Temporal graphs are widely used to model dynamic systems with time-varying interactions. In real-world scenarios, the underlying mechanisms of generating future interactions in dynamic systems are typically governed by a set of recurring substructures within the graph, known as temporal motifs. Despite the success and prevalence of current temporal graph neural networks (TGNN), it remains uncertain which temporal motifs are recognized as the significant indications that trigger a certain prediction from the model, which is a critical challenge for advancing the explainability and trustworthiness of current TGNNs.

Temporal graphs are widely used to model dynamic systems with time-varying interactions. In real-world scenarios, the underlying mechanisms of generating future interactions in dynamic systems are typically governed by a set of recurring substructures within the graph, known as temporal motifs. Despite the success and prevalence of current temporal graph neural networks (TGNN), it remains uncertain which temporal motifs are recognized as the significant indications that trigger a certain prediction from the model, which is a critical challenge for advancing the explainability and trustworthiness of current TGNNs. To address this challenge, we propose a novel approach, called Temporal Motifs Explainer (TempME), which uncovers the most pivotal temporal motifs guiding the prediction of TGNNs. Derived from the information bottleneck principle, TempME extracts the most interaction-related motifs while minimizing the amount of contained information to preserve the sparsity and succinctness of the explanation.

In current medical practice, patients undergoing depression treatment must wait four to six weeks before a clinician can assess medication response due to the delayed noticeable effects of antidepressants. Identification of a treatment response at any earlier stage is of great importance, since it can reduce the emotional and economic burden connected with the treatment. We approach the prediction of a patient response to a treatment as a classification problem, by utilizing the dynamic properties of EEG recordings on the 7th day of the treatment. We present a novel framework that applies motif discovery to extract meaningful features from EEG data distinguishing between depression treatment responders and non-responders. We applied our framework also to classification tasks in other psychiatric EEG datasets, namely to patients with symptoms of schizophrenia, pediatric patients with intractable seizures, and Alzheimer disease and dementia. We achieved high classification precision in all data sets. The results demonstrate that the dynamic properties of the EEGs may support clinicians in decision making both in diagnosis and in the prediction depression treatment response as early as on the 7th day of the treatment. To our best knowledge, our work is the first one using motifs in the depression diagnostics in general.

Time Series Motif Discovery (TSMD), which aims at finding recurring patterns in time series, is an important task in numerous application domains, and many methods for this task exist. These methods are usually evaluated qualitatively. A few metrics for quantitative evaluation, where discovered motifs are compared to some ground truth, have been proposed, but they typically make implicit assumptions that limit their applicability. This paper introduces PROM, a broadly applicable metric that overcomes those limitations, and TSMD-Bench, a benchmark for quantitative evaluation of time series motif discovery. Experiments with PROM and TSMD-Bench show that PROM provides a more comprehensive evaluation than existing metrics, that TSMD-Bench is a more challenging benchmark than earlier ones, and that the combination can help understand the relative performance of TSMD methods. More generally, the proposed approach enables large-scale, systematic performance comparisons in this field.

Our proposed framework attempts to break the trade-off between performance and explainability by introducing an explainable-by-design convolutional neural network (CNN) based on the lateral inhibition mechanism. The ExplaiNet model consists of the predictor, that is a high-accuracy CNN with residual or dense skip connections, and the explainer probabilistic graph that expresses the spatial interactions of the network neurons. The value on each graph node is a local discrete feature (LDF) vector, a patch descriptor that represents the indices of antagonistic neurons ordered by the strength of their activations, which are learned with gradient descent. Using LDFs as sequences we can increase the conciseness of explanations by repurposing EXTREME, an EM-based sequence motif discovery method that is typically used in molecular biology. Having a discrete feature motif matrix for each one of intermediate image representations, instead of a continuous activation tensor, allows us to leverage the inherent explainability of Bayesian networks. By collecting observations and directly calculating probabilities, we can explain causal relationships between motifs of adjacent levels and attribute the model's output to global motifs. Moreover, experiments on various tiny image benchmark datasets confirm that our predictor ensures the same level of performance as the baseline architecture for a given count of parameters and/or layers. Our novel method shows promise to exceed this performance while providing an additional stream of explanations. In the solved MNIST classification task, it reaches a comparable to the state-of-the-art performance for single models, using standard training setup and 0.75 million parameters.

