An introduction to time-resolved decoding analysis for M/EEG

The human brain is constantly processing and integrating information in order to make decisions and interact with the world, for tasks from recognizing a familiar face to playing a game of tennis. These complex cognitive processes require communication between large populations of neurons. The non-invasive neuroimaging methods of electroencephalography (EEG) and magnetoencephalography (MEG) provide population measures of neural activity with millisecond precision that allow us to study the temporal dynamics of cognitive processes. However, multi-sensor M/EEG data is inherently high dimensional, making it difficult to parse important signal from noise. Multivariate pattern analysis (MVPA) or "decoding" methods offer vast potential for understanding high-dimensional M/EEG neural data. MVPA can be used to distinguish between different conditions and map the time courses of various neural processes, from basic sensory processing to high-level cognitive processes. In this chapter, we discuss the practical aspects of performing decoding analyses on M/EEG data as well as the limitations of the method, and then we discuss some applications for understanding representational dynamics in the human brain

Recurrent kernel machines : computing with infinite echo state networks

Echo state networks (ESNs) are large, random recurrent neural networks with a single trained linear readout layer. Despite the untrained nature of the recurrent weights, they are capable of performing universal computations on temporal input data, which makes them interesting for both theoretical research and practical applications. The key to their success lies in the fact that the network computes a broad set of nonlinear, spatiotemporal mappings of the input data, on which linear regression or classification can easily be performed. One could consider the reservoir as a spatiotemporal kernel, in which the mapping to a high-dimensional space is computed explicitly. In this letter, we build on this idea and extend the concept of ESNs to infinite-sized recurrent neural networks, which can be considered recursive kernels that subsequently can be used to create recursive support vector machines. We present the theoretical framework, provide several practical examples of recursive kernels, and apply them to typical temporal tasks