Diffusion models have shown great promise in data generation, yet generating time series data remains challenging due to the need to capture complex temporal dependencies and structural patterns. In this paper, we present TSGDiff, a novel framework that rethinks time series generation from a graph-based perspective. Specifically, we represent time series as dynamic graphs, where edges are constructed based on Fourier spectrum characteristics and temporal dependencies. A graph neural network-based encoder-decoder architecture is employed to construct a latent space, enabling the diffusion process to model the structural representation distribution of time series effectively. Furthermore, we propose the Topological Structure Fidelity (Topo-FID) score, a graph-aware metric for assessing the structural similarity of time series graph representations. Topo-FID integrates two sub-metrics: Graph Edit Similarity, which quantifies differences in adjacency matrices, and Structural Entropy Similarity, which evaluates the entropy of node degree distributions. This comprehensive metric provides a more accurate assessment of structural fidelity in generated time series. Experiments on real-world datasets demonstrate that TSGDiff generates high-quality synthetic time series data generation, faithfully preserving temporal dependencies and structural integrity, thereby advancing the field of synthetic time series generation.

Modeling normal behavior in dynamic, nonlinear time series data is challenging for effective anomaly detection. Traditional methods, such as nearest neighbor and clustering approaches, often depend on rigid assumptions, such as a predefined number of reliable neighbors or clusters, which frequently break down in complex temporal scenarios. To address these limitations, we introduce the Granular-ball One-Class Network (GBOC), a novel approach based on a data-adaptive representation called Granular-ball Vector Data Description (GVDD). GVDD partitions the latent space into compact, high-density regions represented by granular-balls, which are generated through a density-guided hierarchical splitting process and refined by removing noisy structures. Each granular-ball serves as a prototype for local normal behavior, naturally positioning itself between individual instances and clusters while preserving the local topological structure of the sample set. During training, GBOC improves the compactness of representations by aligning samples with their nearest granular-ball centers. During inference, anomaly scores are computed based on the distance to the nearest granular-ball. By focusing on dense, high-quality regions and significantly reducing the number of prototypes, GBOC delivers both robustness and efficiency in anomaly detection. Extensive experiments validate the effectiveness and superiority of the proposed method, highlighting its ability to handle the challenges of time series anomaly detection.

Face age synthesis (FAS) predicts a person's future or past facial appearance. In FAS, modifying one facial attribute usually affects the generation of other attributes during face image generation. Current models directly learn entangled representations of age-related features, resulting in insufficient feature disentanglement, which consequently impairs their causal reasoning capability for FAS tasks. To this end, we propose a hierarchical causal learning model for face age synthesis (HCFace), which integrates hierarchical structures and causal relationships into the facial generative model. Specifically, we propose to leverage hierarchical causal relationships to align with facial features for feature disentanglement. Furthermore, we design a novel nonlinear mapping function that captures the true patterns of facial attribute changes with age, enhancing the disentanglement of these attributes. We conduct extensive experiments to validate the superiority of our proposed model. Compared to other advanced baseline methods, HCFace improves overall accuracy by 2.47%, with improvements of 9.75% and 9.69% in certain age-related attributes, such as skin and hair. Our source code is available at https://github.com/SE-hash/HCFace.

Most existing multi-kernel clustering algorithms, such as multi-kernel K-means, often struggle with computational efficiency and robustness when faced with complex data distributions. These challenges stem from their dependence on point-to-point relationships for optimization, which can lead to difficulty in accurately capturing data sets' inherent structure and diversity. Additionally, the intricate interplay between multiple kernels in such algorithms can further exacerbate these issues, effectively impacting their ability to cluster data points in high-dimensional spaces. In this paper, we leverage granular-ball computing to improve the multi-kernel clustering framework. The core of granular-ball computing is to adaptively fit data distribution by balls from coarse to acceptable levels. Each ball can enclose data points based on a density consistency measurement. Such ball-based data description thus improves the computational efficiency and the robustness to unknown noises. Specifically, based on granular-ball representations, we introduce the granular-ball kernel (GBK) and its corresponding granular-ball multi-kernel K-means framework (GB-MKKM) for efficient clustering. Using granular-ball relationships in multiple kernel spaces, the proposed GB-MKKM framework shows its superiority in efficiency and clustering performance in the empirical evaluation of various clustering tasks.

The diffusion model has been successfully used in many computer vision applications, such as text-guided image generation and image-to-image translation. Recently, there have been attempts on extending the diffusion model for time series data. However, these extensions are fairly straightforward and do not utilize the unique properties of time series data. As different patterns are usually exhibited at multiple scales of a time series, we in this paper leverage this multi-resolution temporal structure and propose the multi-resolution diffusion model (mr-Diff). By using the seasonal-trend decomposition, we sequentially extract fine-to-coarse trends from the time series for forward diffusion. The denoising process then proceeds in an easy-to-hard non-autoregressive manner. The coarsest trend is generated first. Finer details are progressively added, using the predicted coarser trends as condition variables. Experimental results on nine real-world time series datasets demonstrate that mr-Diff outperforms state-of-the-art time series diffusion models. It is also better than or comparable across a wide variety of advanced time series prediction models.

