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Multivariate Time Series Classification with WEASEL+MUSE

Patrick Schäfer, Ulf Leser

arXiv:1711.11343v4cs.LG

TL;DR

Multivariate time-series classifiers must handle interactions among dimensions while filtering irrelevant data and noise. WEASEL+MUSE constructs sensor-aware discrete features from windowed streams, adds derivatives, and selects and weights informative features. Across benchmark and motion data, it is consistently among the most accurate methods, with particular strength on smaller sensor-reading datasets.

  • Problem

    Multivariate time-series classification must capture cross-dimensional feature interplay while dealing with high dimensionality, irrelevant streams, and noise.

  • Method

    WEASEL+MUSE applies bag-of-patterns processing to each dimension, encodes sensor context in discrete features, adds derivatives, and uses feature selection and weighting before classification.

  • Results

    WEASEL+MUSE is consistently among the most accurate classifiers across the evaluation datasets and performs best for smaller sensor-reading datasets.

  • Takeaways & Limitations

    The method provides a domain-agnostic multivariate classifier that is competitive across datasets and robust on motion-capture data.

  • Takeaways & Limitations

    Performance varies by domain: MLSTM-FCN performs best on motion and speech datasets, while WEASEL+MUSE performs best on sensor readings.

Abstract

from arXiv · show

Multivariate time series (MTS) arise when multiple interconnected sensors record data over time. Dealing with this high-dimensional data is challenging for every classifier for at least two aspects: First, an MTS is not only characterized by individual feature values, but also by the interplay of features in different dimensions. Second, this typically adds large amounts of irrelevant data and noise. We present our novel MTS classifier WEASEL+MUSE which addresses both challenges. WEASEL+MUSE builds a multivariate feature vector, first using a sliding-window approach applied to each dimension of the MTS, then extracts discrete features per window and dimension. The feature vector is subsequently fed through feature selection, removing non-discriminative features, and analysed by a machine learning classifier. The novelty of WEASEL+MUSE lies in its specific way of extracting and filtering multivariate features from MTS by encoding context information into each feature. Still the resulting feature set is small, yet very discriminative and useful for MTS classification. Based on a popular benchmark of 20 MTS datasets, we found that WEASEL+MUSE is among the most accurate classifiers, when compared to the state of the art. The outstanding robustness of WEASEL+MUSE is further confirmed based on motion gesture recognition data, where it out-of-the-box achieved similar accuracies as domain-specific methods.

1 INTRODUCTION

Multivariate time series classification must handle both high-dimensional sensor data and feature interplay across dimensions. WEASEL+MUSE addresses these challenges with context-encoded feature extraction, derivatives, feature weighting, and selection, achieving strong benchmark performance.

  • Multivariate time series classification must account for feature interplay across dimensions, not only individual values.
  • Gesture data can contain irrelevant dimensions, noise, and timing variation, requiring relevant features to be extracted from each dimension.
  • WEASEL+MUSE builds a bag-of-patterns feature vector from sliding windows, discrete features, and histograms, then applies machine-learning classification.
  • Sensor identifiers encode feature dimension, allowing the method to distinguish corresponding patterns across different sensors.
  • Derivatives capture differences between neighboring points, representing general shape while reducing dependence on exact values.
  • Feature weighting models cross-dimensional co-occurrence, while histogram counts provide invariance to the order of subsequences.
  • Statistical feature selection removes non-discriminative features from the broad space of dimensions, derivatives, n-grams, and window lengths.
  • Across 20 public benchmark datasets and motion-capture data, WEASEL+MUSE is consistently among the most accurate methods, outperforming all but a recent deep-learning classifier.

2 BACKGROUND: TIME SERIES AND BAG-OF-PATTERNS

Time series are ordered numerical observations, while multivariate time series contain multiple synchronized streams. Bag-of-Patterns converts overlapping subsequences into discrete words and histograms for classification.

  • A univariate time series is an ordered sequence of real values, whereas a multivariate time series is an ordered collection of numerical streams.
  • For synchronized sensor data, timestamps can be ignored because values are aligned across dimensions.
  • A time-series classification model learns to predict a predefined class label from labeled training series.
  • Bag-of-Patterns: Bag-of-Patterns extracts subsequences, discretizes them into words, counts word occurrences, and classifies the resulting histogram features.
  • Discretization: SAX discretizes mean values, whereas SFA discretizes Fourier-transform coefficients.
  • Bag-of-Patterns: BOP similarity depends on frequencies of subsequences, with feature selection and weighting emphasizing informative patterns.

3 RELATED WORK

Related multivariate classifiers use dimensionality reduction, symbolic representations, shapelets, autoregressive models, or deep learning. WEASEL+MUSE extends the WEASEL pipeline with sensor-aware words, unsupervised features, and derivatives for multivariate data.

