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# Major and minor axisprincipal axes using k-PCAkernel PCA on a 2D dataset

x1 = [0.97955,0.7177,0.2374,-0.4374,-1.1126,-0.9457,-0.5329,0.2991,0.9846,1.2218];

y1 = [-0.1727,0.6582,0.7419,0.6433,0.3406,-0.0354,-1.0199,-0.9105,-0.6879,0.2234];

x1 = [0.97955,0.7177,0.2374,-0.4374,-1.1126,-0.9457,-0.5329,0.2991,0.9846,1.2218];

y1 = [-0.1727,0.6582,0.7419,0.6433,0.3406,-0.0354,-1.0199,-0.9105,-0.6879,0.2234];


x2 = [1.7821,1.5386,0.4578,-0.7798,-1.5705,-1.8621,-1.2983,0.1988,1.3197,2.4700];

y2 = [-0.1231,1.4351,1.9311,1.9097,0.5310,-0.9644,-2.0165,-1.8719,-1.3210,-0.03921]

x2 = [1.7821,1.5386,0.4578,-0.7798,-1.5705,-1.8621,-1.2983,0.1988,1.3197,2.4700];

y2 = [-0.1231,1.4351,1.9311,1.9097,0.5310,-0.9644,-2.0165,-1.8719,-1.3210,-0.03921]


I used the Gaussian Kernel PCA algorithm with sigma = sqrt(10)sigma = sqrt(10).

After finding my K$$K$$ matrix, I then sorted the eigenvectors of K$$K$$ and took the first two largest eigenvectors

column1 [0.1528 0.1553 0.0666 -0.0741 -0.2206 -0.2197 -0.2078 -0.0366 0.1155 0.2222 0.2882 0.3119 0.1572 -0.050 -0.275 -0.4011 -0.3586 -0.1172 0.12466 0.36817]

and column2 [0.0930 -0.1122 -0.1716 -0.2018 -0.1777 -0.0861 0.15884 0.20136 0.20255 0.02489 0.13522 -0.1859 -0.3636 -0.4339 -0.2350 0.04714 0.26192 0.35898 0.33280 0.15149]

column1 [0.1528 0.1553 0.0666
-0.0741
-0.2206
-0.2197
-0.2078
-0.0366
0.1155
0.2222
0.2882
0.3119
0.1572
-0.050
-0.275
-0.4011
-0.3586
-0.1172
0.12466
0.36817]

and column2 [0.0930
-0.1122
-0.1716
-0.2018
-0.1777
-0.0861
0.15884
0.20136
0.20255
0.02489
0.13522
-0.1859
-0.3636
-0.4339
-0.2350
0.04714
0.26192
0.35898
0.33280
0.15149]


# Major and minor axis using k-PCA

x1 = [0.97955,0.7177,0.2374,-0.4374,-1.1126,-0.9457,-0.5329,0.2991,0.9846,1.2218];

y1 = [-0.1727,0.6582,0.7419,0.6433,0.3406,-0.0354,-1.0199,-0.9105,-0.6879,0.2234];

x2 = [1.7821,1.5386,0.4578,-0.7798,-1.5705,-1.8621,-1.2983,0.1988,1.3197,2.4700];

y2 = [-0.1231,1.4351,1.9311,1.9097,0.5310,-0.9644,-2.0165,-1.8719,-1.3210,-0.03921]

I used the Gaussian Kernel PCA algorithm with sigma = sqrt(10).

After finding my K matrix, I then sorted the eigenvectors of K and took the first two largest eigenvectors

column1 [0.1528 0.1553 0.0666 -0.0741 -0.2206 -0.2197 -0.2078 -0.0366 0.1155 0.2222 0.2882 0.3119 0.1572 -0.050 -0.275 -0.4011 -0.3586 -0.1172 0.12466 0.36817]

and column2 [0.0930 -0.1122 -0.1716 -0.2018 -0.1777 -0.0861 0.15884 0.20136 0.20255 0.02489 0.13522 -0.1859 -0.3636 -0.4339 -0.2350 0.04714 0.26192 0.35898 0.33280 0.15149]

# Major and minor principal axes using kernel PCA on a 2D dataset

x1 = [0.97955,0.7177,0.2374,-0.4374,-1.1126,-0.9457,-0.5329,0.2991,0.9846,1.2218];

y1 = [-0.1727,0.6582,0.7419,0.6433,0.3406,-0.0354,-1.0199,-0.9105,-0.6879,0.2234];

x2 = [1.7821,1.5386,0.4578,-0.7798,-1.5705,-1.8621,-1.2983,0.1988,1.3197,2.4700];

y2 = [-0.1231,1.4351,1.9311,1.9097,0.5310,-0.9644,-2.0165,-1.8719,-1.3210,-0.03921]


I used the Gaussian Kernel PCA algorithm with sigma = sqrt(10).

After finding my $$K$$ matrix, I then sorted the eigenvectors of $$K$$ and took the first two largest eigenvectors.

column1 [0.1528 0.1553 0.0666
-0.0741
-0.2206
-0.2197
-0.2078
-0.0366
0.1155
0.2222
0.2882
0.3119
0.1572
-0.050
-0.275
-0.4011
-0.3586
-0.1172
0.12466
0.36817]

and column2 [0.0930
-0.1122
-0.1716
-0.2018
-0.1777
-0.0861
0.15884
0.20136
0.20255
0.02489
0.13522
-0.1859
-0.3636
-0.4339
-0.2350
0.04714
0.26192
0.35898
0.33280
0.15149]

1

# Major and minor axis using k-PCA

I have these two data sets:

x1 = [0.97955,0.7177,0.2374,-0.4374,-1.1126,-0.9457,-0.5329,0.2991,0.9846,1.2218];

y1 = [-0.1727,0.6582,0.7419,0.6433,0.3406,-0.0354,-1.0199,-0.9105,-0.6879,0.2234];

and

x2 = [1.7821,1.5386,0.4578,-0.7798,-1.5705,-1.8621,-1.2983,0.1988,1.3197,2.4700];

y2 = [-0.1231,1.4351,1.9311,1.9097,0.5310,-0.9644,-2.0165,-1.8719,-1.3210,-0.03921]

I used the Gaussian Kernel PCA algorithm with sigma = sqrt(10).

After finding my K matrix, I then sorted the eigenvectors of K and took the first two largest eigenvectors

column1 [0.1528 0.1553 0.0666 -0.0741 -0.2206 -0.2197 -0.2078 -0.0366 0.1155 0.2222 0.2882 0.3119 0.1572 -0.050 -0.275 -0.4011 -0.3586 -0.1172 0.12466 0.36817]

and column2 [0.0930 -0.1122 -0.1716 -0.2018 -0.1777 -0.0861 0.15884 0.20136 0.20255 0.02489 0.13522 -0.1859 -0.3636 -0.4339 -0.2350 0.04714 0.26192 0.35898 0.33280 0.15149]

My k-PCA projection points were then calculated. I got this plot:

How do you go about finding the major and minor axes for the k-PCA projected points?