It is open how neurons in the brain are able to learn without supervision to discriminate between spatio-temporal firing patterns of presynaptic neurons. We show that a known unsupervised learning algorithm, Slow Feature Analysis (SFA), is able to acquire the classification capability of Fisher’s Linear Discriminant (FLD), a powerful algorithm for supervised learning, if temporally adjacent samples are likely to be from the same class. We also demonstrate that it enables linear readout neurons of cortical microcircuits to learn the detection of repeating firing patterns within a stream of spike trains with the same firing statistics, as well as discrimination of spoken digits, in an unsupervised manner.Since the presence of supervision in biological learning mechanisms is rare, organisms often have
to rely on the ability of these mechanisms to extract statistical regularities from their environment.
Recent neurobiological experiments have suggested that the brain uses some type of slowness
objective to learn the categorization of external objects without a supervisor. Slow Feature Analysis (SFA) could be a possible mechanism for that. We establish a relationship between the unsupervised SFA learning method and a commonly used method for supervised classification learning: Fisher’s Linear Discriminant (FLD). More precisely, we show that SFA approximates the classification capability of FLD by replacing the supervisor with the simple heuristics that two temporally adjacent samples in the input time series are likely to be from the same class. Furthermore, we demonstrate in simulations of a cortical microcircuit model that SFA could also be an important ingredient in extracting temporally stable information from trajectories of network states and that it supports the idea of anytime computing, i.e., it provides information about the stimulus identity not only at the end of a trajectory of network states, but already much earlier.
This paper is structured as follows. We start in section 2 with brief recaps of the definitions of SFA and FLD. We discuss the relationship between these methods for unsupervised and supervised learning in section 3, and investigate the application of SFA to trajectories in section
4. In section 5 we report results of computer simulations of several SFA readouts of a cortical microcircuit model. Section 6 concludes with a discussion.