Recently, denoising diffusion models have led to significant breakthroughs in the generation of images, audio and text. However, it is still an open question on how to adapt their strong modeling ability to model time series. In this paper, we propose TimeDiff, a non-autoregressive diffusion model that achieves high-quality time series prediction with the introduction of two novel conditioning mechanisms: future mixup and autoregressive initialization. Similar to teacher forcing, future mixup allows parts of the ground-truth future predictions for conditioning, while autoregressive initialization helps better initialize the model with basic time series patterns such as short-term trends. Extensive experiments are performed on nine real-world datasets. Results show that TimeDiff consistently outperforms existing time series diffusion models, and also achieves the best overall performance across a variety of the existing strong baselines (including transformers and FiLM).

Recurrent autoencoder is a popular model for time series anomaly detection, in which outliers or abnormal segments are identified by their high reconstruction errors. However, existing recurrent autoencoders can easily suffer from overfitting and error accumulation due to sequential decoding. In this paper, we propose a simple yet efficient recurrent network ensemble called Recurrent Autoencoder with Multiresolution Ensemble Decoding (RAMED). By using decoders with different decoding lengths and a new coarse-to-fine fusion mechanism, lower-resolution information can help long-range decoding for decoders with higher-resolution outputs. A multiresolution shape-forcing loss is further introduced to encourage decoders' outputs at multiple resolutions to match the input's global temporal shape. Finally, the output from the decoder with the highest resolution is used to obtain an anomaly score at each time step. Extensive empirical studies on real-world benchmark data sets demonstrate that the proposed RAMED model outperforms recent strong baselines on time series anomaly detection.

Real-world timeseries have complex underlying temporal dynamics and the detection of anomalies is challenging. In this paper, we propose the Temporal Hierarchical One-Class (THOC) network, a temporal one-class classification model for timeseries anomaly detection. It captures temporal dynamics in multiple scales by using a dilated recurrent neural network with skip connections. Using multiple hyperspheres obtained with a hierarchical clustering process, a one-class objective called Multiscale Vector Data Description is defined. This allows the temporal dynamics to be well captured by a set of multi-resolution temporal clusters. To further facilitate representation learning, the hypersphere centers are encouraged to be orthogonal to each other, and a self-supervision task in the temporal domain is added. The whole model can be trained end-to-end. Extensive empirical studies on various real-world timeseries demonstrate that the proposed THOC network outperforms recent strong deep learning baselines on timeseries anomaly detection.

Time series with missing values (incomplete time series) are ubiquitous in real life on account of noise or malfunctioning sensors. Time-series imputation (replacing missing data) remains a challenge due to the potential for nonlinear dependence on concurrent and previous values of the time series. In this paper, we propose a novel framework for modeling incomplete time series, called a linear memory vector recurrent neural network (LIME-RNN), a recurrent neural network (RNN) with a learned linear combination of previous history states. The technique bears some similarity to residual networks and graph-based temporal dependency imputation. In particular, we introduce a linear memory vector [called the residual sum vector (RSV)] that integrates over previous hidden states of the RNN, and is used to fill in missing values. A new loss function is developed to train our model with time series in the presence of missing values in an end-to-end way. Our framework can handle imputation of both missing-at-random and consecutive missing inputs. Moreover, when conducting time-series prediction with missing values, LIME-RNN allows imputation and prediction simultaneously. We demonstrate the efficacy of the model via extensive experimental evaluation on univariate and multivariate time series, achieving state-of-the-art performance on synthetic and real-world data. The statistical results show that our model is significantly better than most existing time-series univariate or multivariate imputation methods.

Time series imputation (replacing missing data) plays an important role in time series analysis due to missing values in real world data. How to recover missing values and model the underlying dynamic dependencies from incomplete time series remains a challenge. A recent work has found that residual networks help build very deep networks by leveraging short paths due to skip connections (Veit et al., 2016). Inspired by this, we observe that these short paths can model underlying correlations between missing items and their previous non-missing observations in a graph-like way. Hence, we propose an end-to-end imputation network with residual short paths, called Residual IMPutation LSTM (RIMP-LSTM), a flexible combination of residual short paths with graph-based temporal dependencies. We construct a residual sum unit (RSU), which enables RIMP-LSTM to make full use of previous revealed information to model incomplete time series and reduce the negative impact of missing values. Moreover, a switch unit is designed to detect the missing values and a new loss function is then developed to train our model with time series in the presence of missing values in an end-to-end way, which also allows simultaneous imputation and prediction. Extensive empirical comparisons with other competitive imputation approaches over several synthetic and real world time series with various rates of missing data verify the superiority of our model.

Recognizing human actions represented by 3D trajectories of skeleton joints is a challenging machine learning task. In this paper, the 3D skeleton sequences are regarded as multivariate time series, and their dynamics and multiscale features are efficiently learned from action echo states. Specifically, first the skeleton data from the limbs and trunk are projected into five high dimensional nonlinear spaces, that are randomly generated by five dynamic, training-free recurrent networks, i.e., the reservoirs of echo state networks (ESNs). In this way, the history of the time series is represented as nonlinear echo states of actions. We then use a single multiscale convolutional layer to extract multiscale features from the echo states, and maintain multiscale temporal invariance by a max-over-time pooling layer. We propose two multi-step fusion strategies to integrate the spatial information over the five parts of the human physical structure. Finally, we learn the label distribution using softmax. With one training-free recurrent layer and only layer of convolution, our Convolutional Echo State Network (ConvESN) is a very efficient end-to-end model, and achieves state-of-the-art performance on four skeleton benchmark data sets.