This perspective article is meant to be a self-contained introduction to and review of transfer operators such as the Koopman operator and the Perron-Frobenius operator as well as an overview of different applications. We will first introduce the required foundations and then show how transfer operators can not only be used to analyze highly nonlinear dynamical systems but also complex networks. In particular, we will focus on relationships between transfer operators for continuous-time stochastic processes defined on a continuous state space--whether they be reversible, non-reversible but time-homogeneous, or time-inhomogeneous--and their discrete counterparts associated with random walks on undirected, directed, and time-evolving graphs. Transfer operators play an important role in an increasing number of research fields. A few exemplary applications are illustrated in Figure 1.

Sum-of-norms clustering is a popular convexification of K-means clustering. We show that, if the dataset is made of a large number of independent random variables distributed according to the uniform measure on the union of two disjoint balls of unit radius, and if the balls are sufficiently close to one another, then sum-of-norms clustering will typically fail to recover the decomposition of the dataset into two clusters. As the dimension tends to infinity, this happens even when the distance between the centers of the two balls is taken to be as large as 2 2. In order to show this, we introduce and analyze a continuous version of sum-of-norms clustering, where the dataset is replaced by a general measure. In particular, we state and prove a local-global characterization of the clustering that seems to be new even in the case of discrete datapoints.

Multivariate time series forecasting tasks are usually conducted in a channel-dependent (CD) way since it can incorporate more variable-relevant information. However, it may also involve a lot of irrelevant variables, and this even leads to worse performance than the channel-independent (CI) strategy. This paper combines the strengths of both strategies and proposes the Deep Graph Clustering Transformer (DGCformer) for multivariate time series forecasting. Specifically, it first groups these relevant variables by a graph convolutional network integrated with an autoencoder, and a former-latter masked self-attention mechanism is then considered with the CD strategy being applied to each group of variables while the CI one for different groups. Extensive experimental results on eight datasets demonstrate the superiority of our method against state-of-the-art models, and our code will be publicly available upon acceptance.

This study introduces a machine learning framework tailored to large-scale industrial processes characterized by a plethora of numerical and categorical inputs. The framework aims to (i) discern critical parameters influencing the output and (ii) generate accurate out-of-sample qualitative and quantitative predictions of production outcomes. Specifically, we address the pivotal question of the significance of each input in shaping the process outcome, using an industrial Chemical Vapor Deposition (CVD) process as an example. The initial objective involves merging subject matter expertise and clustering techniques exclusively on the process output, here, coating thickness measurements at various positions in the reactor. This approach identifies groups of production runs that share similar qualitative characteristics, such as film mean thickness and standard deviation. In particular, the differences of the outcomes represented by the different clusters can be attributed to differences in specific inputs, indicating that these inputs are critical for the production outcome. Leveraging this insight, we subsequently implement supervised classification and regression methods using the identified critical process inputs. The proposed methodology proves to be valuable in scenarios with a multitude of inputs and insufficient data for the direct application of deep learning techniques, providing meaningful insights into the underlying processes.

Anomaly detection in distributed systems such as High-Performance Computing (HPC) clusters is vital for early fault detection, performance optimisation, security monitoring, reliability in general but also operational insights. Deep Neural Networks have seen successful use in detecting long-term anomalies in multidimensional data, originating for instance from industrial or medical systems, or weather prediction. A downside of such methods is that they require a static input size, or lose data through cropping, sampling, or other dimensionality reduction methods, making deployment on systems with variability on monitored data channels, such as computing clusters difficult. To address these problems, we present DeepHYDRA (Deep Hybrid DBSCAN/Reduction-Based Anomaly Detection) which combines DBSCAN and learning-based anomaly detection. DBSCAN clustering is used to find point anomalies in time-series data, mitigating the risk of missing outliers through loss of information when reducing input data to a fixed number of channels. A deep learning-based time-series anomaly detection method is then applied to the reduced data in order to identify long-term outliers. This hybrid approach reduces the chances of missing anomalies that might be made indistinguishable from normal data by the reduction process, and likewise enables the algorithm to be scalable and tolerate partial system failures while retaining its detection capabilities. Using a subset of the well-known SMD dataset family, a modified variant of the Eclipse dataset, as well as an in-house dataset with a large variability in active data channels, made publicly available with this work, we furthermore analyse computational intensity, memory footprint, and activation counts. DeepHYDRA is shown to reliably detect different types of anomalies in both large and complex datasets.

