Matrix basis formalism for constraining the number of free parameters.

<p>(<b>a</b>) A complex, structured full rank matrix is generated by symmetrizing a pixel image of a fluid jet, and used as the “true” kernel for our model neuron. (<b>b</b>) Mutual information increases with the number of learning steps, peaks at the step and remains unchanged thereafter. Inset shows the collection of Gaussian matrix basis functions whose peaks densely tile the space of . A trial matrix is constructed as a linear sum (with coefficients ) of the basis matrices, and information optimization is performed over . The black dot at the learning step is the point where is extracted. (<b>c</b>) The reconstructed matrix kernel after maximizing mutual information using the basis coefficients making up the kernel is shown here. (<b>d</b>) The RMS reconstruction error decreases as the number of basis functions increases from to . With enough data perfect reconstruction is possible as approaches the number of independent pixels in .