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Sparse arrays of signatures for online character recognition
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In mathematics the signature of a path is a collection of iterated integrals, commonly used for solving differential equations. We show that the path signature, used as a set of features for consumption by a convolutional neural network (CNN), improves the accuracy of online character recognition---that is the task of reading characters represented as a collection of paths. Using datasets of letters, numbers, Assamese and Chinese characters, we show that the first, second, and even the third iterated integrals contain useful information for consumption by a CNN. On the CASIA-OLHWDB1.1 3755 Chinese character dataset, our approach gave a test error of 3.58%, compared with 5.61% for a traditional CNN [Ciresan et al.]. A CNN trained on the CASIA-OLHWDB1.0-1.2 datasets won the ICDAR2013 Online Isolated Chinese Character recognition competition. Computationally, we have developed a sparse CNN implementation that make it practical to train CNNs with many layers of max-pooling. Extending the MNIST dataset by translations, our sparse CNN gets a test error of 0.31%.
Forward citations
Cited by 4 Pith papers
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Advances in Neural Controlled Differential Equations
Linear NCDEs replace non-linear vector fields with linear ones, enabling parallel-in-time training via associative scans while retaining maximal theoretical expressivity and achieving state-of-the-art time series perf...
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Learning with Expected Signatures: Theory and Applications
The paper proves consistency and asymptotic normality for empirical expected signature estimators under irregular and dependent sampling and proposes a martingale correction that lowers estimator variance.
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Global universal approximation with Brownian signatures
Linear functionals on the signature of the time-extended Brownian motion are dense in L^p of the Wiener measure, and therefore approximate any p-integrable adapted process and any Itô SDE solution.
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Path Signatures for Feature Extraction. An Introduction to the Mathematics Underpinning an Efficient Machine Learning Technique
A tutorial explaining how path signatures, built from iterated integrals, can serve as features for classifying time series.
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