In this paper, we introduce new algorithms for Principal Component Analysis (PCA) with outliers. Utilizing techniques from computational geometry, specifically higher-degree Voronoi diagrams, we navigate to the optimal subspace for PCA even in the presence of outliers. This approach achieves an optimal solution with a time complexity of $n^{d+\mathcal{O}(1)}\text{poly}(n,d)$. Additionally, we present a randomized algorithm with a complexity of $2^{\mathcal{O}(r(d-r))} \times \text{poly}(n, d)$. This algorithm samples subspaces characterized in terms of a Grassmannian manifold. By employing such sampling method, we ensure a high likelihood of capturing the optimal subspace, with the success probability $(1 - \delta)^T$. Where $\delta$ represents the probability that a sampled subspace does not contain the optimal solution, and $T$ is the number of subspaces sampled, proportional to $2^{r(d-r)}$. Our use of higher-degree Voronoi diagrams and Grassmannian based sampling offers a clearer conceptual pathway and practical advantages, particularly in handling large datasets or higher-dimensional settings.

Recent advancements have focused on encoding urban spatial information into high-dimensional spaces, with notable efforts dedicated to integrating sociodemographic data and satellite imagery. These efforts have established foundational models in this field. However, the effective utilization of these spatial representations for urban forecasting applications remains under-explored. To address this gap, we introduce GeoTransformer, a novel structure that synergizes the Transformer architecture with geospatial statistics prior. GeoTransformer employs an innovative geospatial attention mechanism to incorporate extensive urban information and spatial dependencies into a unified predictive model. Specifically, we compute geospatial weighted attention scores between the target region and surrounding regions and leverage the integrated urban information for predictions. Extensive experiments on GDP and ride-share demand prediction tasks demonstrate that GeoTransformer significantly outperforms existing baseline models, showcasing its potential to enhance urban forecasting tasks.

Geometric trees are characterized by their tree-structured layout and spatially constrained nodes and edges, which significantly impacts their topological attributes. This inherent hierarchical structure plays a crucial role in domains such as neuron morphology and river geomorphology, but traditional graph representation methods often overlook these specific characteristics of tree structures. To address this, we introduce a new representation learning framework tailored for geometric trees. It first features a unique message passing neural network, which is both provably geometrical structure-recoverable and rotation-translation invariant. To address the data label scarcity issue, our approach also includes two innovative training targets that reflect the hierarchical ordering and geometric structure of these geometric trees. This enables fully self-supervised learning without explicit labels. We validate our method's effectiveness on eight real-world datasets, demonstrating its capability to represent geometric trees.

In the AIOps (Artificial Intelligence for IT Operations) era, accurately forecasting system states is crucial. In microservices systems, this task encounters the challenge of dynamic and complex spatio-temporal relationships among microservice instances, primarily due to dynamic deployments, diverse call paths, and cascading effects among instances. Current time-series forecasting methods, which focus mainly on intrinsic patterns, are insufficient in environments where spatial relationships are critical. Similarly, spatio-temporal graph approaches often neglect the nature of temporal trend, concentrating mostly on message passing between nodes. Moreover, current research in microservices domain frequently underestimates the importance of network metrics and topological structures in capturing the evolving dynamics of systems. This paper introduces STMformer, a model tailored for forecasting system states in microservices environments, capable of handling multi-node and multivariate time series. Our method leverages dynamic network connection data and topological information to assist in modeling the intricate spatio-temporal relationships within the system. Additionally, we integrate the PatchCrossAttention module to compute the impact of cascading effects globally. We have developed a dataset based on a microservices system and conducted comprehensive experiments with STMformer against leading methods. In both short-term and long-term forecasting tasks, our model consistently achieved a 8.6% reduction in MAE(Mean Absolute Error) and a 2.2% reduction in MSE (Mean Squared Error). The source code is available at https://github.com/xuyifeiiie/STMformer.

Multiple Instance Learning (MIL) models have proven effective for cancer prognosis from Whole Slide Images. However, the original MIL formulation incorrectly assumes the patches of the same image to be independent, leading to a loss of spatial context as information flows through the network. Incorporating contextual knowledge into predictions is particularly important given the inclination for cancerous cells to form clusters and the presence of spatial indicators for tumors. State-of-the-art methods often use attention mechanisms eventually combined with graphs to capture spatial knowledge. In this paper, we take a novel and transversal approach, addressing this issue through the lens of regularization. We propose Context-Aware Regularization for Multiple Instance Learning (CARMIL), a versatile regularization scheme designed to seamlessly integrate spatial knowledge into any MIL model. Additionally, we present a new and generic metric to quantify the Context-Awareness of any MIL model when applied to Whole Slide Images, resolving a previously unexplored gap in the field. The efficacy of our framework is evaluated for two survival analysis tasks on glioblastoma (TCGA GBM) and colon cancer data (TCGA COAD).

