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In-Depth Information
Fig. 4.
UNN
g
embeddings of 100 digits (2's) from the USPS data set. The images are shown that
are assigned to every 14th embedded latent point. Similar digits are neighbored in latent space.
Fig. 5.
Sorting of Galaxies with UNN
g
. Galaxies from similar classes in the Hubble sequence are
neighbored in latent space.
Ta b l e 1 .
Comparison of DSRE for initial data set, and after embedding with strategy UNN, and
UNN
g
2D-
S
3D-S
2
5
10
2
5
10
K
init
201.6 290.0 309.2 691.3 904.5 945.80
UNN
19.6
27.1
66.3
101.9 126.7 263.39
UNN
g
29.2
70.1
64.7 140.4 244.4
296.5
LLE
25.5
37.7
40.6
135.0 514.3
583.6
3D-S
h
digits (7)
K
2
5
10
2
5
10
init
577.0 727.6 810.7 196.6 248.2
265.2
UNN
80.7 108.1 216.4 139.0 179.3
216.6
UNN
g
101.8 204.4 346.8 145.3 195.4
222.1
LLE
94.9 198.9 387.4 147.8 198.1
217.8
to each other, while digits that are dissimilar are further away from each other in latent
space.
DSRE Comparison.
Besides the visual interpretation we compare the DSRE achieved
by both strategies with the initial DSRE, and the DSRE achieved by LLE on all test
problems. For the USPS digits data set we choose the number
7
. Table 1 shows the ex-
perimental results of three settings for the neighborhood size
K
. The lowest DSRE
on each problem is highlighted with bold figures. After application of the iterative
strategies the DSRE is significantly lower than initially. Increasing
K
results in higher
DSREs. With exception of LLE with
K
=10
on 2D-
S
, the UNN strategy always
achieves the best results. UNN achieves lower DSREs than UNN
g
, with exception of
2D-
S
,and
K
=10
. The win in accuracy has to be paid with a constant runtime factor
that may play an important role in case of large sets of high-dimensional data.
Sorting of Galaxies.
In the following, we test UNN on real-world data from astron-
omy, i.e., images of galaxies. Galaxies are a massive, gravitationally bound systems of
