# name
Topology preservation under dimensionality reduction during neural manifold discovery

# metadata.dc.description[].value
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Carles Casacuberta

# metadata.dc.description.abstract[].value
[en] One of the main challenges that neuroscience faces nowadays is to understand how the brain represents different stimuli. This involves dealing with large amounts of data, which are usually high-dimensional and have to be processed to unveil how they are related with the associated cognitive processes. This work describes methods to preserve the topology of recorded data when their dimensionality is reduced, using predictions
from neural coding theory. Relevant dimensionality reduction techniques are exposed, along with a couple of examples where persistent homology is crucial to discriminate the resulting neural manifold from being a circle or a torus. It is impossible to infer this from dimensionality reduction alone. Thus, to combine both techniques is essential for the manifold’s parameterization and the subsequent variable decoding to be successful.

# metadata.dc.rights[].value
cc-by-nc-nd (c) Marian Martı́nez Marı́n, 2021

# metadata.dc.source[].value
Treballs Finals de Grau (TFG) - Matemàtiques

# metadata.dc.title[].value
Topology preservation under dimensionality reduction during neural manifold discovery