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Linear Algebra Methods for Data Mining

Data

Mining

,Linear

Algebra

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Linear Algebra Methods for Data Mining, Spring 2007, University of Helsinki

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Linear Algebra Methods

for Data Mining

Saara Hyv¨onen, Saara.Hyvonen@cs.helsinki.ﬁ

Spring 2007

Overview of some topics covered

and some topics not covered

on this course

Linear Algebra Methods for Data Mining, Spring 2007, University of He lsinki

Linear algebra tool kit

• QR iteration

• eigenvalues, eigenvalue decomposition, generalized eigenvalue problem

• singular value decomposition SVD

• NMF

• power method (for ﬁnding eigenvalues and -vectors)

Linear Algebra Methods for Data Mining, Spring 2007, University of Helsinki 1

Data mining tasks encountered

• regression

• classiﬁcation

• clustering

• ﬁnding latent variables

• visualizing and exploration

• ranking

Linear Algebra Methods for Data Mining, Spring 2007, University of Helsinki 2

QR was used for ...

• orthogonalizing a set of (basis) vectors X = QR.

• solving the least-squares problem:

krk

= kb −Axk

= kQ

b −





= kb

− Rxk

+ kb

• least squares problems were encountered e.g. when we wish to express

a matrix A ∈ R

m×n

in terms of a set of basis vectors X ∈ R

m×k

k < m.

Linear Algebra Methods for Data Mining, Spring 2007, University of Helsinki 3

Eigenvalues/vectors were encountered in...

Linear Algebra Methods for Data Mining, Spring 2007, University of Helsinki 4

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chouun711

2012-12-27

只是整套课件的最后一讲……

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