The Effectiveness of Graph Contrastive Learning on Mathematical Information Retrieval

This paper details an empirical investigation into using Graph Contrastive Learning (GCL) to generate mathematical equation representations, a critical aspect of Mathematical Information Retrieval (MIR). Our findings reveal that this simple approach consistently exceeds the performance of the current leading formula retrieval model, TangentCFT. To support ongoing research and development in this field, we have made our source code accessible to the public at https://github.com/WangPeiSyuan/GCL-Formula-Retrieval/.

Multivariate Beta Mixture Model: Probabilistic Clustering With Flexible Cluster Shapes

This paper introduces the multivariate beta mixture model (MBMM), a new probabilistic model for soft clustering. MBMM adapts to diverse cluster shapes because of the flexible probability density function of the multivariate beta distribution. We introduce the properties of MBMM, describe the parameter learning procedure, and present the experimental results, showing that MBMM fits diverse cluster shapes on synthetic and real datasets. The code is released anonymously at \url{https://github.com/hhchen1105/mbmm/}.

Toward Efficient and Incremental Spectral Clustering via Parametric Spectral Clustering

Spectral clustering is a popular method for effectively clustering nonlinearly separable data. However, computational limitations, memory requirements, and the inability to perform incremental learning challenge its widespread application. To overcome these limitations, this paper introduces a novel approach called parametric spectral clustering (PSC). By extending the capabilities of spectral clustering, PSC addresses the challenges associated with big data and real-time scenarios and enables efficient incremental clustering with new data points. Experimental evaluations conducted on various open datasets demonstrate the superiority of PSC in terms of computational efficiency while achieving clustering quality mostly comparable to standard spectral clustering. The proposed approach has significant potential for incremental and real-time data analysis applications, facilitating timely and accurate clustering in dynamic and evolving datasets. The findings of this research contribute to the advancement of clustering techniques and open new avenues for efficient and effective data analysis. We publish the experimental code at https://github.com/109502518/PSC_BigData.

Detecting Inactive Cyberwarriors from Online Forums

The proliferation of misinformation has emerged as a new form of warfare in the information age. This type of warfare involves cyberwarriors, who deliberately propagate messages aimed at defaming opponents or fostering unity among allies. In this study, we investigate the level of activity exhibited by cyberwarriors within a large online forum, and remarkably, we discover that only a minute fraction of cyberwarriors are active users. Surprisingly, despite their expected role of actively disseminating misinformation, cyberwarriors remain predominantly silent during peacetime and only spring into action when necessary. Moreover, we analyze the challenges associated with identifying cyberwarriors and provide evidence that detecting inactive cyberwarriors is considerably more challenging than identifying their active counterparts. Finally, we discuss potential methodologies to more effectively identify cyberwarriors during their inactive phases, offering insights into better capturing their presence and actions. The experimental code is released for reproducibility: \url{https://github.com/Ryaninthegame/Detect-Inactive-Spammers-on-PTT}.

TTSWING: a Dataset for Table Tennis Swing Analysis

We introduce TTSWING, a novel dataset designed for table tennis swing analysis. This dataset comprises comprehensive swing information obtained through 9-axis sensors integrated into custom-made racket grips, accompanied by anonymized demographic data of the players. We detail the data collection and annotation procedures. Furthermore, we conduct pilot studies utilizing diverse machine learning models for swing analysis. TTSWING holds tremendous potential to facilitate innovative research in table tennis analysis and is a valuable resource for the scientific community. We release the dataset and experimental codes at https://github.com/DEPhantom/TTSWING.

Associated Learning: Decomposing End-to-end Backpropagation based on Auto-encoders and Target Propagation

Backpropagation has been widely used in deep learning approaches, but it is inefficient and sometimes unstable because of backward locking and vanishing/exploding gradient problems, especially when the gradient flow is long. Additionally, updating all edge weights based on a single objective seems biologically implausible. In this paper, we introduce a novel biologically motivated learning structure called Associated Learning, which modularizes the network into smaller components, each of which has a local objective. Because the objectives are mutually independent, Associated Learning can learn the parameters independently and simultaneously when these parameters belong to different components. Surprisingly, training deep models by Associated Learning yields comparable accuracies to models trained using typical backpropagation methods, which aims at fitting the target variable directly. Moreover, probably because the gradient flow of each component is short, deep networks can still be trained with Associated Learning even when some of the activation functions are sigmoid-a situation that usually results in the vanishing gradient problem when using typical backpropagation. We also found that the Associated Learning generates better metafeatures, which we demonstrated both quantitatively (via inter-class and intra-class distance comparisons in the hidden layers) and qualitatively (by visualizing the hidden layers using t-SNE).

Weighted-SVD: Matrix Factorization with Weights on the Latent Factors

The Matrix Factorization models, sometimes called the latent factor models, are a family of methods in the recommender system research area to (1) generate the latent factors for the users and the items and (2) predict users' ratings on items based on their latent factors. However, current Matrix Factorization models presume that all the latent factors are equally weighted, which may not always be a reasonable assumption in practice. In this paper, we propose a new model, called Weighted-SVD, to integrate the linear regression model with the SVD model such that each latent factor accompanies with a corresponding weight parameter. This mechanism allows the latent factors have different weights to influence the final ratings. The complexity of the Weighted-SVD model is slightly larger than the SVD model but much smaller than the SVD++ model. We compared the Weighted-SVD model with several latent factor models on five public datasets based on the Root-Mean-Squared-Errors (RMSEs). The results show that the Weighted-SVD model outperforms the baseline methods in all the experimental datasets under almost all settings.