Sarcoidosis is a rare inflammatory disease characterized by the formation of granulomas in various organs. The disease presents diagnostic and treatment challenges due to its diverse manifestations and unpredictable nature. In this study, we employed a Large Language Model (LLM) to analyze sarcoidosis-related discussions on the social media platform Reddit. Our findings underscore the efficacy of LLMs in accurately identifying sarcoidosis-related content. We discovered a wide array of symptoms reported by patients, with fatigue, swollen lymph nodes, and shortness of breath as the most prevalent. Prednisone was the most prescribed medication, while infliximab showed the highest effectiveness in improving prognoses. Notably, our analysis revealed disparities in prognosis based on age and gender, with women and younger patients experiencing good and polarized outcomes, respectively. Furthermore, unsupervised clustering identified three distinct patient subgroups (phenotypes) with unique symptom profiles, prognostic outcomes, and demographic distributions. Finally, sentiment analysis revealed a moderate negative impact on patients' mental health post-diagnosis, particularly among women and younger individuals. Our study represents the first application of LLMs to understand sarcoidosis through social media data. It contributes to understanding the disease by providing data-driven insights into its manifestations, treatments, prognoses, and impact on patients' lives. Our findings have direct implications for improving personalized treatment strategies and enhancing the quality of care for individuals living with sarcoidosis.

Redacted emails satisfy most privacy requirements but they make it more difficult to detect anomalous emails that may be indicative of data exfiltration. In this paper we develop an enhanced method of Active Learning using an information gain maximizing heuristic, and we evaluate its effectiveness in a real world setting where only redacted versions of email could be labeled by human analysts due to privacy concerns. In the first case study we examined how Active Learning should be carried out. We found that model performance was best when a single highly skilled (in terms of the labelling task) analyst provided the labels. In the second case study we used confidence ratings to estimate the labeling uncertainty of analysts and then prioritized instances for labeling based on the expected information gain (the difference between model uncertainty and analyst uncertainty) that would be provided by labelling each instance. We found that the information maximization gain heuristic improved model performance over existing sampling methods for Active Learning. Based on the results obtained, we recommend that analysts should be screened, and possibly trained, prior to implementation of Active Learning in cybersecurity applications. We also recommend that the information gain maximizing sample method (based on expert confidence) should be used in early stages of Active Learning, providing that well-calibrated confidence can be obtained. We also note that the expertise of analysts should be assessed prior to Active Learning, as we found that analysts with lower labelling skill had poorly calibrated (over-) confidence in their labels.

This paper presents a novel multi-modal Multi-Object Tracking (MOT) algorithm for self-driving cars that combines camera and LiDAR data. Camera frames are processed with a state-of-the-art 3D object detector, whereas classical clustering techniques are used to process LiDAR observations. The proposed MOT algorithm comprises a three-step association process, an Extended Kalman filter for estimating the motion of each detected dynamic obstacle, and a track management phase. The EKF motion model requires the current measured relative position and orientation of the observed object and the longitudinal and angular velocities of the ego vehicle as inputs. Unlike most state-of-the-art multi-modal MOT approaches, the proposed algorithm does not rely on maps or knowledge of the ego global pose. Moreover, it uses a 3D detector exclusively for cameras and is agnostic to the type of LiDAR sensor used. The algorithm is validated both in simulation and with real-world data, with satisfactory results.

This study explores the integration of advanced Natural Language Processing (NLP) and Artificial Intelligence (AI) techniques to analyze and interpret Persian literature, focusing on the poetry of Forough Farrokhzad. Utilizing computational methods, we aim to unveil thematic, stylistic, and linguistic patterns in Persian poetry. Specifically, the study employs AI models including transformer-based language models for clustering of the poems in an unsupervised framework. This research underscores the potential of AI in enhancing our understanding of Persian literary heritage, with Forough Farrokhzad's work providing a comprehensive case study. This approach not only contributes to the field of Persian Digital Humanities but also sets a precedent for future research in Persian literary studies using computational techniques.

Time series clustering is fundamental in data analysis for discovering temporal patterns. Despite recent advancements, learning cluster-friendly representations is still challenging, particularly with long and complex time series. Deep temporal clustering methods have been trying to integrate the canonical k-means into end-to-end training of neural networks but fall back on surrogate losses due to the non-differentiability of the hard cluster assignment, yielding sub-optimal solutions. In addition, the autoregressive strategy used in the state-of-the-art RNNs is subject to error accumulation and slow training, while recent research findings have revealed that Transformers are less effective due to time points lacking semantic meaning, to the permutation invariance of attention that discards the chronological order and high computation cost. In light of these observations, we present LoSTer which is a novel dense autoencoder architecture for the long-sequence time series clustering problem (LSTC) capable of optimizing the k-means objective via the Gumbel-softmax reparameterization trick and designed specifically for accurate and fast clustering of long time series. Extensive experiments on numerous benchmark datasets and two real-world applications prove the effectiveness of LoSTer over state-of-the-art RNNs and Transformer-based deep clustering methods.