  Recently, a novel family of biologically plausible online algorithms for
reducing the dimensionality of streaming data has been derived from the
similarity matching principle. In these algorithms, the number of output
dimensions can be determined adaptively by thresholding the singular values of
the input data matrix. However, setting such threshold requires knowing the
magnitude of the desired singular values in advance. Here we propose online
algorithms where the threshold is self-calibrating based on the singular values
computed from the existing observations. To derive these algorithms from the
similarity matching cost function we propose novel regularizers. As before,
these online algorithms can be implemented by Hebbian/anti-Hebbian neural
networks in which the learning rule depends on the chosen regularizer. We
demonstrate both mathematically and via simulation the effectiveness of these
online algorithms in various settings.
