CS365 Homework-2

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A. Linear Dimensionality Reduction

Reconstructing image 25

Original Image

Using different dimensions,

m=2

Using m=2

m=10

Using m=10

m=30

Using m=30

m=80

Using m=80

B. Nonlinear Dimensionality Reduction - (Isomap)

Residual variance on taking dimensions from 1-10 displayed in the graph with k=7.

Residual Variance

Observation :-
We observe that the residual variance is quite low even for 1-dimension and remains almost the same from 2 dimensions onwards. Hence we can obtain satisfactory results by mapping our data in 2 dimensions, as is displayed by the isomap.



Isomap in 2-D :-

isomap

Nearest Neighbours :-

Image 25

25 neighbours

Image 10

10 neighbours

OBSERVATION :-

The images are well mapped on a 2-D manifold. They are categorised into 3 different areas or lines according to the part of the face visible- front, left and right. Similar looking pictures are well grouped as neighbours. Though a linear manifold is expected since the movement is just 1-D, but probably because of the high number of straight looking faces, with subtle differences, a 1-D mapping is not enough(high residual variance value).