Topic modelling has become increasingly popular for summarizing text data, such as social media posts and articles. However, topic modelling is usually completed in one shot. Assessing the quality of resulting topics is challenging. No effective methods or measures have been developed for assessing the results or for making further enhancements to the topics. In this research, we propose we propose to use an iterative process to perform topic modelling that gives rise to a sense of completeness of the resulting topics when the process is complete. Using the BERTopic package, a popular method in topic modelling, we demonstrate how the modelling process can be applied iteratively to arrive at a set of topics that could not be further improved upon using one of the three selected measures for clustering comparison as the decision criteria. This demonstration is conducted using a subset of the COVIDSenti-A dataset. The early success leads us to believe that further research using in using this approach in conjunction with other topic modelling algorithms could be viable.

Clustering algorithms frequently require the number of clusters to be chosen in advance, but it is usually not clear how to do this. To tackle this challenge when clustering within sequential data, we present a method for estimating the number of clusters when the data is a trajectory of a Block Markov Chain. Block Markov Chains are Markov Chains that exhibit a block structure in their transition matrix. The method considers a matrix that counts the number of transitions between different states within the trajectory, and transforms this into a spectral embedding whose dimension is set via singular value thresholding. The number of clusters is subsequently estimated via density-based clustering of this spectral embedding, an approach inspired by literature on the Stochastic Block Model. By leveraging and augmenting recent results on the spectral concentration of random matrices with Markovian dependence, we show that the method is asymptotically consistent - in spite of the dependencies between the count matrix's entries, and even when the count matrix is sparse. We also present a numerical evaluation of our method, and compare it to alternatives.

In this paper, we develop an unsupervised learning approach to earthquake detection. We train a specific class of deep auto-encoders that learn to reproduce the input waveforms after a data-compressive bottleneck, and then use a simple triggering algorithm at the bottleneck to label waveforms as noise or signal. Our approach is motivated by the intuition that efficient compression of data should represent signals differently from noise, and is facilitated by a time-axis-preserving approach to auto-encoding and intuitively-motivated choices on the architecture and triggering. We demonstrate that the detection performance of the unsupervised approach is comparable to, and in some cases better than, some of the state-of-the-art supervised methods. Moreover, it has strong \emph{cross-dataset generalization}. By experimenting with various modifications, we demonstrate that the detection performance is insensitive to various technical choices made in the algorithm. Our approach has the potential to be useful for other signal detection problems with time series data.

Cavities on the structures of proteins are formed due to interaction between proteins and some small molecules, known as ligands. These are basically the locations where ligands bind with proteins. Actual detection of such locations is all-important to succeed in the entire drug design process. This study proposes a Voronoi Tessellation based novel cavity detection model that is used to detect cavities on the structure of proteins. As the atom space of protein structure is dense and of large volumes and the DBSCAN (Density Based Spatial Clustering of Applications with Noise) algorithm can handle such type of data very well as well as it is not mandatory to have knowledge about the numbers of clusters (cavities) in data as priori in this algorithm, this study proposes to implement the proposed algorithm with the DBSCAN algorithm.

Representing and quantifying Minimal Residual Disease (MRD) in Acute Myeloid Leukemia (AML), a type of cancer that affects the blood and bone marrow, is essential in the prognosis and follow-up of AML patients. As traditional cytological analysis cannot detect leukemia cells below 5\%, the analysis of flow cytometry dataset is expected to provide more reliable results. In this paper, we explore statistical learning methods based on optimal transport (OT) to achieve a relevant low-dimensional representation of multi-patient flow cytometry measurements (FCM) datasets considered as high-dimensional probability distributions. Using the framework of OT, we justify the use of the K-means algorithm for dimensionality reduction of multiple large-scale point clouds through mean measure quantization by merging all the data into a single point cloud. After this quantization step, the visualization of the intra and inter-patients FCM variability is carried out by embedding low-dimensional quantized probability measures into a linear space using either Wasserstein Principal Component Analysis (PCA) through linearized OT or log-ratio PCA of compositional data. Using a publicly available FCM dataset and a FCM dataset from Bordeaux University Hospital, we demonstrate the benefits of our approach over the popular kernel mean embedding technique for statistical learning from multiple high-dimensional probability distributions. We also highlight the usefulness of our methodology for low-dimensional projection and clustering patient measurements according to their level of MRD in AML from FCM. In particular, our OT-based approach allows a relevant and informative two-dimensional representation of the results of the FlowSom algorithm, a state-of-the-art method for the detection of MRD in AML using multi-patient FCM.

