.53 0.53 0 0.85 1.62 0 0 1 0 S = VT = 0 0 0 0.62 0 1 0 0.53 0 -0.85 0.85 0 0.53 Perform a dimensionality reduction on this by removing one singular value, and reconstructing the matrix, Â.
Question
Transcribed Image Text:Here is a term co-occurrence matrix, given three documents and two terms:
A =
100
0 1 1
0 0 1
and here is its singular value decomposition:
A = USVT
0
1
0
U =
0.85 0 -0.53
0.53 0 0.85
1.62 0
0
1
0
S =
VT
=
0 0
0 0.62
0 1 0
0.53 0 -0.85
0.85 0 0.53
Perform a dimensionality reduction on this by removing one singular value, and reconstructing the matrix,
Â.
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