The Matrix Profile (MP), a versatile tool for time series data mining, has been shown effective in time series anomaly detection (TSAD). This paper delves into the problem of anomaly detection in multidimensional time series, a common occurrence in real-world applications. For instance, in a manufacturing factory, multiple sensors installed across the site collect time-varying data for analysis. The Matrix Profile, named for its role in profiling the matrix storing pairwise distance between subsequences of univariate time series, becomes complex in multidimensional scenarios. If the input univariate time series has$n$subsequences, the pairwise distance matrix is a$n\times n$matrix. In a multidimensional time series with$d$dimensions, the pairwise distance information must be stored in a$n\times n\times d$tensor. In this paper, we first analyze different strategies for condensing this tensor into a profile vector. We then investigate the potential of extending the MP to efficiently find k-nearest neighbors for anomaly detection. Finally, we benchmark the multidimensional MP against 19 baseline methods on 119 multidimensional TSAD datasets. The experiments covers three learning setups: unsupervised, supervised, and semi-supervised. MP is the only method that consistently delivers high performance across all setups.

Spatial-temporal forecasting systems play a crucial role in addressing numerous real-world challenges. In this paper, we investigate the potential of addressing spatial-temporal forecasting problems using general time series forecasting models, i.e., models that do not leverage the spatial relationships among the nodes. We propose a all-Multi-Layer Perceptron (all-MLP) time series forecasting architecture called RPMixer. The all-MLP architecture was chosen due to its recent success in time series forecasting benchmarks. Furthermore, our method capitalizes on the ensemble-like behavior of deep neural networks, where each individual block within the network behaves like a base learner in an ensemble model, particularly when identity mapping residual connections are incorporated. By integrating random projection layers into our model, we increase the diversity among the blocks' outputs, thereby improving the overall performance of the network. Extensive experiments conducted on the largest spatial-temporal forecasting benchmark datasets demonstrate that the proposed method outperforms 14 alternative methods.

Prompts, which are pieces of text injected into the inputs of NLP models, can significantly enhance these models’ performance. Despite their effectiveness, a straightforward method for exploring a large number of possible prompts and assessing their quality in down-stream tasks is lacking. This paper introduces PromptLandscape, a visualization approach to exploring prompts in the zero-shot image classification context. Our focus is on the CLIP model [26], which has been pre-trained on a large number of image-text pairs and exhibits exceptional performance in zero-shot image classifications. However, its performance is also considerably influenced by the text labels. Prompts were introduced to refine the text labels and improve the classification performance. Nevertheless, the prompts are often proposed through trial-and-error and it is challenging to find the best prompts for different image datasets. PromptLandscape presents the large number of possible prompts as points in a 3D space to guide their exploration and enables users to decode any points back as texts for better interpretation. Through concrete case studies, we demonstrate the effectiveness of PromptLandscape in (1) finding the best prompts for image classifications and (2) interpreting the prompts to reveal the crucial features of the studied image datasets.

Time series data is ubiquitous across various domains such as finance, healthcare, and manufacturing, but their properties can vary significantly depending on the domain they originate from. The ability to perform Content-based Time Series Retrieval (CTSR) is crucial for identifying unknown time series examples. However, existing CTSR works typically focus on retrieving time series from a single domain database, which can be inadequate if the user does not know the source of the query time series. This limitation motivates us to investigate the CTSR problem in a scenario where the database contains time series from multiple domains. To facilitate this investigation, we introduce a CTSR benchmark dataset that comprises time series data from a variety of domains, such as motion, power demand, and traffic. This dataset is sourced from a publicly available time series classification dataset archive, making it easily accessible to researchers in the field. We compare several popular methods for modeling and retrieving time series data using this benchmark dataset. Additionally, we propose a novel distance learning model that outperforms the existing methods. Overall, our study highlights the importance of addressing the CTSR problem across multiple domains and provides a useful benchmark dataset for future research.

Time series classification is a widely studied problem in the field of time series data mining. Previous research has predominantly focused on scenarios where relevant or foreground subsequences have already been extracted, with each subsequence corresponding to a single label. However, real-world time series data often contain foreground subsequences that are intertwined with background subsequences. Successfully classifying these relevant subsequences requires not only distinguishing between different classes but also accurately identifying the foreground subsequences amidst the background. To address this challenge, we propose a novel subsequence classification method that represents each subsequence as an ego-network, providing crucial nearest neighbor information to the model. The ego-networks of all subsequences collectively form a time series subsequence graph, and we introduce an algorithm to efficiently construct this graph. Furthermore, we have demonstrated the significance of enforcing temporal consistency in the prediction of adjacent subsequences for the subsequence classification problem. To evaluate the effectiveness of our approach, we conducted experiments using 128 univariate and 30 multivariate time series datasets. The experimental results demonstrate the superior performance of our method compared to alternative approaches. Specifically, our method outperforms the baseline on 104 out of 158 datasets.

Spatial-temporal graph neural networks (STGNNs) are promising in solving real-world spatial-temporal forecasting problems. Recognizing the inherent sequential relationship of spatial-temporal data, it is natural to explore the integration of boosting training mechanism to further enhance the performance of STGNNs. However, few studies have touched this research area. To bridge this gap, in this work, we propose spatial-temporal graph boosting networks, namely STGBN, which to the best of our knowledge is the first attempt to leverage gradient boosting for enhancing STGNNs. STGBN follows the general training procedure of conventional gradient boosting, but incorporates two distinctive designs to improve its efficiency in training on spatial-temporal graphs. Specifically, we design an incremental learning strategy that progressively includes spatial-temporal data into training. Additionally, we enforce an identical architecture for the base learner in all boosting iterations with each base learner inheriting from the one in the previous iteration. These designs facilitate rapid convergence of the base learner and expedite the overall training process. The base learner in STGBN is designed as a Transformer sandwich, which consists of two temporal Transformers on the top and bottom and a spatial Transformer in the middle. Structuring them in such a way helps the model capture long-range temporal dynamics, global spatial dependencies, and deep spatial-temporal interactions. We perform extensive spatial-temporal forecasting experiments on four spatial-temporal graph benchmarks. Promising results demonstrate the outstanding performance of STGBN against a wide range of state-of-the-art baseline models.

