Scientists worked on
several researches to identify the behavior of the brain. They have been working
on different types of programs aiming the connection between neurons. Scientists
found that Calcium Imaging Data can be used in order to solve this problem.
Calcium Imaging allows real time and simultaneous observation s of neuron activities
from the thousands of neurons which is in the brain. This provides an
individual time series which will represents the fluorescent intensity when messages
are passing between neurons. There are many methods scientists have used in
order to learn the behavior of the neurons using calcium Imaging Data. Considering
all of these methods partial correlation method is being used mostly because
this method helps to differentiate direct connections with indirect
connections. Partial correlation method measures the unconditional linear
dependence between variables and it should not be able to filter out indirect
interactions between neurons. This method is basically builds on Transfer entropy
method to measure the association between neurons.
Partial correlation method in Connectomics.
This can be
considered as one of the best methodology to reconstruct the neuron network. This
is done by removing the relationship of neural spike trains with other neurons.
The detect ability decreases with the number of neurons included in the
analysis and increases with the recording time. This consists of two major
parts. One is to identify the peak activities of neurons which will be detected
by the raw signals while other one is to interpret the interconnection of
neurons from partial correlation information.
The density of the partial covariance will
give additional information about the direction and the type of the
connections. When considering a large neural network many problems arrive. There
may be a problem to identify at what extent the association between processes because
of the direct connection between two neurons or there may be a problem to
identify whether the observed correlation is due to a common input from other
neurons. These problems were handled by
the method of partialization. partial spectral
coherence was used in analyzing patialization ( | Rab|c
) |2 ) in the frequency domain with the partial spectral
densities. Where,
) |2 ) in the frequency domain with the partial spectral
densities. Where,
Rab|c) | = 
) | =
For investigating
undirected graphs which will visualize the correlation structure of a
multivariate point process, partial correlation graphs can be used. This will
lead to identify the synaptic connections from the neural spike data. Here it
is not possible to say that this partial correlation graphs will directly reflect
the physiological connectivity structure of the neuron network. Using a
directed graph we can indicate a direct connection from vertex a to vertex b when
there is a synaptic connection from one neuron to another. We can denote a as
the parent and b as the child. So that edges will not be coinciding either. To
obtain the partial correlation graph we have to join all the parents of a joint
child by an edge. By observing this directed graph we can identify vertices
without children and their adjacent edges can be correctly identify from the
partial co variance density scales. After these vertices have been removed from
the graph and using remaining set we can identify all directed edges.
