On the Preservation of Spatio-temporal Information in Machine Learning Applications

In conventional machine learning applications, each data attribute is assumed to be orthogonal to others. Namely, every pair of dimension is orthogonal to each other and thus there is no distinction of in-between relations of dimensions. However, this is certainly not the case in real world signals which naturally originate from a spatio-temporal configuration. As a result, the conventional vectorization process disrupts all of the spatio-temporal information about the order/place of data whether it be $1$D, $2$D, $3$D, or $4$D. In this paper, the problem of orthogonality is first investigated through conventional $k$-means of images, where images are to be processed as vectors. As a solution, shift-invariant $k$-means is proposed in a novel framework with the help of sparse representations. A generalization of shift-invariant $k$-means, convolutional dictionary learning, is then utilized as an unsupervised feature extraction method for classification. Experiments suggest that Gabor feature extraction as a simulation of shallow convolutional neural networks provides a little better performance compared to convolutional dictionary learning. Many alternatives of convolutional-logic are also discussed for spatio-temporal information preservation, including a spatio-temporal hypercomplex encoding scheme.