This unsupervised learning method is widely used in various applications, including image analysis, information retrieval, text analysis, bioinformatics, and many more [1, 2, 3, 4]. Clustering helps uncover the underlying structure of the data, facilitates data summarization, and sometimes serves as a preprocessing step for other algorithms [2]. Despite its widespread use, one of the primary challenges many traditional clustering algorithms face is that they often assume that the data points form clusters with convex shapes. For example, centroid-based algorithms like k -means and distribution-based models like Gaussian Mixture Models (GMM) typically produce clusters that are hyperspherical or ellipsoidal [5]. Although this assumption simplifies the clustering process, it restricts the flexibility of these models to handle complex data distributions that do not conform to convex shapes.

Traditional clustering methods typically focus on either cluster-wise global clustering or point-wise local clustering to reveal the intrinsic structures in unlabeled data. Global clustering optimizes an objective function to explore the relationships between clusters, but this approach may inevitably lead to coarse partition. In contrast, local clustering heuristically groups data based on detailed point relationships, but it tends to be less coherence and efficient. To bridge the gap between these two concepts and utilize the strengths of both, we propose Graph Probability Aggregation Clustering (GPAC), a graph-based fuzzy clustering algorithm. GPAC unifies the global clustering objective function with a local clustering constraint. The entire GPAC framework is formulated as a multi-constrained optimization problem, which can be solved using the Lagrangian method. Through the optimization process, the probability of a sample belonging to a specific cluster is iteratively calculated by aggregating information from neighboring samples within the graph. We incorporate a hard assignment variable into the objective function to further improve the convergence and stability of optimization. Furthermore, to efficiently handle large-scale datasets, we introduce an acceleration program that reduces the computational complexity from quadratic to linear, ensuring scalability. Extensive experiments conducted on synthetic, real-world, and deep learning datasets demonstrate that GPAC not only exceeds existing state-of-the-art methods in clustering performance but also excels in computational efficiency, making it a powerful tool for complex clustering challenges.

Community detection in network analysis has become more intricate due to the recent hike in social networks (Cai et al., 2024). This paper suggests a new approach named ELPMeans that strives to address this challenge. For community detection in the whole network, ELPMeans combines Laplacian, Hierarchical Clustering as well as K-means algorithms. Our technique employs Laplacian centrality and minimum distance metrics for central node identification while k-means learning is used for efficient convergence to final community structure. Remarkably, ELPMeans is an unsupervised method which is not only simple to implement but also effectively tackles common problems such as random initialization of central nodes, or finding of number of communities (K). Experimental results show that our algorithm improves accuracy and reduces time complexity considerably outperforming recent approaches on real world networks. Moreover, our approach has a wide applicability range in various community detection tasks even with nonconvex shapes and no prior knowledge about the number of communities present.

We study beyond worst-case dimensionality reduction for $s$-sparse vectors. Our work is divided into two parts, each focusing on a different facet of beyond worst-case analysis: We first consider average-case guarantees. A folklore upper bound based on the birthday-paradox states: For any collection $X$ of $s$-sparse vectors in $\mathbb{R}^d$, there exists a linear map to $\mathbb{R}^{O(s^2)}$ which \emph{exactly} preserves the norm of $99\%$ of the vectors in $X$ in any $\ell_p$ norm (as opposed to the usual setting where guarantees hold for all vectors). We give lower bounds showing that this is indeed optimal in many settings: any oblivious linear map satisfying similar average-case guarantees must map to $\Omega(s^2)$ dimensions. The same lower bound also holds for a wide class of smooth maps, including `encoder-decoder schemes', where we compare the norm of the original vector to that of a smooth function of the embedding. These lower bounds reveal a separation result, as an upper bound of $O(s \log(d))$ is possible if we instead use arbitrary (possibly non-smooth) functions, e.g., via compressed sensing algorithms. Given these lower bounds, we specialize to sparse \emph{non-negative} vectors. For a dataset $X$ of non-negative $s$-sparse vectors and any $p \ge 1$, we can non-linearly embed $X$ to $O(s\log(|X|s)/\epsilon^2)$ dimensions while preserving all pairwise distances in $\ell_p$ norm up to $1\pm \epsilon$, with no dependence on $p$. Surprisingly, the non-negativity assumption enables much smaller embeddings than arbitrary sparse vectors, where the best known bounds suffer exponential dependence. Our map also guarantees \emph{exact} dimensionality reduction for $\ell_{\infty}$ by embedding into $O(s\log |X|)$ dimensions, which is tight. We show that both the non-linearity of $f$ and the non-negativity of $X$ are necessary, and provide downstream algorithmic improvements.

This work proposes a scalable probabilistic latent variable model based on Gaussian processes (Lawrence, 2004) in the context of multiple observation spaces. We focus on an application in astrophysics where data sets typically contain both observed spectral features and scientific properties of astrophysical objects such as galaxies or exoplanets. In our application, we study the spectra of very luminous galaxies known as quasars, along with their properties, such as the mass of their central supermassive black hole, accretion rate, and luminosity-resulting in multiple observation spaces. A single data point is then characterized by different classes of observations, each with different likelihoods. Our proposed model extends the baseline stochastic variational Gaussian process latent variable model (GPLVM) introduced by Lalchand et al. (2022) to this setting, proposing a seamless generative model where the quasar spectra and scientific labels can be generated simultaneously using a shared latent space as input to different sets of Gaussian process decoders, one for each observation space. Additionally, this framework enables training in a missing data setting where a large number of dimensions per data point may be unknown or unobserved. We demonstrate high-fidelity reconstructions of the spectra and scientific labels during test-time inference and briefly discuss the scientific interpretations of the results, along with the significance of such a generative model.

