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MultiRocket: Multiple pooling operators and transformations for fast and effective time series classification
Chang Wei Tan, Angus Dempster, Christoph Bergmeir, Geoffrey I. Webb
TL;DR
Accurate time series classification methods often sacrifice scalability, motivating a faster alternative that preserves strong accuracy. MultiRocket extends MiniRocket with first-order differencing and multiple pooling operators to diversify features; on UCR datasets, it is significantly more accurate than MiniRocket, competitive with HIVE-COTE 2.0, and still much faster than other state-of-the-art methods.
Problem
Many accurate TSC methods have high computational complexity, while scalable Rocket-family methods are somewhat less accurate than HIVE-COTE variants.
Method
MultiRocket extends MiniRocket by convolving both raw and first-order-differenced series and applying multiple pooling operators to generate diverse features.
Results
MultiRocket is significantly more accurate than MiniRocket, not significantly less accurate than HIVE-COTE 2.0, and significantly faster than other state-of-the-art TSC algorithms.
Takeaways & Limitations
MultiRocket offers a scalable TSC method combining accuracy competitive with the strongest cited method and substantially lower computational cost than most alternatives.
Takeaways & Limitations
The authors identify multivariate time series and regression tasks as promising directions for future work.
Abstract
from arXiv · showhide
We propose MultiRocket, a fast time series classification (TSC) algorithm that achieves state-of-the-art performance with a tiny fraction of the time and without the complex ensembling structure of many state-of-the-art methods. MultiRocket improves on MiniRocket, one of the fastest TSC algorithms to date, by adding multiple pooling operators and transformations to improve the diversity of the features generated. In addition to processing the raw input series, MultiRocket also applies first order differences to transform the original series. Convolutions are applied to both representations, and four pooling operators are applied to the convolution outputs. When benchmarked using the University of California Riverside TSC benchmark datasets, MultiRocket is significantly more accurate than MiniRocket, and competitive with the best ranked current method in terms of accuracy, HIVE-COTE 2.0, while being orders of magnitude faster.
1 Introduction
MultiRocket extends MiniRocket to improve time series classification accuracy through transformed inputs and diverse pooling, while retaining strong computational scalability. Across UCR datasets, it is significantly more accurate than MiniRocket and competitive with HIVE-COTE 2.0.
- Motivation: High-accuracy TSC methods often incur high computational complexity and limited scalability.Rocket and MiniRocket are exceptions among scalable methods, but are somewhat less accurate than HIVE-COTE variants.
- Method: MultiRocket extends MiniRocket with first-order differencing, additional pooling operators, and more diverse extracted features.It convolves both the raw and differenced series using MiniRocket kernels before generating features for a linear classifier.
- Accuracy: MultiRocket is significantly more accurate than MiniRocket and not significantly less accurate than HIVE-COTE 2.0 on UCR datasets.The comparison uses 50,000 features and reports average accuracy over the benchmark datasets.
- Computational cost: 5 minutes: MultiRocket processes all 109 UCR datasets using 32 threads, remaining at least an order of magnitude faster than several leading methods.The reported timing includes transformation, convolution, training, and testing, with averages over 30 resamples.
- Computational cost: 20% longer: default MultiRocket processes the full repository compared with MiniRocket using the same number of features.With 50,000 features, MultiRocket is up to an order of magnitude slower than 10,000-feature MiniRocket, but the same-feature comparison narrows substantially.
2 Related work
Related work frames MultiRocket against accurate but computationally expensive TSC ensembles and faster Rocket-family methods. It also motivates multiple representations and transformations as ways to capture complementary time-series information.
- State of the art: Most state-of-the-art TSC methods achieve high accuracy but scale poorly in computational cost.Processing the 109-dataset UCR archive takes days or weeks for several ensemble methods on a single CPU thread.
- Ensemble methods: HIVE-COTE 2.0 uses diverse representation-specific components, while InceptionTime and TS-CHIEF use ensembles to capture complementary patterns.HIVE-COTE 2.0 has the best average accuracy rank among the cited univariate and multivariate archive benchmarks.