High-dimensional single-cell data poses significant challenges in identifying underlying biological patterns due to the complexity and heterogeneity of cellular states. We propose a comprehensive gene-cell dependency visualization via unsupervised clustering, Growing Hierarchical Self-Organizing Map (GHSOM), specifically designed for analyzing high-dimensional single-cell data like single-cell sequencing and CRISPR screens. GHSOM is applied to cluster samples in a hierarchical structure such that the self-growth structure of clusters satisfies the required variations between and within. We propose a novel Significant Attributes Identification Algorithm to identify features that distinguish clusters. This algorithm pinpoints attributes with minimal variation within a cluster but substantial variation between clusters. These key attributes can then be used for targeted data retrieval and downstream analysis. Furthermore, we present two innovative visualization tools: Cluster Feature Map and Cluster Distribution Map. The Cluster Feature Map highlights the distribution of specific features across the hierarchical structure of GHSOM clusters. This allows for rapid visual assessment of cluster uniqueness based on chosen features. The Cluster Distribution Map depicts leaf clusters as circles on the GHSOM grid, with circle size reflecting cluster data size and color customizable to visualize features like cell type or other attributes. We apply our analysis to three single-cell datasets and one CRISPR dataset (cell-gene database) and evaluate clustering methods with internal and external CH and ARI scores. GHSOM performs well, being the best performer in internal evaluation (CH=4.2). In external evaluation, GHSOM has the third-best performance of all methods.

Multi-relational graph clustering has demonstrated remarkable success in uncovering underlying patterns in complex networks. Representative methods manage to align different views motivated by advances in contrastive learning. Our empirical study finds the pervasive presence of imbalance in real-world graphs, which is in principle contradictory to the motivation of alignment. In this paper, we first propose a novel metric, the Aggregation Class Distance, to empirically quantify structural disparities among different graphs. To address the challenge of view imbalance, we propose Balanced Multi-Relational Graph Clustering (BMGC), comprising unsupervised dominant view mining and dual signals guided representation learning. It dynamically mines the dominant view throughout the training process, synergistically improving clustering performance with representation learning. Theoretical analysis ensures the effectiveness of dominant view mining. Extensive experiments and in-depth analysis on real-world and synthetic datasets showcase that BMGC achieves state-of-the-art performance, underscoring its superiority in addressing the view imbalance inherent in multi-relational graphs. The source code and datasets are available at https://github.com/zxlearningdeep/BMGC.

Social event detection refers to extracting relevant message clusters from social media data streams to represent specific events in the real world. Social event detection is important in numerous areas, such as opinion analysis, social safety, and decision-making. Most current methods are supervised and require access to large amounts of data. These methods need prior knowledge of the events and carry a high risk of leaking sensitive information in the messages, making them less applicable in open-world settings. Therefore, conducting unsupervised detection while fully utilizing the rich information in the messages and protecting data privacy remains a significant challenge. To this end, we propose a novel social event detection framework, ADP-SEMEvent, an unsupervised social event detection method that prioritizes privacy. Specifically, ADP-SEMEvent is divided into two stages, i.e., the construction stage of the private message graph and the clustering stage of the private message graph. In the first stage, an adaptive differential privacy approach is used to construct a private message graph. In this process, our method can adaptively apply differential privacy based on the events occurring each day in an open environment to maximize the use of the privacy budget. In the second stage, to address the reduction in data utility caused by noise, a novel 2-dimensional structural entropy minimization algorithm based on optimal subgraphs is used to detect events in the message graph. The highlight of this process is unsupervised and does not compromise differential privacy. Extensive experiments on two public datasets demonstrate that ADP-SEMEvent can achieve detection performance comparable to state-of-the-art methods while maintaining reasonable privacy budget parameters.

To enhance therapeutic outcomes from a pharmacological perspective, we propose MiranDa, designed for medication recommendation, which is the first actionable model capable of providing the estimated length of stay in hospitals (ELOS) as counterfactual outcomes that guide clinical practice and model training. In detail, MiranDa emulates the educational trajectory of doctors through two gradient-scaling phases shifted by ELOS: an Evidence-based Training Phase that utilizes supervised learning and a Therapeutic Optimization Phase grounds in reinforcement learning within the gradient space, explores optimal medications by perturbations from ELOS. Evaluation of the Medical Information Mart for Intensive Care III dataset and IV dataset, showcased the superior results of our model across five metrics, particularly in reducing the ELOS. Surprisingly, our model provides structural attributes of medication combinations proved in hyperbolic space and advocated "procedure-specific" medication combinations. These findings posit that MiranDa enhanced medication efficacy. Notably, our paradigm can be applied to nearly all medical tasks and those with information to evaluate predicted outcomes. The source code of the MiranDa model is available at https://github.com/azusakou/MiranDa.

We study the problem of estimating the means of well-separated mixtures when an adversary may add arbitrary outliers. While strong guarantees are available when the outlier fraction is significantly smaller than the minimum mixing weight, much less is known when outliers may crowd out low-weight clusters - a setting we refer to as list-decodable mixture learning (LD-ML). In this case, adversarial outliers can simulate additional spurious mixture components. Hence, if all means of the mixture must be recovered up to a small error in the output list, the list size needs to be larger than the number of (true) components. We propose an algorithm that obtains order-optimal error guarantees for each mixture mean with a minimal list-size overhead, significantly improving upon list-decodable mean estimation, the only existing method that is applicable for LD-ML. Although improvements are observed even when the mixture is non-separated, our algorithm achieves particularly strong guarantees when the mixture is separated: it can leverage the mixture structure to partially cluster the samples before carefully iterating a base learner for list-decodable mean estimation at different scales.