A leitmotif is a recurring theme in literature, movies or music that carries symbolic significance for the piece it is contained in. When this piece can be represented as a multi-dimensional time series (MDTS), such as acoustic or visual observations, finding a leitmotif is equivalent to the pattern discovery problem, which is an unsupervised and complex problem in time series analytics. Compared to the univariate case, it carries additional complexity because patterns typically do not occur in all dimensions but only in a few - which are, however, unknown and must be detected by the method itself. In this paper, we present the novel, efficient and highly effective leitmotif discovery algorithm LAMA for MDTS. LAMA rests on two core principals: (a) a leitmotif manifests solely given a yet unknown number of sub-dimensions - neither too few, nor too many, and (b) the set of sub-dimensions are not independent from the best pattern found therein, necessitating both problems to be approached in a joint manner. In contrast to most previous methods, LAMA tackles both problems jointly - instead of independently selecting dimensions (or leitmotifs) and finding the best leitmotifs (or dimensions). Our experimental evaluation on a novel ground-truth annotated benchmark of 14 distinct real-life data sets shows that LAMA, when compared to four state-of-the-art baselines, shows superior performance in detecting meaningful patterns without increased computational complexity.

A time series motif intuitively is a short time series that repeats itself approximately the same within a larger time series. Such motifs often represent concealed structures, such as heart beats in an ECG recording, the riff in a pop song, or sleep spindles in EEG sleep data. Motif discovery (MD) is the task of finding such motifs in a given input series. As there are varying definitions of what exactly a motif is, a number of different algorithms exist. As central parameters they all take the length l of the motif and the maximal distance r between the motif's occurrences. In practice, however, especially suitable values for r are very hard to determine upfront, and found motifs show a high variability even for very similar r values. Accordingly, finding an interesting motif requires extensive trial-and-error. In this paper, we present a different approach to the MD problem. We define k-Motiflets as the set of exactly k occurrences of a motif of length l, whose maximum pairwise distance is minimal. This turns the MD problem upside-down: The central parameter of our approach is not the distance threshold r, but the desired number of occurrence k of the motif, which we show is considerably more intuitive and easier to set. Based on this definition, we present exact and approximate algorithms for finding k-Motiflets and analyze their complexity. To further ease the use of our method, we describe statistical tools to automatically determine meaningful values for its input parameters. By evaluation on several real-world data sets and comparison to four SotA MD algorithms, we show that our proposed algorithm is both quantitatively superior to its competitors, finding larger motif sets at higher similarity, and qualitatively better, leading to clearer and easier to interpret motifs without any need for manual tuning.

While self-supervised graph pretraining techniques have shown promising results in various domains, their application still experiences challenges of limited topology learning, human knowledge dependency, and incompetent multi-level interactions. To address these issues, we propose a novel solution, Dual-level Graph self-supervised Pretraining with Motif discovery (DGPM), which introduces a unique dual-level pretraining structure that orchestrates node-level and subgraph-level pretext tasks. Unlike prior approaches, DGPM autonomously uncovers significant graph motifs through an edge pooling module, aligning learned motif similarities with graph kernel-based similarities. A cross-matching task enables sophisticated node-motif interactions and novel representation learning. Extensive experiments on 15 datasets validate DGPM's effectiveness and generalizability, outperforming state-of-the-art methods in unsupervised representation learning and transfer learning settings. The autonomously discovered motifs demonstrate the potential of DGPM to enhance robustness and interpretability.

Most of existing methods for DNA motif discovery consider only a single set of sequences to find an over-represented motif. In contrast, we consider multiple sets of sequences where we group sets associated with the same motif into a cluster, assuming that each set involves a single motif. Clustering sets of sequences yields clusters of coherent motifs, improving signal-to-noise ratio or enabling us to identify multiple motifs. We present a probabilistic model for DNA motif discovery where we identify multiple motifs through searching for patterns which are shared across multiple sets of sequences. Our model infers cluster-indicating latent variables and learns motifs simultaneously, where these two tasks interact with each other.

Over the last decade, time series motif discovery has emerged as a useful primitive for many downstream analytical tasks, including clustering, classification, rule discovery, segmentation, and summarization. In parallel, there has been an increased understanding that Dynamic Time Warping (DTW) is the best time series similarity measure in a host of settings. Surprisingly however, there has been virtually no work on using DTW to discover motifs. The most obvious explanation of this is the fact that both motif discovery and the use of DTW can be computationally challenging, and the current best mechanisms to address their lethargy are mutually incompatible. In this work, we present the first scalable exact method to discover time series motifs under DTW. Our method automatically performs the best trade-off between time-to-compute and tightness-of-lower-bounds for a novel hierarchy of lower bounds representation we introduce. We show that under realistic settings, our algorithm can admissibly prune up to 99.99% of the DTW computations.