This study introduces a parameter-efficient Hierarchical Spatial Temporal Network (HiSTN) specifically designed for the task of emotion classification using multi-channel electroencephalogram data. The network incorporates a graph hierarchy constructed from bottom-up at various abstraction levels, offering the dual advantages of enhanced task-relevant deep feature extraction and a lightweight design. The model's effectiveness is further amplified when used in conjunction with a proposed unique label smoothing method. Comprehensive benchmark experiments reveal that this combined approach yields high, balanced performance in terms of both quantitative and qualitative predictions. HiSTN, which has approximately 1,000 parameters, achieves mean F1 scores of 96.82% (valence) and 95.62% (arousal) in subject-dependent tests on the rarely-utilized 5-classification task problem from the DREAMER dataset. In the subject-independent settings, the same model yields mean F1 scores of 78.34% for valence and 81.59% for arousal. The adoption of the Sequential Top-2 Hit Rate (Seq2HR) metric highlights the significant enhancements in terms of the balance between model's quantitative and qualitative for predictions achieved through our approach when compared to training with regular one-hot labels. These improvements surpass 50% in subject-dependent tasks and 30% in subject-independent tasks. The study also includes relevant ablation studies and case explorations to further elucidate the workings of the proposed model and enhance its interpretability.

Vehicle trajectories provide valuable movement information that supports various downstream tasks and powers real-world applications. A desirable trajectory learning model should transfer between different regions and tasks without retraining, thus improving computational efficiency and effectiveness with limited training data. However, a model's ability to transfer across regions is limited by the unique spatial features and POI arrangements of each region, which are closely linked to vehicle movement patterns and difficult to generalize. Additionally, achieving task transferability is challenging due to the differing generation schemes required for various tasks. Existing efforts towards transferability primarily involve learning embedding vectors for trajectories, which perform poorly in region transfer and still require retraining of prediction modules for task transfer. To address these challenges, we propose TrajFM, a vehicle trajectory foundation model that excels in both region and task transferability. For region transferability, we introduce STRFormer as the main learnable model within TrajFM. It integrates spatial, temporal, and POI modalities of trajectories to effectively manage variations in POI arrangements across regions and includes a learnable spatio-temporal Rotary position embedding module for handling spatial features. For task transferability, we propose a trajectory masking and recovery scheme. This scheme unifies the generation processes of various tasks into the masking and recovery of modalities and sub-trajectories, allowing TrajFM to be pre-trained once and transferred to different tasks without retraining. Experiments on two real-world vehicle trajectory datasets under various settings demonstrate the effectiveness of TrajFM. Code is available at https://anonymous.4open.science/r/TrajFM-30E4.

Accurate taxi-demand prediction is essential for optimizing taxi operations and enhancing urban transportation services. However, using customers' data in these systems raises significant privacy and security concerns. Traditional federated learning addresses some privacy issues by enabling model training without direct data exchange but often struggles with accuracy due to varying data distributions across different regions or service providers. In this paper, we propose CC-Net: a novel approach using collaborative learning enhanced with contrastive learning for taxi-demand prediction. Our method ensures high performance by enabling multiple parties to collaboratively train a demand-prediction model through hierarchical federated learning. In this approach, similar parties are clustered together, and federated learning is applied within each cluster. The similarity is defined without data exchange, ensuring privacy and security. We evaluated our approach using real-world data from five taxi service providers in Japan over fourteen months. The results demonstrate that CC-Net maintains the privacy of customers' data while improving prediction accuracy by at least 2.2% compared to existing techniques.

In the last two decades, with the increasing need to analyze big amounts of data, which are usually complex and of high dimension, it was revealed meaningful and helpful to discover further methodologies to provide new information from data. This has brought to the birth of Topological Data Analysis (TDA), whose aim is to extract intrinsic, topological features, related to the so-called "shape of data". Thanks to its main tool, Persistent Homology (PH), it can provide new qualitative information that it would be impossible to extract in any other way. These kinds of features that can be collected in the so-called Persistence Diagram (PD), have been winning in many different applications, mainly related to applied science, improving the performances of models or classifiers, as in our context. Thanks to the strong basis of algebraic topology behind it, the TDA is very versatile and can be applied to data with a priori any kind of structure, as we will explain in the following.

The objective of the panoramic activity recognition task is to identify behaviors at various granularities within crowded and complex environments, encompassing individual actions, social group activities, and global activities. Existing methods generally use either parameter-independent modules to capture task-specific features or parameter-sharing modules to obtain common features across all tasks. However, there is often a strong interrelatedness and complementary effect between tasks of different granularities that previous methods have yet to notice. In this paper, we propose a model called MPT-PAR that considers both the unique characteristics of each task and the synergies between different tasks simultaneously, thereby maximizing the utilization of features across multi-granularity activity recognition. Furthermore, we emphasize the significance of temporal and spatial information by introducing a spatio-temporal relation-enhanced module and a scene representation learning module, which integrate the the spatio-temporal context of action and global scene into the feature map of each granularity. Our method achieved an overall F1 score of 47.5\% on the JRDB-PAR dataset, significantly outperforming all the state-of-the-art methods.