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공부한 것

선형대수 - 4

1. Gramian Angular Field

Gramian Angular Field — pyts 0.11.0 documentation

 

Gramian Angular Field — pyts 0.11.0 documentation

Note Click here to download the full example code Gramian Angular Field A Gramian Angular Field is an image obtained from a time series, representing some temporal correlation between each time point. Two methods are available: Gramian Angular Summation Fi

pyts.readthedocs.io

" ...an image obtained from a time series, representing some temporal correlation between each time point... "

time point 간의 상관관계를 이미지화 시킨 것이라 이해하면 될 듯.

 

2.  Haversine Distance

sklearn.metrics.pairwise.haversine_distances — scikit-learn 1.0 documentation

 

sklearn.metrics.pairwise.haversine_distances

 

scikit-learn.org

D(x, y) = 2\arcsin[\sqrt{\sin^2((x1 - y1) / 2) + \cos(x1)\cos(y1)\sin^2((x2 - y2) / 2)}]

1, 2는 각각 위도와 경도.

지구는 구형에 가깝기 때문에 haversine distance는 지구 표면의 두 지점 간의 거리에 오차범위 1% 내의 정교한 값을 제시한다.

 

3. Gram-Schmidt Method

Gram-Schmidt Method – Calculus Tutorials (hmc.edu)

 

Gram-Schmidt Method – Calculus Tutorials

The Gram-Schmidt Algorithm – HMC Calculus Tutorial In any inner product space, we can choose the basis in which to work. It often greatly simplifies calculations to work in an orthogonal basis. For one thing, if $ S = \{ {\bf v}_1, {\bf v}_2, \dots , {\b

math.hmc.edu

직각이 아닌 기저를 직각으로 처리하여 계산 처리를 단순화하기 위함.

 

4. Eigen

- eigenvector : a vector that lies along the same span both before and after aplying a linear trasform to a space

- 선형변환을 가해도 동일한 방향으로 스팬하는 벡터. 크기만 변하는 고유 벡터 정도로 이해해도 좋을 듯.

- eigenvalue : the amount that an eigenvector has been stretched in the process

- 3차원에서 eigenvector를 구하려면 회전축을 찾으면 된다.

Eigenvalues and Eigenvectors (swarthmore.edu)

 

Eigenvalues and Eigenvectors

This page is a brief introduction to eigenvalue/eigenvector problems (don't worry if you haven't heard of the latter).  Before reading this you should feel comfortable with basic matrix operations.  If you are confident in your ability with this material

lpsa.swarthmore.edu

 

5. Diagonalisation

Diagonalizable matrix - Wikipedia

 

Diagonalizable matrix - Wikipedia

From Wikipedia, the free encyclopedia Jump to navigation Jump to search matrices similar to diagonal matrices This article is about matrix diagonalization in linear algebra. For other uses, see Diagonalization. In linear algebra, a square matrix A {\displa

en.wikipedia.org

- 이건 아직 명확히 이해 못했다. 좀더 공부해보고 보충하기.

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