Highly comparative feature-based time-series classification

A highly comparative, feature-based approach to time series classification is introduced that uses an extensive database of algorithms to extract thousands of interpretable features from time series. These features are derived from across the scientific time-series analysis literature, and include summaries of time series in terms of their correlation structure, distribution, entropy, stationarity, scaling properties, and fits to a range of time-series models. After computing thousands of features for each time series in a training set, those that are most informative of the class structure are selected using greedy forward feature selection with a linear classifier. The resulting feature-based classifiers automatically learn the differences between classes using a reduced number of time-series properties, and circumvent the need to calculate distances between time series. Representing time series in this way results in orders of magnitude of dimensionality reduction, allowing the method to perform well on very large datasets containing long time series or time series of different lengths. For many of the datasets studied, classification performance exceeded that of conventional instance-based classifiers, including one nearest neighbor classifiers using Euclidean distances and dynamic time warping and, most importantly, the features selected provide an understanding of the properties of the dataset, insight that can guide further scientific investigation.

💡 Research Summary

The paper introduces a highly comparative, feature‑based framework for time‑series classification that replaces traditional instance‑based distance measures (e.g., Euclidean distance, Dynamic Time Warping) with a data‑driven selection of informative statistical and dynamical descriptors. Building on a previously compiled library of more than 9 000 time‑series analysis operations—ranging from basic moments, autocorrelations, and spectral features to entropy measures, nonlinear invariants (e.g., correlation dimension, Lyapunov exponents), model‑fit parameters (ARMA, GARCH, Gaussian processes), and wavelet coefficients—the authors treat each operation as a feature‑extracting function that maps a series of length N to a single real value. After discarding operations that produce undefined or non‑finite results on a given dataset, each of the 20 UCR benchmark data sets (varying in length from 60 to 637 points, number of classes from 2 to 50, and training set sizes from 28 to 1 000) is represented by a high‑dimensional feature vector containing between 6 200 and 7 600 valid features.

Feature selection is performed with a greedy forward algorithm coupled to a simple linear discriminant analysis (LDA) classifier. First, the classification accuracy of each individual feature is evaluated on the training set using LDA; the best performing feature becomes the first element of the reduced set. Subsequently, each remaining feature is tested in combination with the already selected ones, and the feature that yields the greatest increase in training accuracy is added. The process stops when the marginal improvement falls below 3 % or when the training error reaches zero. In practice, most data sets require only one to five selected features to achieve near‑optimal performance.

The final classifier is a multivariate normal model with a pooled covariance matrix, i.e., a linear discriminant that is computationally cheap and highly interpretable. The authors compare this feature‑based approach against 1‑Nearest‑Neighbour classifiers using Euclidean distance and Dynamic Time Warping, the two most common baselines in the time‑series mining literature. Across the 20 benchmark problems, the feature‑based method either matches or exceeds the accuracy of the distance‑based baselines, often with a dramatic reduction in dimensionality (from thousands of raw time‑point values to a handful of features). Notably, the method excels on data sets with many classes or with short, noisy series where alignment‑based distances struggle.

Beyond raw classification performance, the study highlights the scientific insight gained from the selected features. Because each feature corresponds to a well‑understood statistical or dynamical property, the resulting model provides a transparent description of what distinguishes the classes (e.g., variance, autocorrelation at a specific lag, entropy, or a particular model‑fit parameter). This interpretability can guide domain experts toward hypotheses about underlying mechanisms, a benefit not readily available from black‑box distance‑based or kernel methods.

In summary, the authors demonstrate that a “highly comparative” approach—systematically evaluating thousands of existing time‑series descriptors and automatically selecting the most discriminative subset—offers a powerful alternative to traditional distance‑based classification. It delivers competitive (often superior) accuracy, massive dimensionality reduction, and, crucially, interpretable models that can inform further scientific investigation across diverse fields such as medicine, finance, engineering, and climate science.