In this paper we give a broad overview of the intersection of partial differential equations (PDEs) and graph-based semi-supervised learning. The overview is focused on a large body of recent work on PDE continuum limits of graph-based learning, which have been used to prove well-posedness of semi-supervised learning algorithms in the large data limit. We highlight some interesting research directions revolving around consistency of graph-based semi-supervised learning, and present some new results on the consistency of p-Laplacian semi-supervised learning using the stochastic tug-of-war game interpretation of the p-Laplacian. We also present the results of some numerical experiments that illustrate our results and suggest directions for future work.

Predicting click-through rate (CTR) is the core task of many ads online recommendation systems, which helps improve user experience and increase platform revenue. In this type of recommendation system, we often encounter two main problems: the joint usage of multi-page historical advertising data and the cold start of new ads. In this paper, we proposed GACE, a graph-based cross-page ads embedding generation method. It can warm up and generate the representation embedding of cold-start and existing ads across various pages. Specifically, we carefully build linkages and a weighted undirected graph model considering semantic and page-type attributes to guide the direction of feature fusion and generation. We designed a variational auto-encoding task as pre-training module and generated embedding representations for new and old ads based on this task. The results evaluated in the public dataset AliEC from RecBole and the real-world industry dataset from Alipay show that our GACE method is significantly superior to the SOTA method. In the online A/B test, the click-through rate on three real-world pages from Alipay has increased by 3.6%, 2.13%, and 3.02%, respectively. Especially in the cold-start task, the CTR increased by 9.96%, 7.51%, and 8.97%, respectively.

Within the scope of natural language processing, the domain of multi-label text classification is uniquely challenging due to its expansive and uneven label distribution. The complexity deepens due to the demand for an extensive set of annotated data for training an advanced deep learning model, especially in specialized fields where the labeling task can be labor-intensive and often requires domain-specific knowledge. Addressing these challenges, our study introduces a novel deep active learning strategy, capitalizing on the Beta family of proper scoring rules within the Expected Loss Reduction framework. It computes the expected increase in scores using the Beta Scoring Rules, which are then transformed into sample vector representations. These vector representations guide the diverse selection of informative samples, directly linking this process to the model's expected proper score. Comprehensive evaluations across both synthetic and real datasets reveal our method's capability to often outperform established acquisition techniques in multi-label text classification, presenting encouraging outcomes across various architectural and dataset scenarios.

Clustering algorithms aim to organize data into groups or clusters based on the inherent patterns and similarities within the data. They play an important role in today's life, such as in marketing and e-commerce, healthcare, data organization and analysis, and social media. Numerous clustering algorithms exist, with ongoing developments introducing new ones. Each algorithm possesses its own set of strengths and weaknesses, and as of now, there is no universally applicable algorithm for all tasks. In this work, we analyzed existing clustering algorithms and classify mainstream algorithms across five different dimensions: underlying principles and characteristics, data point assignment to clusters, dataset capacity, predefined cluster numbers and application area. This classification facilitates researchers in understanding clustering algorithms from various perspectives and helps them identify algorithms suitable for solving specific tasks. Finally, we discussed the current trends and potential future directions in clustering algorithms. We also identified and discussed open challenges and unresolved issues in the field.

A multi-modal emotional speech Mandarin database including articulatory kinematics, acoustics, glottal and facial micro-expressions is designed and established, which is described in detail from the aspects of corpus design, subject selection, recording details and data processing. Where signals are labeled with discrete emotion labels (neutral, happy, pleasant, indifferent, angry, sad, grief) and dimensional emotion labels (pleasure, arousal, dominance). In this paper, the validity of dimension annotation is verified by statistical analysis of dimension annotation data. The SCL-90 scale data of annotators are verified and combined with PAD annotation data for analysis, so as to explore the internal relationship between the outlier phenomenon in annotation and the psychological state of annotators. In order to verify the speech quality and emotion discrimination of the database, this paper uses 3 basic models of SVM, CNN and DNN to calculate the recognition rate of these seven emotions. The results show that the average recognition rate of seven emotions is about 82% when using acoustic data alone. When using glottal data alone, the average recognition rate is about 72%. Using kinematics data alone, the average recognition rate also reaches 55.7%. Therefore, the database is of high quality and can be used as an important source for speech analysis research, especially for the task of multimodal emotional speech analysis.

In the stochastic contextual low-rank matrix bandit problem, the expected reward of an action is given by the inner product between the action's feature matrix and some fixed, but initially unknown $d_1$ by $d_2$ matrix $\Theta^*$ with rank $r \ll \{d_1, d_2\}$, and an agent sequentially takes actions based on past experience to maximize the cumulative reward. In this paper, we study the generalized low-rank matrix bandit problem, which has been recently proposed in \cite{lu2021low} under the Generalized Linear Model (GLM) framework. To overcome the computational infeasibility and theoretical restrain of existing algorithms on this problem, we first propose the G-ESTT framework that modifies the idea from \cite{jun2019bilinear} by using Stein's method on the subspace estimation and then leverage the estimated subspaces via a regularization idea. Furthermore, we remarkably improve the efficiency of G-ESTT by using a novel exclusion idea on the estimated subspace instead, and propose the G-ESTS framework. We also show that G-ESTT can achieve the $\tilde{O}(\sqrt{(d_1+d_2)MrT})$ bound of regret while G-ESTS can achineve the $\tilde{O}(\sqrt{(d_1+d_2)^{3/2}Mr^{3/2}T})$ bound of regret under mild assumption up to logarithm terms, where $M$ is some problem dependent value. Under a reasonable assumption that $M = O((d_1+d_2)^2)$ in our problem setting, the regret of G-ESTT is consistent with the current best regret of $\tilde{O}((d_1+d_2)^{3/2} \sqrt{rT}/D_{rr})$~\citep{lu2021low} ($D_{rr}$ will be defined later). For completeness, we conduct experiments to illustrate that our proposed algorithms, especially G-ESTS, are also computationally tractable and consistently outperform other state-of-the-art (generalized) linear matrix bandit methods based on a suite of simulations.

