Comparing Cross Correlation-Based Similarities
- URL: http://arxiv.org/abs/2111.08513v1
- Date: Mon, 8 Nov 2021 08:50:13 GMT
- Title: Comparing Cross Correlation-Based Similarities
- Authors: Luciano da F. Costa
- Abstract summary: Multiset-based correlations based on the real-valued multiset Jaccard and coincidence indices are compared.
Results have immediate implications not only in pattern recognition and deep learning, but also in scientific modeling in general.
- Score: 1.0152838128195467
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: The common product between two multisets or functions can be understood as
being analogue to the inner product in real vector or function spaces in spite
of its non-linear nature. In addition to other interesting features, it also
allows respective correlations to be derived which, in addition to their
conceptual and computational simplicity, have been verified to be able to
provide enhanced results in tasks such as template matching. The multiset-based
correlations based on the real-valued multiset Jaccard and coincidence indices
are compared in this work, with encouraging results which have immediate
implications not only in pattern recognition and deep learning, but also in
scientific modeling in general. As expected, the multiset correlation methods,
and especially the coincidence index, presented remarkable performance
characterized by sharper and narrower peaks while secondary peaks were
attenuated, even in presence of noise. In particular, the two methods derived
from the coincidence index led to the sharpest and narrowest peaks, as well as
intense attenuation of the secondary peaks. The cross correlation, however,
presented the best robustness to symmetric additive noise, which suggested a
combination of the considered approaches. After a preliminary investigation of
the performance of the multiset approaches, as well as the classic
cross-correlation, a systematic comparison framework is proposed and applied
for the study of the aforementioned methods. Several interesting results are
reported, including the confirmation, at least for the considered type of data,
of the coincidence correlation as providing enhanced performance regarding
detection of narrow, sharp peaks while secondary matches are duly attenuated.
The combined method also confirmed its good performance for signals in presence
of intense additive noise.
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