![](bg6.png)
number of hyperslabs p = 8, the weight coefficient
ω = 0.1250 and the kernel parameter γ = 1.
The obtained results lead to the following obser-
vations:
• The four algorithms presented in this experiment
have a fast performance, taking less than 1 minute
in the estimation with 1000 training samples. As
is showed in Table I, the KSCP achieves the mini-
mum mean square error, the KAP and the KLMS-
SCAL1 achieves more velocity in execution but
with a higher mean square error. It is important
to highlight that the settings of the T
1
and T
2
pa-
rameters are essential for the execution time and
the accuracy. The abnormality threshold parame-
ter T
1
can be adjusted for achieving more velocity
and the redundancy threshold parameter T
2
must
be adequately limited to guarantee high accuracy.
• The learning curve figure showed that in the Ker-
nel Affine Projection algorithm, the mean square
error begins to grow exponentially in the iteration
number 400; the KLMS-SCAL1 takes several ite-
rations to stabilize and the EXKRLS and KSCP
reach zero and remain stable from the first 50 ite-
rations for the considered situation.
5 CONCLUSIONS
This paper presents our proposed algorithm KSCP
for adaptive nonlinear estimation. The KSCP impro-
ves the estimation performance based on 3 aspects:
First, an effective dictionary control is established,
guaranteeing an exhaustive selection of the most im-
portant data for the estimation, and low computational
complexity, basing not on heuristics but on a strong
mathematical foundation approach with statistical and
probabilistic techniques. Second, we take advantage
of the Kernel Least Mean Square and the Surprise Cri-
terion combining them to reduce the complexity of
the calculations of variance prediction and error pre-
diction of the incoming data. Third, for the high accu-
racy goal, we use the Parallel Hyperslab Projection
Along Affine Subspace.
With all of these ideas, we achieve a fast conver-
gence, high accuracy, small size of dictionary and fast
performance algorithm, which is demonstrated by the
computational experiment and the comparison with
some important and recognized algorithms like Ker-
nel Affine Projection with Coherence Criterion, Ker-
nel Least Mean Square with Coherence-Sparsification
criterion and Adaptive L1-norm regularization and
Extended Recursive Least Squares.
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