The Great Time Series Classification Bake Off: An Experimental Evaluation of Recently Proposed Algorithms. Extended Version

In the last five years there have been a large number of new time series classification algorithms proposed in the literature. These algorithms have been evaluated on subsets of the 47 data sets in the University of California, Riverside time series classification archive. The archive has recently been expanded to 85 data sets, over half of which have been donated by researchers at the University of East Anglia. Aspects of previous evaluations have made comparisons between algorithms difficult. For example, several different programming languages have been used, experiments involved a single train/test split and some used normalised data whilst others did not. The relaunch of the archive provides a timely opportunity to thoroughly evaluate algorithms on a larger number of datasets. We have implemented 18 recently proposed algorithms in a common Java framework and compared them against two standard benchmark classifiers (and each other) by performing 100 resampling experiments on each of the 85 datasets. We use these results to test several hypotheses relating to whether the algorithms are significantly more accurate than the benchmarks and each other. Our results indicate that only 9 of these algorithms are significantly more accurate than both benchmarks and that one classifier, the Collective of Transformation Ensembles, is significantly more accurate than all of the others. All of our experiments and results are reproducible: we release all of our code, results and experimental details and we hope these experiments form the basis for more rigorous testing of new algorithms in the future

Asymmetric Learning Vector Quantization for Efficient Nearest Neighbor Classification in Dynamic Time Warping Spaces

The nearest neighbor method together with the dynamic time warping (DTW) distance is one of the most popular approaches in time series classification. This method suffers from high storage and computation requirements for large training sets. As a solution to both drawbacks, this article extends learning vector quantization (LVQ) from Euclidean spaces to DTW spaces. The proposed LVQ scheme uses asymmetric weighted averaging as update rule. Empirical results exhibited superior performance of asymmetric generalized LVQ (GLVQ) over other state-of-the-art prototype generation methods for nearest neighbor classification

Time series classification with ensembles of elastic distance measures

Several alternative distance measures for comparing time series have recently been proposed and evaluated on time series classification (TSC) problems. These include variants of dynamic time warping (DTW), such as weighted and derivative DTW, and edit distance-based measures, including longest common subsequence, edit distance with real penalty, time warp with edit, and move–split–merge. These measures have the common characteristic that they operate in the time domain and compensate for potential localised misalignment through some elastic adjustment. Our aim is to experimentally test two hypotheses related to these distance measures. Firstly, we test whether there is any significant difference in accuracy for TSC problems between nearest neighbour classifiers using these distance measures. Secondly, we test whether combining these elastic distance measures through simple ensemble schemes gives significantly better accuracy. We test these hypotheses by carrying out one of the largest experimental studies ever conducted into time series classification. Our first key finding is that there is no significant difference between the elastic distance measures in terms of classification accuracy on our data sets. Our second finding, and the major contribution of this work, is to define an ensemble classifier that significantly outperforms the individual classifiers. We also demonstrate that the ensemble is more accurate than approaches not based in the time domain. Nearly all TSC papers in the data mining literature cite DTW (with warping window set through cross validation) as the benchmark for comparison. We believe that our ensemble is the first ever classifier to significantly outperform DTW and as such raises the bar for future work in this area

Accel: A Corrective Fusion Network for Efficient Semantic Segmentation on Video

We present Accel, a novel semantic video segmentation system that achieves high accuracy at low inference cost by combining the predictions of two network branches: (1) a reference branch that extracts high-detail features on a reference keyframe, and warps these features forward using frame-to-frame optical flow estimates, and (2) an update branch that computes features of adjustable quality on the current frame, performing a temporal update at each video frame. The modularity of the update branch, where feature subnetworks of varying layer depth can be inserted (e.g. ResNet-18 to ResNet-101), enables operation over a new, state-of-the-art accuracy-throughput trade-off spectrum. Over this curve, Accel models achieve both higher accuracy and faster inference times than the closest comparable single-frame segmentation networks. In general, Accel significantly outperforms previous work on efficient semantic video segmentation, correcting warping-related error that compounds on datasets with complex dynamics. Accel is end-to-end trainable and highly modular: the reference network, the optical flow network, and the update network can each be selected independently, depending on application requirements, and then jointly fine-tuned. The result is a robust, general system for fast, high-accuracy semantic segmentation on video.Comment: CVPR 2019 (oral

Trainable Time Warping: Aligning Time-Series in the Continuous-Time Domain

DTW calculates the similarity or alignment between two signals, subject to temporal warping. However, its computational complexity grows exponentially with the number of time-series. Although there have been algorithms developed that are linear in the number of time-series, they are generally quadratic in time-series length. The exception is generalized time warping (GTW), which has linear computational cost. Yet, it can only identify simple time warping functions. There is a need for a new fast, high-quality multisequence alignment algorithm. We introduce trainable time warping (TTW), whose complexity is linear in both the number and the length of time-series. TTW performs alignment in the continuous-time domain using a sinc convolutional kernel and a gradient-based optimization technique. We compare TTW and GTW on 85 UCR datasets in time-series averaging and classification. TTW outperforms GTW on 67.1% of the datasets for the averaging tasks, and 61.2% of the datasets for the classification tasks.Comment: ICASSP 201

