Invariant representation, information retrieval, and network data dynamics
One of the things that strikes me about the nature of the data that I analyze for MusicStrands is the remarkable amount of coherence that arises from simple “network” data. In this case, I’m speaking of network data in terms of information related to connections and connection weights between arbitrary elements. Often, this data can be stored/conceived of as a simple matrix:
_ a b c d e f
a 9 3 4 5 1 0
b 3 8 7 4 1 2
c 4 7 7 2 3 1
d 5 4 2 6 3 0
e 1 1 3 3 5 2
f 0 2 1 0 2 9
There is a large number of methods for decomposing matrices (like the one above) in order to identify trends and clustering inherent in the elements. Often, these methods form the basis for information retrieval functions, such as methods related to pattern recognition and so forth. The idea of pattern recognition is important, both for scientists, as well as any life form in general, and scientists have shown how a brain’s response to a given stimuli approximates many of these more exacting level of decompositions.
As an aside, one may fault the brain for not “fully solving” the decomposition for such data sets. However, in my opinion there is a very good reason for why the brain doesn’t perform at full precision here. Data sets like these are extremely calculation intensive to break down, and in most cases, “the most important” trends in the data is what the brain should be focusing on anyways.
So, it can be shown that the brain is forming invariant responses to a range of related stimuli such as faces in different lighting/angles. This is an impressive feat, as many supercomputers can take a long time to reach similar conclusions about the particular individual they are looking at.
What’s even more amazing, is that these abstractions become simpler at higher levels, to the point that individual neurons can be found that serve as indicators that a given individual is represented, revealed recently in this study. In this case, a single neuron was identified that would fire whenever Jennifer Aniston was present in a picture… from any angle, and with any haircut/outfit.
The notion of such a robust invariant representation is intriguing to me from the angle of information retrieval. If it’s possible to gear a system so that it forms higher level representations of the data, a more essential analysis of the data could be performed. For network data, such as the data I work with at MusicStrands, these analyses could reveal and compare high level trends that are occuring within the data, such as the gradual shifting, dissipation, or emergence of genres.
In my opinion, the missing ingredient for these analyses is the characterization of time. If you think about it, our brains are honed in to a very specific “clock” speed for our existence on this planet. We can respond to gravitational effects (falling rocks), yet we cannot directly perceive a sun rising (we can’t tell that it’s moving…unless we look really hard at dawn or dusk). It’s pretty safe to say that time is crucial to the formation of invariant representations in this context, and a system that functions in this manner must have a solid notion of what “clock speed” it is operating on. In other words, the data must be fed into it at the right rate, and this rate must accomodate the trends that an information scientist wishes to observe.
I lack the background necessary to characterize network dynamics in this fashion, but I’m aware of several people at SLIS that are working towards a better understanding of networks in this context. I look forward to focusing on this more in the future.