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This paper examines the relationship between the behavior of a neural networkand the distribution formed from the projections of the data records into thespace spanned by the low-order principal components of the training data. Forexample, in a benchmark calculation involving rotated and unrotated MNISTdigits, classes (digits) that are mapped far from the origin in alow-dimensional principal component space and that overlap minimally with otherdigits converge rapidly and exhibit high degrees of accuracy in neural networkcalculations that employ the associated components of each data record asinputs. Further, if the space spanned by these low-order principal componentsis divided into bins and the input data records that are mapped into a givenbin averaged, the resulting pattern can be distinguished by its geometricfeatures which interpolate between those of adjacent bins in an analogousmanner to variational autoencoders. Based on this observation, a simplyrealized data balancing procedure can be realized by evaluating the entropyassociated with each histogram bin and subsequently repeating the originalimage data associated with the bin by a number of times that is determined fromthis entropy.

Neural Network Characterization and Entropy Regulated Data Balancing through Principal Component Analysis