We have developed packages for doing high-capacity data-mining of both physiological and simulated signals. Data files from both experimental and modeling techniques can run to tens of gigabytes or more, making it unfeasible to view all of the data directly. Instead algorithms are developed to scan through thousands or millions of recordings to find those of interest or to generate scatter-plots or other graphical devices to view everything at once through some simplifying "lens."
Data-mining is also called [i]KDD[/i] which means knowledge discovery and data-mining. The phrase "knowledge discovery" helps to explicate how these procedures differ from traditional methods of data reduction using statistical methods. In statistics, one has a prior hypothesis, sometimes well-founded and sometimes not, regarding the structure of the data. Often, for example, data is assumed to follow a normal distribution and can therefore be described by the Gaussian parameters of mean and standard deviation. By contrast KDD proceeds via explorations with no [i]a priori[/i] assumptions. Instead in KDD, the investigator generates hypotheses quickly on the fly which then can either be supported or discarded through further exploration. KDD is sometimes denigrated as being "fishing" for random facts that are pulled up randomly rather than being tracked and hunted down. Perhaps it is somewhere in between, fishing with one of those new-fangled sonars that allow one to quickly identify the location and approximate composition of a school of fish.
The brain is an example of a non-stationary system -- one where the signals occurring now will never be repeated. If one sees the same image 100 times, one doesn't see it each time in quite the same way. If nothing else, ones response to the image is conditioned by the fact that it has been seen before -- it either gets boring so that ones mind (and brain) wanders, or one finds new facets of the image to focus on. Although there will clearly be some common repeated aspects of brain state with repetitive viewing, the most interesting, and revealing, aspects of brain states will be thoese that change. The brain isn't a passive system but instead is always actively correlating and recombining thoughts, memories, and sense perceptions.
For these reasons and others, we are generally skeptical about the common practice of averaging brain signals. As above, averaging represents a set of statistical assumptions - one of which is stationarity.