Information Technology Reference
In-Depth Information
(a)
p
=0
.
1
(b)
p
=0
.
2
(c)
p
=0
.
4
(d)
p
=0
.
1
(e)
p
=0
.
2
(f)
p
=0
.
4
Fig. 10.
UNN embedding of 3D-S with missing data for missing rates
p
=0
.
1
,
0
.
2
,and
p
=0
.
4
for repair-and-embed (upper row), and for embed-and-repair (lower row)
values (complete). Embed-and-repair achieves the lowest imputation error
E
in seven
of the eight cases, but much worse results for the DSRE. While the DSRE results are
still satisfactory with
1%
of incomplete data, the approach fails for higher missing rates.
Obviously, it is difficult for MAR data to first determine the structure from incomplete
patterns.
Figure 10 shows the embeddings of UNN on the 3D-S data set for increasing missing
rates
p
, and repair-and-embed in the upper row. The patterns are colorized w.r.t. their
latent colors (similar colors are neighbored). Hence, similar colors in data space show
that the embedding has been successful. Figure 10 (a) shows the embedding with a low
missing rate of
p
=0
.
1
. The figure shows that the 3D-S is almost completely recon-
structed, while the colors of the embedding show that a reasonable learning process
took place: neighbored solutions in latent space have similar colors. The higher the rate
of incomplete data the worse is the embedding (different colors are neighbored). But
higher missing rates can also be recognized by deviations from the S-structure.
The lower row shows the corresponding experimental results for UNN with embed-
and-repair, also with increasing missing rates
p
. The colors show that the embeddings
are worse for high missing rates. For example, Figure 10 (f) shows that the embedding
for missing rate
p
=0
.
4
with repair-and-embed is comparably bad, a result that is
consistent with the DSRE of Table 4.
6
Conclusions
Fast dimensionality reduction methods are required that are able to process huge data
sets, and large dimensions. With UNN regression we have fitted a well-known regres-
sion technique into the unsupervised setting for dimensionality reduction. The two