- Scalability: MultiRocket completes the 109-dataset benchmark in around 5 minutes with 32 threads, compared with more than two weeks for HIVE-COTE 2.0 on one thread.On the same hardware, MiniRocket takes around 2 minutes and default MultiRocket around 5 minutes.
- Rocket family: Rocket applies 10,000 random convolutional kernels and PPV and Max pooling, producing 20,000 features for a linear classifier.Dilation and PPV are identified as key aspects of Rocket’s state-of-the-art accuracy.
- Rocket family: MiniRocket uses a small fixed kernel set and PPV features, preserving Rocket’s accuracy while reducing single-core training and testing to under 10 minutes.Because it is much faster at the same accuracy, MiniRocket is recommended as Rocket’s default variant.
- Time-series representations: Time-series transformations can reveal different information, while poor representations may lose discriminative performance.Differencing is a mapping-based transform, and simple differencing is used to estimate first-order derivatives.
3 MultiRocket
MultiRocket extends MiniRocket by combining first-order differencing with additional pooling operators to increase feature diversity while retaining its convolutional architecture.
- MultiRocket shares MiniRocket’s architecture: convolutional transformation, feature computation, and linear classification.
- The method’s transformations and pooling choices were tuned on 40 development datasets to avoid overfitting the full UCR archive.
- Time series representations: First-order differencing injects representation diversity by adding a transformed series alongside the original input.The first-order difference captures the rate of change between adjacent time steps.
- Convolution operation: Convolution is applied to both the base and first-order difference series using separate dilation and bias settings.The representations differ in length and value range, requiring distinct parameter sets.
3.3 Convolution operation
MultiRocket uses distinct dilation and bias sets for the base and first-order difference representations because their lengths and value ranges differ.
- The first-order difference representation is one value shorter, so its maximum dilation and resulting kernel set differ from the base representation.
- Different value ranges also require separate bias values for the two representations.
3.4 Pooling operators
MultiRocket summarizes each convolution output with four pooling operators that capture positivity, magnitude, location, and consecutive positive runs.
- MultiRocket computes PPV, MPV, MIPV, and LSPV for each convolution output.These four features summarize the output values and are illustrated using a convolution output of length 100.
- Proportion of Positive Values: PPV measures the proportion of positive values in a convolution output and is retained because of its strong performance in MiniRocket.
- Mean of Positive Values: MPV captures the magnitude or intensity of positive convolution values, adding information discarded by PPV.It can be computed with negligible additional cost because it uses information related to PPV’s positive values.
- Mean of Indices of Positive Values: MIPV captures the relative location of positive values by averaging their indices, returning −1 when no positive values exist.For example, positive values at indices [6, 7, 8, 9] produce MIPV = 7.5.
- Longest Stretch of Positive Values: LSPV records the maximum length of a consecutive positive subsequence, distinguishing patterns that MIPV pools together.Unlike MPV and MIPV, LSPV incurs a slight computational overhead.
3.5 Classifier
MultiRocket’s transformed features are used with a linear classifier, with ridge regression as the default and logistic regression recommended for larger datasets.
- MultiRocket produces 49,728 features by default from 6,216 kernels, two representations, and four pooling operators.
- The transformed features train a linear classifier, using ridge regression by default.
- Logistic regression is preferable for larger datasets because it is faster to train.The experiments reported in Section 4 used the ridge classifier.
4 Experiments
Across 109 UCR datasets and 30 resamples, MultiRocket delivers accuracy competitive with leading ensemble methods while retaining substantially lower computational cost. Its gains over MiniRocket are associated with combining first-order differences and multiple pooling operators, with 50,000 features selected as the default.
- Comparing with current state of the art: MultiRocket is significantly more accurate than MiniRocket and not significantly less accurate than HIVE-COTE 2.0, TS-CHIEF, or InceptionTime.The comparison uses post-hoc statistical testing with a two-sided Wilcoxon signed-rank test and Holm correction.
- Comparing with current state of the art: 59 wins out of 109 datasets belong to HIVE-COTE 2.0, although their accuracy difference from MultiRocket remains within ±5%.MultiRocket and InceptionTime are not significantly different, but their dataset-level accuracy differences show large variance.