A Content-based Time Series Retrieval (CTSR) system is an information retrieval system for users to interact with time series emerged from multiple domains, such as finance, healthcare, and manufacturing. For example, users seeking to learn more about the source of a time series can submit the time series as a query to the CTSR system and retrieve a list of relevant time series with associated metadata. By analyzing the retrieved metadata, users can gather more information about the source of the time series. Because the CTSR system is required to work with time series data from diverse domains, it needs a high-capacity model to effectively measure the similarity between different time series. On top of that, the model within the CTSR system has to compute the similarity scores in an efficient manner as the users interact with the system in real-time. In this paper, we propose an effective and efficient CTSR model that outperforms alternative models, while still providing reasonable inference runtimes. To demonstrate the capability of the proposed method in solving business problems, we compare it against alternative models using our in-house transaction data. Our findings reveal that the proposed model is the most suitable solution compared to others for our transaction data problem.

A foundation model is a machine learning model trained on a large and diverse set of data, typically using self-supervised learning-based pre-training techniques, that can be adapted to various downstream tasks. However, current research on time series pre-training has predominantly focused on models trained exclusively on data from a single domain. As a result, these models possess domain-specific knowledge that may not be easily transferable to time series from other domains. In this paper, we aim to develop an effective time series foundation model by leveraging unlabeled samples from multiple domains. To achieve this, we repurposed the publicly available UCR Archive and evaluated four existing self-supervised learning-based pre-training methods, along with a novel method, on the datasets. We tested these methods using four popular neural network architectures for time series to understand how the pre-training methods interact with different network designs. Our experimental results show that pre-training improves downstream classification tasks by enhancing the convergence of the fine-tuning process. Furthermore, we found that the proposed pre-training method, when combined with the Transformer, outperforms the alternatives. The proposed method outperforms or achieves equal performance compared to the second best method in ~93% of downstream tasks.

Sequential tabular data is one of the most commonly used data types in real-world applications. Different from conventional tabular data, where rows in a table are independent, sequential tabular data contains rich contextual and sequential information, where some fields aredynamically changing over time and others arestatic. Existing transformer-based approaches analyzing sequential tabular data overlook the differences between dynamic and static fields by replicating and filling static fields into each record, and ignore temporal information between rows, which leads to three major disadvantages: (1) computational overhead, (2) artificially simplified data for masked language modeling pre-training task that may yield less meaningful representations, and (3) disregarding the temporal behavioral patterns implied by time intervals. In this work, we propose FATA-Trans, a model with two field transformers for modeling sequential tabular data, where each processes static and dynamic field information separately. FATA-Trans isfield - andtime -aware for sequential tabular data. Thefield -type embedding in the method enables FATA-Trans to capture differences between static and dynamic fields. Thetime -aware position embedding exploits both order and time interval information between rows, which helps the model detect underlying temporal behavior in a sequence. Our experiments on three benchmark datasets demonstrate that the learned representations from FATA-Trans consistently outperform state-of-the-art solutions in the downstream tasks. We also present visualization studies to highlight the insights captured by the learned representations, enhancing our understanding of the underlying data. Our codes are available at https://github.com/zdy93/FATA-Trans.

Multitask learning (MTL) aims to develop a unified model that can handle a set of closely related tasks simultaneously. By optimizing the model across multiple tasks, MTL generally surpasses its non-MTL counterparts in terms of generalizability. Although MTL has been extensively researched in various domains such as computer vision, natural language processing, and recommendation systems, its application to time series data has received limited attention. In this paper, we investigate the application of MTL to the time series classification (TSC) problem. However, when we integrate the state-of-the-art 1D convolution-based TSC model with MTL, the performance of the TSC model actually deteriorates. By comparing the 1D convolution-based models with the Dynamic Time Warping (DTW) distance function, it appears that the underwhelming results stem from the limited expressive power of the 1D convolutional layers. To overcome this challenge, we propose a novel design for a 2D convolution-based model that enhances the model's expressiveness. Leveraging this advantage, our proposed method outperforms competing approaches on both the UCR Archive and an industrial transaction TSC dataset.

Vision transformer (ViT) expands the success of transformer models from sequential data to images. The model decomposes an image into many smaller patches and arranges them into a sequence. Multi-head self-attentions are then applied to the sequence to learn the attention between patches. Despite many successful interpretations of transformers on sequential data, little effort has been devoted to the interpretation of ViTs, and many questions remain unanswered. For example, among the numerous attention heads, which one is more important? How strong are individual patches attending to their spatial neighbors in different heads? What attention patterns have individual heads learned? In this work, we answer these questions through a visual analytics approach. Specifically, we first identify what heads are more important in ViTs by introducing multiple pruning-based metrics. Then, we profile the spatial distribution of attention strengths between patches inside individual heads, as well as the trend of attention strengths across attention layers. Third, using an autoencoder-based learning solution, we summarize all possible attention patterns that individual heads could learn. Examining the attention strengths and patterns of the important heads, we answer why they are important. Through concrete case studies with experienced deep learning experts on multiple ViTs, we validate the effectiveness of our solution that deepens the understanding of ViTs from head importance, head attention strength, and head attention pattern.