Abstract |
A central tenet of neuroscience is the remarkable computational abilities of our brains that arise
as a result of populations of interconnected neurons. Indeed, we find ourselves at an exciting
moment in the history of neuroscience, as the field is experiencing rapid growth in the complexity
and quantity of the recorded neural activity, as advances in experimental design, measurement
techniques, and computational analysis allow us unprecedented access to the dynamics of neural
activity in different brain areas. Thus, one of the goals of neuroscience is to find interpretable
descriptions of what the brain represents and computes, and also to explain complex phenomena
in simple terms. Considering this task from the perspective of dimensionality reduction provides
an entry point into principled mathematical techniques that allows us to discover these
representations directly from experimental data, a key step to developing rich yet
comprehensible models for brain function. Dimensionality reduction methods produce lowdimensional
representations of high-dimensional data, where the representation is chosen to
preserve or highlight some feature of interest in the data.
In this master thesis, we employ two real binary datasets that refer to the spontaneous neuronal
activity of two laboratory mice over time, and we aim to their efficient low-dimensional
representation. Real datasets compared to synthetic ones are not so highly structured and
background noise is more intense. Noise could be a result of mistakes during the creation or the
processing of the datasets or it could also exist due to accidental firings produced by neurons. So,
in order to get insights regarding how neurons are connected to each other, we also need to be
able to discriminate the true from the noisy activation patterns. In order to address both
challenges, namely the low-dimensional representation of the data and the discrimination
between true and spurious activation patterns, we combine dimensionality reduction techniques
with supervised machine learning. More specifically, we propose a Sequential Adversarial
Dictionary Learning Algorithm, which selects sequentially the elements that are included in the
dataset and fills the dictionary, namely the new reduced space, only with those elements that
contribute to the better representation of the true, rather than the noisy activation patterns,
which have been synthetically created. The entry of an element in the dictionary, which is based
on the use of true and noisy activation patterns, justifies the name "Adversarial", which is used in
the title of our algorithm. This method searches only for repeated patterns with total synchronous
firing activity. Thus, we also consider the idea of a more relaxed approach, where we can discover
patterns that have also some temporal correlation within a time window interval. Subsequently,
a supervised classifier is used, which takes as input the reconstructed signals in order to
discriminate the true from the noisy activation patterns.
Experimental results show that our algorithm creates a dictionary which, when used to produce
the reconstructed patterns given to the classifier, it results to a classification accuracy of 60% in
the case of synchronous firing activity and 90% when we search for patterns in bigger time
window intervals. By comparison, the classifier achieves a classification rate of only 51% when
raw data is used as input. We also demonstrate that our system achieves better results both
quantitatively as well as qualitatively when compared with K-SVD, an established dictionary
learning algorithm.
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