Hippocampus as an Independent Component Analyzer

Suppose we have two sources of data which produce two time signals, and there are two receivers of data located in different places. Each receiver accepts the combination of data with different amplitudes. The two recorded signals are denoted by x ₁ ( t ) and x ₂ ( t ). Each of these signals is a weighted sum of the source signals, denoted by s ₁ ( t ) and s ₂ ( t ). We express this combination by applying two equations:

x ₁ (t) = a ₁₁ s ₁ (t) + a ₁₂ s ₂ (t)

x ₂ (t) = a ₂₁ s ₁ (t) + a ₂₂ s ₂ (t)

where a ₁₁, a ₁₂, a ₂₁ and a ₂₂ are weighting parameters. We can calculate two sources of signals from two received signals; this is called a cocktail-party problem. Actually it would be easy to solve the system of linear equations by classical methods if we knew parameters a _ij . The problem here is that we do not know the parameters and this is considerably complicated.

One way for solving this problem would be to use some information on the statistical properties of two source signals si(t ) to estimate a _ij . To solve this problem it is enough to assume that s ₁ ( t ) and s ₂ ( t ) at each time constant are statically independent. Also, if we expand the problem to n sources of signal, the assumption would be on mutual independence of all sources with each other. This is a realistic assumption and it does not need to be exactly true in practice. The only constraint for this approach is that sources should not have Gaussian distribution. Independent component analysis is to deal with problems that are closely related to a cocktail-party problem.

Now we express similarities between a cocktail-party problem and memory storage and retrieval in the brain. Suppose independent components (sources) are producing data independently. Some receivers are placed in different positions so that every receiver accepts independent components with different amplitudes. For example if the assumed property is the red color, the amplitude of the component indicates the intensity of redness. By these assumptions, we can apply independent component analysis methods on memory storage and retrieval. 4, 5

We assume that every memory pattern is made up of different numbers of independent components. For example, a red ball can be expressed by two properties or independent components, the sphere shape and the red color. The red color also could be used in explaining many other objects or phenomena. Thus, it can be stored and used whenever the brain desires to recall red things. From the example, it is apparent that any memory pattern could be extracted into independent components. Our hypothesis is that the hippocampus acts as an independent component analyzer. We suggest that the dentate gyrus extracts independent components of memory patterns. These components, with their degree of association, are stored in CA3, so CA3 acts as a memory database. Finally, CA1 processes the recalled data of CA3 and makes them appropriate to use in entorhinal cortex.

Since every module performs its separate job, modulation permits performing complicated activities in an easier way. By storing memory patterns this way, capacity increment is also inevitable because some components are frequently used in different memory patterns and storing the component once and associating it with other components to represent a memory pattern is more efficient than storing the component each time a new pattern is stored.

It is believed that degeneration of the hippocampus may be a cause of some common neurological disorders such as Alzheimer’s disease and dementia. 6, 7 It seems that considering our hypothesis on the mechanism of data processing in the hippocampus may help in designing new behavioral diagnostic tests. It also may aid physicians in better analyzing patient symptoms. Surely, experimental and clinical studies are needed to validate our hypothesis.