Vertebrae identification in arbitrary fields-of-view plays a crucial role in diagnosing spine disease. Most spine CT contain only local regions, such as the neck, chest, and abdomen. Therefore, identification should not depend on specific vertebrae or a particular number of vertebrae being visible. Existing methods at the spine-level are unable to meet this challenge. In this paper, we propose a three-stage method to address the challenges in 3D CT vertebrae identification at vertebrae-level. By sequentially performing the tasks of vertebrae localization, segmentation, and identification, the anatomical prior information of the vertebrae is effectively utilized throughout the process. Specifically, we introduce a dual-factor density clustering algorithm to acquire localization information for individual vertebra, thereby facilitating subsequent segmentation and identification processes. In addition, to tackle the issue of interclass similarity and intra-class variability, we pre-train our identification network by using a supervised contrastive learning method. To further optimize the identification results, we estimated the uncertainty of the classification network and utilized the message fusion module to combine the uncertainty scores, while aggregating global information about the spine. Our method achieves state-of-the-art results on the VerSe19 and VerSe20 challenge benchmarks. Additionally, our approach demonstrates outstanding generalization performance on an collected dataset containing a wide range of abnormal cases.

Recently, sharpness-aware minimization (SAM) has attracted a lot of attention because of its surprising effectiveness in improving generalization performance. However, training neural networks with SAM can be highly unstable since the loss does not decrease along the direction of the exact gradient at the current point, but instead follows the direction of a surrogate gradient evaluated at another point nearby. To address this issue, we propose a simple renormalization strategy, dubbed StableSAM, so that the norm of the surrogate gradient maintains the same as that of the exact gradient. Our strategy is easy to implement and flexible enough to integrate with SAM and its variants, almost at no computational cost. With elementary tools from convex optimization and learning theory, we also conduct a theoretical analysis of sharpness-aware training, revealing that compared to stochastic gradient descent (SGD), the effectiveness of SAM is only assured in a limited regime of learning rate. In contrast, we show how StableSAM extends this regime of learning rate and when it can consistently perform better than SAM with minor modification. Finally, we demonstrate the improved performance of StableSAM on several representative data sets and tasks.

Irregularly sampled time series are ubiquitous, presenting significant challenges for analysis due to missing values. Despite existing methods address imputation, they predominantly focus on leveraging intra-series information, neglecting the potential benefits that inter-series information could provide, such as reducing uncertainty and memorization effect. To bridge this gap, we propose PRIME, a Prototype Recurrent Imputation ModEl, which integrates both intra-series and inter-series information for imputing missing values in irregularly sampled time series. Our framework comprises a prototype memory module for learning inter-series information, a bidirectional gated recurrent unit utilizing prototype information for imputation, and an attentive prototypical refinement module for adjusting imputations. We conducted extensive experiments on three datasets, and the results underscore PRIME's superiority over the state-of-the-art models by up to 26% relative improvement on mean square error.

Traffic cameras remain the primary source data for surveillance activities such as congestion and incident monitoring. To date, State agencies continue to rely on manual effort to extract data from networked cameras due to limitations of the current automatic vision systems including requirements for complex camera calibration and inability to generate high resolution data. This study implements a three-stage video analytics framework for extracting high-resolution traffic data such vehicle counts, speed, and acceleration from infrastructure-mounted CCTV cameras. The key components of the framework include object recognition, perspective transformation, and vehicle trajectory reconstruction for traffic data collection. First, a state-of-the-art vehicle recognition model is implemented to detect and classify vehicles. Next, to correct for camera distortion and reduce partial occlusion, an algorithm inspired by two-point linear perspective is utilized to extracts the region of interest (ROI) automatically, while a 2D homography technique transforms the CCTV view to bird's-eye view (BEV). Cameras are calibrated with a two-layer matrix system to enable the extraction of speed and acceleration by converting image coordinates to real-world measurements. Individual vehicle trajectories are constructed and compared in BEV using two time-space-feature-based object trackers, namely Motpy and BYTETrack. The results of the current study showed about +/- 4.5% error rate for directional traffic counts, less than 10% MSE for speed bias between camera estimates in comparison to estimates from probe data sources. Extracting high-resolution data from traffic cameras has several implications, ranging from improvements in traffic management and identify dangerous driving behavior, high-risk areas for accidents, and other safety concerns, enabling proactive measures to reduce accidents and fatalities.