142 research outputs found
Topological feature selection for time series data
We use tools from applied topology for feature selection on vector-valued
time series data. We employ persistent homology and sliding window embeddings
to quantify the coordinated dynamics of time series. We describe an algorithm
for gradient descent to assign scores, or weights, to the variables of the time
series based on their contribution to the dynamics as quantified by persistent
homology; the result is a convex combination of a subset of the variables. In
this setting, we prove persistence vineyards are piecewise linear and we give a
simple formula for the derivatives of the vines. We demonstrate our method of
topological feature selection with synthetic data and C. elegans neuronal data.Comment: 15 page
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