Information Technology Reference
In-Depth Information
y
data space
2
y'
(y , 0.5( y' + y'' ))
*
1
y''
y
(y , . )
*
1
1
latent space
x
*
Fig. 9.
Embed-and-repair: The incomplete pattern
y
∗
is embedded at the position where it leads
to the lowest DSRE w.r.t. the first dimension: between
x
,and
x
, then the gap
y
2
x'
x''
is filled with
KNN and
K
=2
Ta b l e 4 .
Comparison of imputation Error
E
, and DSRE with UNN embedding with repair-and-
embed (R-a-E) and embed-and-repair (E-a-R) on 3D-S, and 3D-S
h
w.r.t. increasing data missing
rate
p
R-a-E
E-a-R
complete
p
data
UNN
E
DSRE
E
DSRE
3D-S
0.01
0.0507
147.2
0.0269
165.39
142.8
0.1
0.3129
143.8
0.2884
265.2
142.8
0.2
0.6454
149.0
0.6146
369.2
142.8
0.3
0.9557
152.7
0.9265
452.3
142.8
3D-S
h
0.01
0.0235
104.2
0.0309
119.7
105.5
0.1
0.2671
101.9
0.2595
217.6
105.5
0.2
0.5509
122.2
0.5007
296.8
105.5
0.3
0.8226
129.5
0.5285
301.8
105.5
5.4
Experimental Analysis
In the following, we describe the experimental setup for the comparison between both
approaches. We generate the missing data scenario by removing entries
y
ij
from
Y
with
probability
p
, and experimentally analyze the final DSRE in comparison to the DSRE
for the complete reference matrix (without missing entries), and the imputation error
E
=
i
y
i
−
, which is the deviation from the original complete patterns
y
i
,
and the repaired pendants
y
of the incomplete versions.
Table 4 shows the experimental results for various degrees of missing data modeled
by increasing
p
on the data set 3D-S. For embedding we employ UNN. The experi-
mental results show that repair-and-embed achieves the lowest DSRE on both data sets.
The results are even very close to the DSRE achieved on the data set without missing
y
i
