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Multi-Scale Convolutional Neural Networks for Time Series Classification
Zhicheng Cui, Wenlin Chen, Yixin Chen
TL;DR
Time series classification remains difficult because traditional methods separate feature extraction from classification and often miss features at different scales. MCNN combines multi-scale, multi-frequency feature learning with classification in an end-to-end model, achieving state-of-the-art performance and especially strong results with sufficient training data. Its reported advantages are most directly supported for benchmark datasets of limited size, while its performance with much larger datasets remains an expectation.
Problem
Time series classification is challenging because existing methods separate feature extraction from classification and often fail to adapt representations to different time scales.
Method
MCNN is an end-to-end convolutional network that jointly learns classification and multi-scale features from time- and frequency-domain transformations.
Results
MCNN achieves state-of-the-art performance, outperforming many existing models by a large margin, especially when enough training data is present.
Takeaways & Limitations
MCNN provides a unified framework for learning time- and frequency-domain representations at different scales without handcrafted features.
Takeaways & Limitations
The available TSC datasets are generally small, so MCNN's behavior on massive datasets is presented as an expectation rather than demonstrated evidence.
Abstract
from arXiv · showhide
Time series classification (TSC), the problem of predicting class labels of time series, has been around for decades within the community of data mining and machine learning, and found many important applications such as biomedical engineering and clinical prediction. However, it still remains challenging and falls short of classification accuracy and efficiency. Traditional approaches typically involve extracting discriminative features from the original time series using dynamic time warping (DTW) or shapelet transformation, based on which an off-the-shelf classifier can be applied. These methods are ad-hoc and separate the feature extraction part with the classification part, which limits their accuracy performance. Plus, most existing methods fail to take into account the fact that time series often have features at different time scales. To address these problems, we propose a novel end-to-end neural network model, Multi-Scale Convolutional Neural Networks (MCNN), which incorporates feature extraction and classification in a single framework. Leveraging a novel multi-branch layer and learnable convolutional layers, MCNN automatically extracts features at different scales and frequencies, leading to superior feature representation. MCNN is also computationally efficient, as it naturally leverages GPU computing. We conduct comprehensive empirical evaluation with various existing methods on a large number of benchmark datasets, and show that MCNN advances the state-of-the-art by achieving superior accuracy performance than other leading methods.
1. INTRODUCTION
Time series classification remains challenging because traditional distance- and feature-based methods rely on separate, often handcrafted representations and may not adapt to different time scales. MCNN addresses this by learning multi-scale representations and classification jointly in an end-to-end convolutional framework.
- Time series classification predicts class labels from time series and supports applications including clinical prediction.
- Existing approaches primarily use distance-based or feature-based methods, including DTW similarity and handcrafted feature vectors.Feature-based schemes include window statistics, spectral features, and shapelet transformations.
- Shapelet methods require extensive searches over candidate subsequences, while jointly learned shapelets provide only linear separation ability.
- CNNs automatically learn complex feature representations through convolutional layers, motivating their use for time series.
- MCNN uses multiple transformation branches and learnable convolutional layers to extract features across time scales and frequencies.It integrates feature extraction and classification in one convolutional neural network designed specifically for time series.
2. MULTI-SCALE CONVOLUTIONAL NEURAL NETWORK (MCNN) FOR TSC
MCNN is an end-to-end framework for time series classification that jointly learns feature extraction and prediction while representing patterns across multiple time scales and frequencies.
- Problem and framework: MCNN addresses time series classification by mapping an input time series directly to its predicted label.The framework is designed for categorical labels and does not require all series to have equal timestamp counts.
- Framework architecture: The framework has three stages: transformation, local convolution, and full convolution, with parameters trained jointly through backpropagation.The full convolution stage concatenates branch features before further convolutions, fully connected layers, and softmax prediction.
- Transformation stage: Transformation branches generate representations at multiple scales and frequencies using identity mapping, down-sampling, and spectral or smoothing transformations.Down-sampling captures different temporal scales, while low-frequency filters and moving averages make trends clearer amid perturbations and noise.
- Local convolution stage: Independent 1-D local convolutions use a shared filter size across transformed series, so shorter inputs provide larger receptive fields in the original series.This design lets local convolution outputs capture different scales of the original time series.
- Pooling: Max pooling with multiple sizes reduces feature-map and parameter sizes, introduces shift invariance, and can improve computational efficiency and robustness.Pooling also encourages filters to learn local features by updating them from relatively few activated convolution parts.
- Data augmentation: Window slicing augments smaller datasets by treating slices as independent training instances and aggregating slice predictions by majority vote.The procedure can also accommodate time series with unequal lengths by cutting them into common-length windows.
3. DISCUSSION
MCNN uses convolution filters and max pooling to extract class-discriminative patterns, including patterns that vary in time scale. Its convolutional representation also relates closely to learned shapelets and can efficiently implement Euclidean-distance computations.
- 3.1 Effectiveness of convolution filters: Convolution filters can expose local characteristics such as neighboring-point gradients, depending on their learned weights.The example filter f = [1, −1] produces the gradient between adjacent points.