Predicting Ambulance Demand: Challenges and Methods

Predicting ambulance demand accurately at a fine resolution in time and space (e.g., every hour and 1 km$^2$) is critical for staff / fleet management and dynamic deployment. There are several challenges: though the dataset is typically large-scale, demand per time period and locality is almost always zero. The demand arises from complex urban geography and exhibits complex spatio-temporal patterns, both of which need to captured and exploited. To address these challenges, we propose three methods based on Gaussian mixture models, kernel density estimation, and kernel warping. These methods provide spatio-temporal predictions for Toronto and Melbourne that are significantly more accurate than the current industry practice.Comment: presented at 2016 ICML Workshop on #Data4Good: Machine Learning in Social Good Applications, New York, N

Elastic bands across the path: A new framework and methods to lower bound DTW

There has been renewed recent interest in developing effective lower bounds for Dynamic Time Warping (DTW) distance between time series. These have many applications in time series indexing, clustering, forecasting, regression and classification. One of the key time series classification algorithms, the nearest neighbor algorithm with DTW distance (NN-DTW) is very expensive to compute, due to the quadratic complexity of DTW. Lower bound search can speed up NN-DTW substantially. An effective and tight lower bound quickly prunes off unpromising nearest neighbor candidates from the search space and minimises the number of the costly DTW computations. The speed up provided by lower bound search becomes increasingly critical as training set size increases. Different lower bounds provide different trade-offs between computation time and tightness. Most existing lower bounds interact with DTW warping window sizes. They are very tight and effective at smaller warping window sizes, but become looser as the warping window increases, thus reducing the pruning effectiveness for NN-DTW. In this work, we present a new class of lower bounds that are tighter than the popular Keogh lower bound, while requiring similar computation time. Our new lower bounds take advantage of the DTW boundary condition, monotonicity and continuity constraints to create a tighter lower bound. Of particular significance, they remain relatively tight even for large windows. A single parameter to these new lower bounds controls the speed-tightness trade-off. We demonstrate that these new lower bounds provide an exceptional balance between computation time and tightness for the NN-DTW time series classification task, resulting in greatly improved efficiency for NN-DTW lower bound search

A Shapelet Transform for Multivariate Time Series Classification

Shapelets are phase independent subsequences designed for time series classification. We propose three adaptations to the Shapelet Transform (ST) to capture multivariate features in multivariate time series classification. We create a unified set of data to benchmark our work on, and compare with three other algorithms. We demonstrate that multivariate shapelets are not significantly worse than other state-of-the-art algorithms

Robust 3D Human Motion Reconstruction Via Dynamic Template Construction

In multi-view human body capture systems, the recovered 3D geometry or even the acquired imagery data can be heavily corrupted due to occlusions, noise, limited field of- view, etc. Direct estimation of 3D pose, body shape or motion on these low-quality data has been traditionally challenging.In this paper, we present a graph-based non-rigid shape registration framework that can simultaneously recover 3D human body geometry and estimate pose/motion at high fidelity.Our approach first generates a global full-body template by registering all poses in the acquired motion sequence.We then construct a deformable graph by utilizing the rigid components in the global template. We directly warp the global template graph back to each motion frame in order to fill in missing geometry. Specifically, we combine local rigidity and temporal coherence constraints to maintain geometry and motion consistencies. Comprehensive experiments on various scenes show that our method is accurate and robust even in the presence of drastic motions.Comment: 3DV 2017 pape

Twofold Video Hashing with Automatic Synchronization

Video hashing finds a wide array of applications in content authentication, robust retrieval and anti-piracy search. While much of the existing research has focused on extracting robust and secure content descriptors, a significant open challenge still remains: Most existing video hashing methods are fallible to temporal desynchronization. That is, when the query video results by deleting or inserting some frames from the reference video, most existing methods assume the positions of the deleted (or inserted) frames are either perfectly known or reliably estimated. This assumption may be okay under typical transcoding and frame-rate changes but is highly inappropriate in adversarial scenarios such as anti-piracy video search. For example, an illegal uploader will try to bypass the 'piracy check' mechanism of YouTube/Dailymotion etc by performing a cleverly designed non-uniform resampling of the video. We present a new solution based on dynamic time warping (DTW), which can implement automatic synchronization and can be used together with existing video hashing methods. The second contribution of this paper is to propose a new robust feature extraction method called flow hashing (FH), based on frame averaging and optical flow descriptors. Finally, a fusion mechanism called distance boosting is proposed to combine the information extracted by DTW and FH. Experiments on real video collections show that such a hash extraction and comparison enables unprecedented robustness under both spatial and temporal attacks.Comment: submitted to Image Processing (ICIP), 2014 21st IEEE International Conference o