- Runtime analysis: 5 minutes of training and classification across all 109 datasets with 32 threads makes MultiRocket at least an order of magnitude faster than HIVE-COTE 2.0, TS-CHIEF, and InceptionTime.With a single thread, the default 50,000-feature MultiRocket is about 10 times slower than 10,000-feature MiniRocket but only 4 times slower at the same feature count.
- Time series representations: Combining the base series with first-order differences improves MiniRocket, with first-order differences producing the most accurate representation combination.Using any transformed representation alone does not improve accuracy, whereas combining it with the base series does.
- Pooling operators: Using all four pooling operators performs best overall, while PPV remains a strong feature and individual operators perform significantly worse than PPV alone.The comparison uses MultiRocket with 10,000 features against MiniRocket variants.
- Number of features: 50,000 features is the most accurate setting, with MultiRocket significantly outperforming 50,000-feature MiniRocket and the MiniRocket base-plus-difference variant on 76 and 68 datasets, respectively.Increasing to 100,000 features provides little additional benefit because increasingly many features are similar.
5 Conclusion
MultiRocket extends MiniRocket with additional pooling operators and transformations, improving feature diversity and accuracy while retaining a substantial speed advantage over other state-of-the-art classifiers.
- MultiRocket adds multiple pooling operators and transformations to MiniRocket to improve the diversity of generated features.
- MultiRocket is significantly more accurate than MiniRocket and not significantly less accurate than HIVE-COTE 2.0 on the UCR archive.
- Although approximately 10 times slower than MiniRocket, MultiRocket remains significantly faster than other state-of-the-art time series classification algorithms.
- The method applies first-order differencing and uses PPV, MPV, MIPV, and LSPV to summarize convolution outputs from both representations.
- Future work includes evaluating MultiRocket on multivariate time series, regression tasks, and data beyond time series.
A Features in MultiRocket
The feature-computation procedure scans each convolution output and returns four summary statistics: PPV, MPV, MIPV, and LSPV.
- Algorithm 1 computes all four features for a given convolution output Z.
- The algorithm initializes counters and variables for positive values, means, indices, and the longest positive stretch.
- The procedure iterates through Z to extract the information required for feature computation, then performs a final check on the last value.
- The output F is an array containing PPV, MPV, MIPV, and LSPV after kernels produce convolution output Z.
B Example for Longest Stretch of Positive Values
The longest-stretch feature distinguishes convolution outputs whose positive responses occur at the beginning and end from those concentrated in the middle, illustrated by crop-season patterns.
- MIPV can assign the same value, 4.5, to outputs C and D despite their different positive-value locations.
- Outputs C and D reflect different temporal patterns: C has peaks at the start and end of the year, whereas D peaks in midyear.
- The example associates C with winter wheat and D with summer corn in southern France satellite time series.
C Pairwise comparisons
Pairwise comparisons across 109 UCR datasets show MultiRocket is significantly more accurate than the compared state-of-the-art methods, while achieving accuracy similar to HIVE-COTE 2.0.
- MultiRocket is significantly more accurate than the compared state-of-the-art methods, although most improvements fall within the ±5% interval.
- 109 UCR datasets are compared using average accuracy over 30 resamples per dataset, with dotted lines marking a ±5% accuracy interval.
- MultiRocket has accuracy similar to HIVE-COTE 2.0, with more datasets within the ±5% range than for any other compared state-of-the-art method.
- The HIVE-COTE 2.0 comparison uses the same 109 UCR datasets and averages accuracy over 30 resamples for each dataset.
D MultiRocket versus MiniRocket
On 109 UCR datasets, MultiRocket was compared with MiniRocket using both its default 50,000-feature configuration and a smaller 10,000-feature variant. MultiRocket was more accurate overall, although most wins fell within a 5% accuracy interval.
- Experimental setup: 50,000 features is MultiRocket’s default, five times MiniRocket’s feature count; a 10,000-feature variant was created for comparable evaluation.The comparison used 109 UCR datasets.
- Figure 16: Figure 16 plots pairwise average accuracy over 30 resamples for MiniRocket versus both MultiRocket configurations.Dotted lines mark ±5% intervals on classification accuracy.
- Results: 70 datasets favored the 10,000-feature MultiRocket variant over MiniRocket.This smaller variant was evaluated to match MiniRocket’s default feature scale.