- 3.1 Effectiveness of convolution filters: A single learned filter followed by max pooling can distinguish Gun Point classes despite similar shapes occurring at different time scales.The blue curves produce larger post-convolution maxima than the red curve, while differing plateau lengths make classification challenging for DTW or shapelet methods.
- 3.1 Effectiveness of convolution filters: MCNN provides a degree of interpretability by revealing the characteristic detected by a filter and the feature emphasized through max pooling.In the Gun Point example, max pooling selects the larger response associated with the downward part of the signals.
- 3.2 Relation to learning shapelets: MCNN and learned time-series shapelets jointly learn filters or shapelets with a classifier, but MCNN measures similarity through inner products rather than Euclidean distance.A one-branch convolutional MCNN special case represents each input window through its inner product with a filter.
- 3.2 Relation to learning shapelets: Learning shapelets is a special case of learning convolution filters when the filters are constrained to have equal ℓ2 norms.The full MCNN framework is more general because its multi-scale and multi-frequency branches address different time scales and noise.
- 3.2 Relation to learning shapelets: Convolutional implementations can compute Euclidean distances between time series and shapelets efficiently using deep-learning packages and GPU speedups.The Euclidean distance combines convolution with the ℓ2 norms of the filter and an input segment.
4. RELATED WORK
TSC research includes traditional distance-, feature-, ensemble-, and neural-network-based approaches. MCNN focuses on univariate series while adding multi-scale and multi-frequency processing to jointly learn representations and classification.
- 4. RELATED WORK: Traditional TSC methods commonly use distance measures with kNN or feature extraction followed by conventional classifiers, while ensemble methods combine multiple classifiers.Distance-based methods compare time series, whereas feature-based methods use deterministic time- or frequency-domain features.
- 4. RELATED WORK: Deep neural networks combine hierarchical feature extraction and classification, and prior comparisons report stronger feature extraction from CNN convolutions than from ad-hoc feature selection.Applications of CNNs to TSC had only recently begun to receive attention in the cited discussion.
- 4. RELATED WORK: A multichannel CNN for multivariate series assigns each series to a separate CNN, concatenates the extracted features, and processes them with another CNN framework.The cited architecture requires large multivariate datasets for training, whereas MCNN targets univariate series and adds multi-scale and multi-frequency branches.
- 4. RELATED WORK: CNNs have also been applied to time-series metric learning, while shapelets remain useful because their detected shapes can provide insight and interpretability.The cited metric-learning model uses CNN-based embeddings with 1-NN classification.
- 4. RELATED WORK: Pooling can provide scale invariance to some extent, motivating multi-scale branches that preserve short-term and long-term features.MCNN downsamples raw data into different time scales before extracting features.
5. EXPERIMENTAL RESULTS
MCNN is evaluated against standard CNN, classical baselines, recent state-of-the-art methods, and ensembles on 44 UCR datasets. It achieves strong overall accuracy, significantly outperforms standard CNN and most alternatives, and closely matches COTE while using a single algorithm.
- Experimental setup: MCNN is evaluated on 44 UCR datasets using default UCR splits, with comparisons against classical, recent, convolutional, and ensemble classifiers.Baseline results are collected from prior authoritative evaluations, and MCNN hyperparameters are tuned by cross-validation.
- CNN comparison: MCNN achieves better test accuracy than a parameter-matched standard CNN on 41 of 44 datasets, with significance confirmed at the 1% level.The comparison isolates the contribution of MCNN’s multi-scale transformations and local convolutions.
- Comprehensive evaluation: MCNN attains the highest accuracy on 10 datasets and a mean rank of 3.95, lower than every state-of-the-art method except COTE.Table 1 ranks all 15 classifiers for each dataset, with lower mean rank indicating better performance.
- Statistical comparison: MCNN is significantly better than all compared methods except BOSS and COTE at the 1% level, while differences among MCNN, BOSS, and COTE are not significant.The comparison uses binomial and Wilcoxon signed rank tests.
- Classifier groups: MCNN has the lowest accumulated rank among distance-based and feature-based classifiers, remaining consistently ahead of the feature-based group by a large margin.Accumulated ranks are plotted across datasets ordered alphabetically.
- Ensemble comparison: MCNN performs very close to COTE and matches its state-of-the-art performance despite COTE combining 35 classifiers.Critical-difference analysis finds no significant difference between the two methods; MCNN is also orthogonal to flat-COTE.
6. CONCLUSIONS
MCNN unifies feature extraction and classification while learning representations across time and frequency scales. Experiments report state-of-the-art performance, particularly with sufficient training data, while current TSC datasets remain relatively small.
- MCNN unifies feature extraction and classification and jointly learns parameters through backpropagation across time and frequency domains.Its multiple branches extract features at different frequency and time scales.
- MCNN achieves state-of-the-art performance and outperforms many existing models by a large margin, especially with enough training data.
- Current TSC datasets range from approximately 50 to a few thousand training examples, limiting the available training scale.The authors expect MCNN to show greater advantages with much larger datasets.
- Future work will augment MCNN with side information from multiple sources, including text, image, and speech.