  When there are signals and noises, physicists try to identify signals by
modeling them, whereas statisticians oppositely try to model noise to identify
signals. In this study, we applied the statisticians' concept of signal
detection of physics data with small-size samples and high dimensions without
modeling the signals. Most of the data in nature, whether noises or signals,
are assumed to be generated by dynamical systems; thus, there is essentially no
distinction between these generating processes. We propose that the correlation
length of a dynamical system and the number of samples are crucial for the
practical definition of noise variables among the signal variables generated by
such a system. Since variables with short-term correlations reach normal
distributions faster as the number of samples decreases, they are regarded to
be ``noise-like'' variables, whereas variables with opposite properties are
``signal-like'' variables. Normality tests are not effective for data of
small-size samples with high dimensions. Therefore, we modeled noises on the
basis of the property of a noise variable, that is, the uniformity of the
histogram of the probability that a variable is a noise. We devised a method of
detecting signal variables from the structural change of the histogram
according to the decrease in the number of samples. We applied our method to
the data generated by globally coupled map, which can produce time series data
with different correlation lengths, and also applied to gene expression data,
which are typical static data of small-size samples with high dimensions, and
we successfully detected signal variables from them. Moreover, we verified the
assumption that the gene expression data also potentially have a dynamical
system as their generation model, and found that the assumption is compatible
with the results of signal extraction.
