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Analysis
of Dynamic Interactions
State-space analysis of dynamic interactions |
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Histogram
Optimization | Kernel
Optimization |
Dynamic Interactions |
Last Update
2012-06-13 16:50
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| STATE-SPACE METHOD |
| - Original paper |
| - Illustration |
| - Presentation |
| - Matlab Code |
| Links |
| - Histogram Optimization |
| - Kernel Optimization |
| - HOME Page |
| Tweet by author |
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Shimazaki, Amari, Brown, and Gruen. PLoS Comput Biol 8(3): e1002385. Open Access |
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2012 June 20 Workshop on neural information flow Tracking dynamic neural interactions in awake behaving animals Hideaki Shimazaki, RIKEN Brain Science Institute Neurons embedded in a network are correlated, and can produce synchronous spiking activities with millisecond precision. It is likely that these correlated activities organize dynamically during behavior and cognition, and this may be independent from spike rates of individual neurons. Consequently current analysis tools must be extended so that they can directly estimate time-varying neural interactions. The log-linear model is known to be useful for analysis of the correlated spiking activities but is limited to stationary data. In our approach, we developed a `state-space log-linear model’ that can estimate ever-changing neural interactions: this method is an extension of the familiar Kalman filter which can track system’s parameters as used in, e.g., automotive navigation systems. We applied this method to three neurons recorded from the primary motor cortex of a monkey engaged in a delayed motor task (data from Riehle et al., Science,1997). We found that depending on the behavioral demands of the task these neurons dynamically organized into a group which was characterized by the presence of higher-order (triple-wise) interaction. There was, however, no noticeable change in their firing rates. These results demonstrate that time-varying higher-order analysis allows us to detect subsets of correlated neurons that may belong to a larger set of neurons comprising a cell assembly. This is a collaboration work with Shun-ichi Amari (RIKEN), Emery N. Brown (MIT), and Sonja Gruen (Julich). Original paper: Shimazaki et al., PLoS CB 8(3): e1002385 |
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Download full paper
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Snapshot of analysis of three
simulated neurons |
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Neurons are communicating each other, and jointly work to accomplish their task. When we look at the population of the neurons, there may be a collective state that many neurons interact as a whole, the state that is explained by higher-order interactions. Since it resembles people's activities in our society, here we explain the higher-order interactions, using an example from Twitter. If a twitter user tweets more than once in a 2-minutes window, we consider the user is active in that period, and use a vertical bar to represent the active state. Otherwise, the user is inactive. Suppose two twitter users independently tweet, and then started conversation, the activities may look like...
It is possible that two users tweet almost simultaneously even if they tweet independently. That event is refered to as a chance coincidence. If they simultaneously tweet more frequently than the chance level, we conclude that these two users are `correlated'. The above example explains a pair-wise interaction among two users. In the analysis of population, there may be a collective state of interactions, that can be revealed only by looking at the population as a whole. This state is described using the 'higher-order' interactions. What are the higher-order interactions? We start from a peculiar example. Suppose many people tweet independently each other. Suppose then, all of sudden they tweet simultaneously. The twitter activities may look like... Such activities require higher-order interactions to explain. Why? The synchronous event is a rare event. If you pick up a pair from the population, you can not discern them from a chance coincidence of two users: Their frequency is as low as a chance coincidence of the two users. Nevertheless, if you look at the population, the synchronous event that all users join is not likely to happen by chance. You need higher-order analysis to detect the sparse, yet synchronous events that many users join. More specifically, higher-order interactions explain collective activities of many elements (users) that can not be explained by the occurrence rates of each elements and their pairwise correlations. What can causes the higher-order activities? Well, there are many mechanisms that can lead to higher-order interactions. It is possible that the users interact each other to produce higher-order interactions. Another mechanism is an apparent interaction due to an unobserved common input to the population. If a certain striking event happens, e.g., announcement of British royal marriage, people are driven by the same event, and tweet simultaneously. It may be thus possible to detect occurrence of an external event by looking at the higher-order activities of users. Why do we need a time-resolved method? The answer is simple. The frequencies of tweets vary in a day. Accordingly, the occurrence frequency of chance coincidence changes. Thus we need to adjust significance level of occurrence rate of synchronous events. Additionally, the pair and higher-order interactions may also vary in time. The method described in the PLoS CB sequentially estimate the dynamics of higher-order interactions on top of the time-varying occurrence frequencies of individual events. The tweet bird icons are designed by chethstudios. |
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IEEE ICASSP 2009 |
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Cosyne09 Poster
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Links to co-authors' pages Prof. Sonja Gruen @ Juelich Research Center link Prof. Shun-ichi Amari @ RIKEN Brain Science Institute link Prof. Emery N. Brown @ MIT, Massachusettes General Hospital link |
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Input data structure
Output d ata structure
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The codes are written in Matlab (Mathworks Inc.).
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if you are interested in using the codes. I would like to have
feedbacks to improves the tools before I put it open repository.
->
The codes are now available at GitHub. 