  • Univariate foundations: Univariate time-series classification methods broadly use similarity-based or feature-based comparisons, including DTW, shapelets, and Bag-of-Patterns.
  • WEASEL and WEASEL+MUSE: WEASEL combines supervised symbolic representations, statistical feature selection, and logistic regression, but its univariate design loses accuracy on multivariate series.
  • WEASEL and WEASEL+MUSE: WEASEL+MUSE adapts WEASEL by adding sensor identifiers, unsupervised discrete features, and derivatives to its feature space.
  • Multivariate alternatives: Basic multivariate approaches concatenate dimensions or reduce them with methods such as PCA before applying univariate classification.
  • Multivariate alternatives: SMTS uses random-forest codebook learning and bag-of-words representations, while UFS and gRSF use randomly extracted shapelets.
  • Multivariate alternatives: LPS learns structural dependencies with regression trees and represents multivariate series using bag-of-words leaf labels.
  • Multivariate alternatives: mv-ARF models multivariate relationships with autoregressive forests, while Multivariate LSTM-FCN combines LSTM, convolutional, and squeeze-and-excitation components.

4 WEASEL+MUSE

WEASEL+MUSE is a domain-agnostic MTSC method that represents multivariate signals through dimension-aware symbolic features, derivatives, and feature co-occurrences. It combines per-dimension BOP models with multiple window lengths and feature selection to address phase variation, irrelevant dimensions, noise, and cross-dimensional structure.

  • Challenges: WEASEL+MUSE targets dimensional interplay, phase variation, and irrelevant sensor streams in multivariate time series classification.The method is motivated by gesture-recognition data where relevant events may occur at different times and only some dimensions contain useful information.
  • Feature representation: A WEASEL+MUSE feature encodes the sensor identifier, window length, and discretized word, retaining context for multivariate classification.The model can also count word occurrences and represent co-occurrences through bigrams.
  • Pipeline: Each dimension is transformed separately with SFA-based BOP models, preserving dimension-specific features while allowing phase variation across streams.The pipeline extracts normalized windows, applies a truncated Fourier transform, discretizes coefficients into words, and builds per-dimension representations.
  • Symbolic representation: Truncated Fourier approximation and coefficient discretization produce symbolic words while filtering rapid changes and improving robustness to noise.SFA keeps lower-frequency components, then maps Fourier coefficients to symbols; each window becomes a word of length l.
  • Feature construction: The feature space combines derivatives, local and global windows, unigrams, bigrams, and identifiers before aggressive reduction through feature selection.Multiple window lengths capture patterns at different scales, while derivatives encode signal changes over time.

5 EVALUATION

Across 20 public MTS datasets and motion-capture data, WEASEL+MUSE was among the most accurate classifiers, with strong robustness to noise and competitive prediction speed. Its best performance was associated with multivariate feature encoding, derivatives, and feature selection.

  • Accuracy: WEASEL+MUSE and MLSTM-FCN had the lowest overall ranks and formed the group of best classifiers, significantly outperforming baseline DTW.Compared with plain WEASEL, WEASEL+MUSE improved average rank from 6.05 to 2.45.
  • Accuracy: WEASEL+MUSE achieved 12 wins or ties across 20 datasets, the highest total, with mean accuracy of 93.5%.MLSTM-FCN had a similar mean accuracy of 92.1%.
  • Domain effects: WEASEL+MUSE performed best for sensor-reading datasets, while MLSTM-FCN performed best for motion and speech datasets.The paper links this pattern to smaller sample or feature counts in sensor readings and larger training corpora in motion and speech datasets.
  • Noise robustness: WEASEL+MUSE remained stable at 100% Gaussian-noise level, whereas DTW accuracy dropped by up to 30 percentage points as noise increased.The method uses truncated Fourier transformation and discretization, which act as a low-pass filter.
  • Prediction times: WEASEL+MUSE was faster than DTW on all but three datasets, averaging 43 times faster and reaching 400-fold speedups on Robot Failure LP1.DTW was faster on WalkvsRun, KickvsPunch, and CMU-MOCAP, which had the highest dimensionality at m = 62.
  • Design decisions: Ablation results showed that univariate variants were least accurate, while combining multivariate feature identifiers with derivatives improved ranks most.The univariate approach loses the association between features and sensors.

6 CONCLUSION

WEASEL+MUSE is presented as a highly competitive multivariate time series classifier whose engineered feature space supports robustness across noisy, high-dimensional data. Across 21 datasets, it is consistently among the most accurate classifiers, while future work could explore alternative selection, runtime benchmarking, and ensembling.

  • WEASEL+MUSE is consistently among the most accurate classifiers across 21 datasets and outperforms state-of-the-art similarity-measure and shapelet-based approaches.
  • Its feature-space engineering combines statistical feature selection, derivatives, variable window lengths, bi-grams, and symbolic representations to generate discriminative words.
  • WEASEL+MUSE provides tolerance to noise, phase invariance, and robustness to superfluous data or dimensions while weighting characteristic local and global substructures.
  • The method performs well on small datasets and is strongest for sensor readings, followed by speech, motion, and handwriting recognition tasks.
  • Future work could investigate different feature-selection methods, train and prediction-time benchmarks, and ensemble classifiers.
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