![Mathematical Implementation
X 2.5 0.5 2.2 1.9 3.1 2.3 2 1 1.5 1.1
Y 2.4 0.7 2.9 2.2 3.0 2.7 1.6 1.1 1.6 0.9
X’ = 1.81, Y’ = 1.91 C = [cov(x,x) cov(x,y)
cov(y,x) cov(y,y)]
Cov(x,y) =](https://image.slidesharecdn.com/principalcomponentanalysispca-241126145401-5fef1cb1/85/Principal-Component-Analysis-PCA-lecture-13-320.jpg)
![X X-X’ (X-X’)(X-X’)
2.5 0.69 0.476
0.5 -1.31 1.7161
Y Y-Y’ (Y-Y’)(Y-Y’)
2.4 0.49 0.1401
0.7 -1.21 1.4641
X Y X-X’ Y-Y’ (X-X’)(Y-Y’)
2.5 2.4 0.69 0.49 0.3381
0.5 0.7 -1.31 -1.21 1.5851
Sum = 5.5490/n-1 Sum = 6.449
Sum = 5.5390
C = [0.6165 0.6154
0.6154 0.7165]](https://image.slidesharecdn.com/principalcomponentanalysispca-241126145401-5fef1cb1/85/Principal-Component-Analysis-PCA-lecture-14-320.jpg)
![C – λ I = 0
[0.6165 0.6154 - λ [ 1 0 = 0
0.6154 0.7165] 0 1]
[0.6165 - λ 0.6154 = 0
0.6154 0.7165 - λ]
λ2
- 1.333λ + 0.0630 = 0
λ 1 = 0.0490
λ 2 = 1.2840
C V =
λV](https://image.slidesharecdn.com/principalcomponentanalysispca-241126145401-5fef1cb1/85/Principal-Component-Analysis-PCA-lecture-16-320.jpg)
Principal Component Analysis(PCA) lecture
- 1. Principal Component Analysis(PCA) Presented By: Vishal Gour Deep Learning
- 2. Contents 1. Theory 2. Mathematical Calculation 3. Python Implementation
- 6. What if we get rid of non-important features? 1.Faster Training. 2.Data Visualization becomes easier.
- 12. PCA is called the dimensionality reduction technique as it can help reduce dimensions.
- 13. Mathematical Implementation X 2.5 0.5 2.2 1.9 3.1 2.3 2 1 1.5 1.1 Y 2.4 0.7 2.9 2.2 3.0 2.7 1.6 1.1 1.6 0.9 X’ = 1.81, Y’ = 1.91 C = [cov(x,x) cov(x,y) cov(y,x) cov(y,y)] Cov(x,y) =
- 14. X X-X’ (X-X’)(X-X’) 2.5 0.69 0.476 0.5 -1.31 1.7161 Y Y-Y’ (Y-Y’)(Y-Y’) 2.4 0.49 0.1401 0.7 -1.21 1.4641 X Y X-X’ Y-Y’ (X-X’)(Y-Y’) 2.5 2.4 0.69 0.49 0.3381 0.5 0.7 -1.31 -1.21 1.5851 Sum = 5.5490/n-1 Sum = 6.449 Sum = 5.5390 C = [0.6165 0.6154 0.6154 0.7165]
- 15. The eigenvectors of the Covariance matrix are actually the directions of the axes where there is the most variance(most information) and that we call Principal Components. And eigenvalues are simply the coefficients attached to eigenvectors, which give the amount of variance carried in each Principal Component.
- 16. C – λ I = 0 [0.6165 0.6154 - λ [ 1 0 = 0 0.6154 0.7165] 0 1] [0.6165 - λ 0.6154 = 0 0.6154 0.7165 - λ] λ2 - 1.333λ + 0.0630 = 0 λ 1 = 0.0490 λ 2 = 1.2840 C V = λV
- 17. Final_Data = Eigen_VectorT X Original_dataT