Interpretability in multivariate time series classification is crucial for understanding model decisions. However, the complexity of these classifiers often results in overwhelming feature spaces, hindering interpretability. To address this issue, we propose two novel methods: 1) Dimension selection based on segmentation of time series (DST) and 2) Feature selection based on discretization similarity (FDS). DST segments time series data and applies dimension selection to each segment, capturing distinct properties across diferent time ranges. FDS reduces feature redundancy by comparing discretization techniques and eliminating those with similar bin boundaries. Experiments on 24 UEA multivariate datasets demonstrate that our methods can significantly reduce the number of features while maintaining accuracy, ofering a practical solution for enhancing interpretability in multivariate time series classification.
Time series datasets involve large quantities of data across multiple dimensions. The complexity of multivariate time series classification can quickly become overwhelming due to the interactions between diferent dimensions, which may negatively impact the classification outcome. Consequently, multivariate time series classifiers have grown increasingly complex in their model structures and feature spaces to enhance predictive performance. However, these classifiers often lack interpretability, posing both a challenge and a requirement.
Interpretable time series classifiers, such as MR-SEQL [
In this paper, we suggest that interpretability should be evaluated not only by the architecture
of models and features but also by the number of features used for classification. While
dimensionality reduction is a common approach in various machine learning tasks [
Our main contributions and novelty of this paper include:
• Novelty. We introduce the use of segmentation and discretization similarity to reduce
the number of interpretable features in multivariate time series.
• Efectiveness and eficiency. Our proposed techniques can reduce the number of
features by up to 86% while maintaining accuracy, with an average accuracy drop of only
up to 9% on the UEA multivariate time series datasets [
• Reproducibility. Our code is publicly available on our GitHub repository1.
While many algorithms for multivariate time series classification have leveraged ensembles [
Let t = {1, . . . , } represent a time series spanning time points. A collection of such time series forms a time series instance T = {t1, . . . , t}, consisting of variables or dimensions. If = 1, T is univariate; if > 1, T is multivariate. Each time series instance T is assigned a class label ∈ y, where y is a list of class labels corresponding to each instance. The goal of time series classification models is to predict these class labels correctly.
Recent work by [
These methods assume that the selected dimensions span the entire time series. While ECP is regarded as the best among them, it sometimes fails to choose smaller dimensions, returning the whole set of dimensions. We address this issue by suggesting a segmentation-based application.
Discretization techniques have been actively used in interpretable time series classifiers to
convert time series into sets of symbols. Each time step ∈ t is converted into an event ,
creating an event sequence e. Each event value can take a unique event type . Z-Time uses the
following three techniques:
• Equal width discretization (EWD): Assuming t follows a uniform distribution,
discretization boundaries are defined so that all event labels have value ranges of equal
length, i.e., − = − [
Our assumption is that important dimensions may vary across diferent time ranges, whereas current methods select dimensions by treating the time series as a whole. Selecting dimensions from segments of the time series could potentially enhance performance. This approach might not be feasible for interpretable classifiers that use sliding windows and ensemble structures, but Z-Time applies segmentation to capture the distinct properties of diferent time periods. This method is efective for time series with many unrelated parts or where the distribution changes over time. Unlike sliding windows, which overlap over time points and discretize values within these windows, segmentation ofers a more straightforward approach to interpretability since each time point is discretized only once.
First, a time series instance T is divided into equal-length segments {T1, . . . , T}. Then, a dimension selection algorithm such as ECP or ECS is applied to each segment T, resulting in diferent dimensions being selected for each segment. When multiple time series instances are considered, the dimension selection algorithm is applied to a set of instances to ensure consistent dimension selection. Second, after segmentation, Z-Time is applied to each segment individually. This results in diferent feature sets, which are concatenated to create a single feature set for input to an interpretable linear classifier.
While segmentation has improved Z-Time’s performance, it has the side efect of linearly increasing the number of features, as each feature created from each segment must be distinguishable. This necessitates an additional step to significantly reduce the number of features.
The second proposed strategy to reduce features involves finding similarities among discretization techniques. Z-Time uses three diferent discretizations, each with and without PAA, creating six diferent representations for each dimension of a time series instance. Sometimes, diferent techniques can produce similar bin boundaries, making it redundant to retain all of them. This method compares the boundaries of the bins created by each discretization technique by calculating the diferences in boundary values. After computing the sum of boundary diferences, the elbow method is used to select dimensions with significant diferences.
Z-Time uses equal width discretization (EWD), equal frequency discretization (EFD), and SAX. Suppose a set of boundaries for a technique is g = {1, 2, . . . , }. The average diference is calculated as follows: 1 ∑︁(, − ,)2
The elbow method is then applied to identify the number of techniques with suficiently high average diferences, resulting in a set g′ where |g′| ≤ | g|. While this strategy does not reduce the number of dimensions, it significantly reduces the number of features, since in the worst case, the number is quadratic to the number of discretization techniques. Each technique creates a diferent set of event labels, thereby enhancing the overall interpretability of the classification model.
Our experiment aims to evaluate the efectiveness of our proposed methods in reducing the
number of features created by Z-Time. We used 26 UEA multivariate datasets with no missing
values for our experiments [
In total, there are 16 diferent combinations per dataset. While detailed results are available in our repository, we present the average values in Table 1. Table 1 shows relative numbers for the number of features, the number of dimensions, accuracy, and the total runtime compared to the default setting without any feature reduction technique. The best technique is marked in bold, while the second best is underlined.
First, we observe that FDS significantly reduces the number of features, achieving an additional average reduction of 24.9% of the original features for the same setting. Without FDS, the minimum feature number is 26% of the original, but it can be further reduced to 12% with FDS. Additionally, while ECP generally shows better accuracy than ECS, ECP reduces features to 26% of the original, whereas ECS can reduce them to 12% while maintaining the same accuracy with = 2.
Since Table 1 only shows average values, it might obscure the efect of DST, as results always appear inferior without DST. While standard ECP and ECS maintain better accuracy on average, ECP and ECS after segmentation show better accuracy in many instances. ECP after segmentation performs better in terms of accuracy on 16 datasets, considering all diferent settings (FDS and the number of segments). Table 2 shows the number of datasets where better accuracy is achieved by using DST. ECS with DST shows better accuracy than ECS without DST on 16 datasets with = 4 and on 13 datasets with = 2, which is more than half in both cases. However, with ECP, there is no meaningful improvement from applying DST. ECS after segmentation shows a significant drop in specific datasets, afecting the overall average, mainly due to the incorrect choice of the number of segments.
In this paper, we introduced two methods to enhance the interpretability of multivariate time series classifiers: 1) Dimension selection based on segmentation of time series (DST) and 2) Feature selection based on discretization similarity (FDS). Our experiments on 24 UEA multivariate datasets demonstrated that these methods could significantly reduce the number of features, by up to 86%, while maintaining accuracy, with only an average accuracy drop of up to 9%. These methods simplify the feature space and enhance interpretability, ofering a practical solution for multivariate time series classification without compromising predictive performance. Future work can explore optimizing segmentation processes with dynamic lengths and refining similarity measures in FDS to enhance the quality of features.