Abstract Time series classification (TSC) is a challenging task due to the diversity of types of features that may be relevant for different classification tasks, including trends, variance, frequency, magnitude, and various patterns. To address this challenge, several alternative classes of approach have been developed. While kernel, neural network, and hybrid approaches perform well overall, some specialized approaches are better suited for specific tasks. In this paper, we propose a new similarity-based classifier, Proximity Forest version 2.0 (PF 2.0), which outperforms previous state-of-the-art similarity-based classifiers across the UCR benchmark and outperforms other state-of-the-art methods on specific datasets in the benchmark that are best addressed by similarity-base methods. PF 2.0 incorporates three recent advances in time series similarity measures — (1) computationally efficient early abandoning and pruning to speedup elastic similarity computations; (2) a new elastic similarity measure, Amerced Dynamic Time Warping ( $${{\,\textrm{ADTW}\,}}$$ ADTW ); and (3) cost function tuning. It rationalizes the set of similarity measures employed, reducing the eight base measures of the original PF to four and using the first derivative transform with all similarity measures, rather than a limited subset. It also incorporates HYDRA, a dictionary-based transform. We have re-implemented PF 1.0 and implemented PF 2.0 framework in Java, making the PF framework more efficient.

Abstract Dynamic time warping (DTW) is a popular time series distance measure that aligns the points in two series with one another. These alignments support warping of the time dimension to allow for processes that unfold at differing rates. The distance is the minimum sum of costs of the resulting alignments over any allowable warping of the time dimension. The cost of an alignment of two points is a function of the difference in the values of those points. The original cost function was the absolute value of this difference. Other cost functions have been proposed. A popular alternative is the square of the difference. However, to our knowledge, this is the first investigation of both the relative impacts of using different cost functions and the potential to tune cost functions to different time series classification tasks. We do so in this paper by using a tunable cost function $$\lambda _{\gamma }$$ λ γ with parameter $$\gamma $$ γ . We show that higher values of $$\gamma $$ γ place greater weight on larger pairwise differences, while lower values place greater weight on smaller pairwise differences. We demonstrate that training $$\gamma $$ γ significantly improves the accuracy of both the $${ DTW }$$ DTW nearest neighbor and Proximity Forest classifiers.

Abstract Nearest neighbour similarity measures are widely used in many time series data analysis applications. They compute a measure of similarity between two time series. Most applications require tuning of these measures’ meta-parameters in order to achieve good performance. However, most measures have at least $$O(L^2)$$ O ( L 2 ) complexity, making them computationally expensive and the process of learning their meta-parameters burdensome, requiring days even for datasets containing only a few thousand series. In this paper, we propose UltraFastMPSearch, a family of algorithms to learn the meta-parameters for different types of time series distance measures. These algorithms are significantly faster than the prior state of the art. Our algorithms build upon the state of the art, exploiting the properties of a new efficient exact algorithm which supports early abandoning and pruning for most time series distance measures. We show on 128 datasets from the UCR archive that our new family of algorithms are up to an order of magnitude faster than the previous state of the art.

The Dynamic Time Warping (DTW) similarity measure is widely used in many time series data mining applications. It computes the cost of aligning two series, smaller costs indicating more similar series. Most applications require tuning of DTW’s Warping Window (WW) parameter in order to achieve good performance. This parameter controls the amount of warping allowed, reducing pathological alignments, with the added benefit of speeding up computation. However, since DTW is in itself very costly, learning the WW is a burdensome process, requiring days even for datasets containing only a few thousand series. In this paper, we propose ULTRAFASTWWSEARCH, a new algorithm able to learn the WW significantly faster than the state-of-the-art FASTWWSEARCH method. ULTRAFASTWWSEARCH builds upon the latter, exploiting the properties of a new efficient exact DTW algorithm which supports early abandoning and pruning (EAP). We show on 128 datasets from the UCR archive that ULTRAFASTWWSEARCH is up to an order of magnitude faster than the previous state of the art.

Time series classification maps time series to labels. The nearest neighbor algorithm (NN) using the Dynamic Time Warping (DTW) similarity measure is a leading algorithm for this task and a component of the current best ensemble classifiers for time series. However, NN-DTW is only a winning combination when its meta-parameter – its warping window – is learned from the training data. The warping window (WW) intuitively controls the amount of distortion allowed when comparing a pair of time series. With a training database of N time series of lengths L, a naive approach to learning the WW requires Θ(N2·L3) operations. This often results in NN-DTW requiring days for training on datasets containing a few thousand time series only. In this paper, we introduce FastWWSearch: an efficient and exact method to learn WW. We show on 86 datasets that our method is always faster than the state of the art, with at least one order of magnitude and up to 1000x speed-up.