We propose a novel methodology for feature extraction from time series data based on topological data analysis. The proposed procedure applies a dimensionality reduction technique via principal component analysis to the point cloud of the Takens' embedding from the observed time series and then evaluates the persistence landscape and silhouettes based on the corresponding Rips complex . We define a new notion of Rips distance function that is especially suited for persistence homologies built on Rips complexes and prove stability theorems for it. We use these results to demonstrate in turn some stability properties of the topological features extracted using our procedure with respect to additive noise and sampling . We further apply our method to the problem of trend forecasting for cryptocurrency prices, where we manage to achieve significantly lower error rates than more standard, non TDA-based methodologies in complex pattern classification tasks. We expect our method to provide a new insight on feature engineering for granular, noisy time series data.
We develop a novel algorithm for feature extraction in time series data by leveraging tools from topological data analysis. Our algorithm provides a simple, efficient way to successfully harness topological features of the attractor of the underlying dynamical system for an observed time series . The proposed methodology relies on the persistent landscapes and silhouette of the Rips complex obtained after a de-noising step based on principal components applied to a time-delayed embedding of a noisy, discrete time series sample. We analyze the stability properties of the proposed approach and show that the resulting TDA-based features are robust to sampling noise. Experiments on synthetic and real-world data demonstrate the effectiveness of our approach . We expect our method to provide new insights on feature extraction from granular, noisy time series data.
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The proposed procedure applies a dimensionality reduction technique via principal component analysis to the point cloud of the Takens' embedding from the
Our algorithm provides a simple, efficient way to successfully harness topological features of the attractor of the underlying dynamical system for an
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and then evaluates the persistence landscape and silhouettes based on the corresponding Rips complex . We define a new notion of Rips distance function that is especially suited for persistence homologies built on Rips complexes and prove stability theorems for it. We use these results to demonstrate in turn some
. The proposed methodology relies on the persistent landscapes and silhouette of the Rips complex obtained after a de-noising step based on principal components applied to a time-delayed embedding of a noisy, discrete time series sample. We analyze the
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topological features extracted using our procedure with respect to additive noise and sampling
proposed approach and show that the resulting TDA-based features are robust to sampling noise. Experiments on synthetic and real-world data demonstrate the effectiveness of our approach
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We further apply our method to the problem of trend forecasting for cryptocurrency prices, where we manage to achieve significantly lower error rates than more standard, non TDA-based methodologies in complex pattern classification tasks.
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