In this paper we present the results of an experiment aimed to use machine learning methods to obtain models that can be used for the automatic classification of products. In order to apply automatic classification methods, we transformed the product names from a text representation to numeric vectors, a process called word embedding. We used several embedding methods: Count Vectorization, TF-IDF, Word2Vec, FASTTEXT, and GloVe. Having the product names in a form of numeric vectors, we proceeded with a set of machine learning methods for automatic classification: Logistic Regression, Multinomial Naive Bayes, kNN, Artificial Neural Networks, Support Vector Machines, and Decision trees with several variants. The results show an impressive accuracy of the classification process for Support Vector Machines, Logistic Regression, and Random Forests. Regarding the word embedding methods, the best results were obtained with the FASTTEXT technique.

The substantial growth of textual content in diverse domains and platforms has led to a considerable need for Automatic Text Summarization (ATS) techniques that aid in the process of text analysis. The effectiveness of text summarization models has been significantly enhanced in a variety of technical domains because of advancements in Natural Language Processing (NLP) and Deep Learning (DL). Despite this, the process of summarizing textual information continues to be significantly constrained by the intricate writing styles of a variety of texts, which involve a range of technical complexities. Text summarization techniques can be broadly categorized into two main types: abstractive summarization and extractive summarization. Extractive summarization involves directly extracting sentences, phrases, or segments of text from the content without making any changes. On the other hand, abstractive summarization is achieved by reconstructing the sentences, phrases, or segments from the original text using linguistic analysis. Through this study, a linguistically diverse categorizations of text summarization approaches have been addressed in a constructive manner. In this paper, the authors explored existing hybrid techniques that have employed both extractive and abstractive methodologies. In addition, the pros and cons of various approaches discussed in the literature are also investigated. Furthermore, the authors conducted a comparative analysis on different techniques and matrices to evaluate the generated summaries using language generation models. This survey endeavors to provide a comprehensive overview of ATS by presenting the progression of language processing regarding this task through a breakdown of diverse systems and architectures accompanied by technical and mathematical explanations of their operations.

Most techniques for explainable machine learning focus on feature attribution, i.e., values are assigned to the features such that their sum equals the prediction. Example attribution is another form of explanation that assigns weights to the training examples, such that their scalar product with the labels equals the prediction. The latter may provide valuable complementary information to feature attribution, in particular in cases where the features are not easily interpretable. Current example-based explanation techniques have targeted a few model types only, such as k-nearest neighbors and random forests. In this work, a technique for obtaining example-based explanations from deep neural networks (EBE-DNN) is proposed. The basic idea is to use the deep neural network to obtain an embedding, which is employed by a k-nearest neighbor classifier to form a prediction; the example attribution can hence straightforwardly be derived from the latter. Results from an empirical investigation show that EBE-DNN can provide highly concentrated example attributions, i.e., the predictions can be explained with few training examples, without reducing accuracy compared to the original deep neural network. Another important finding from the empirical investigation is that the choice of layer to use for the embeddings may have a large impact on the resulting accuracy.

--Cryptocurrencies fluctuate in markets with high price volatility, which becomes a great challenge for investors. T o aid investors in making informed decisions, systems predicting cryptocurrency market movements have been developed, commonly framed as feature-driven regression problems that focus solely on historical patterns favored by domain experts. However, these methods overlook three critical factors that significantly influence the cryptocurrency market dynamics: 1) the macro investing environment, reflected in major cryp-tocurrency fluctuations, which can affect investors collaborative behaviors, 2) overall market sentiment, heavily influenced by news, which impacts investors strategies, and 3) technical indicators, which offer insights into overbought or oversold conditions, momentum, and market trends are often ignored despite their relevance in shaping short-term price movements. In this paper, we propose a dual prediction mechanism that enables the model to forecast the next day's closing price by incorporating macroeconomic fluctuations, technical indicators, and individual cryptocurrency price changes. Furthermore, we introduce a novel refinement mechanism that enhances the prediction through market sentiment-based rescaling and fusion. In experiments, the proposed model achieves state-of-the-art performance (SOT A), consistently outperforming ten comparison methods in most cases. Cryptocurrencies have recently become a topic of conversation due to their great impact on the financial world. This heightened attention is fueled by several factors including the sudden drops and shocks in cryptocurrency markets [1], which offer opportunities for substantial returns, and the innovative technologies underpinning these assets, such as Blockchain [2], [3]. Unlike traditional financial markets such as bonds and stocks, the cryptocurrency market is characterized by a comparatively smaller market capitalization and pronounced volatility in short-term fluctuations [4], creating a unique and challenging investment landscape. This volatility stems from a complex interplay of factors that perpetuate a self-fulfilling cycle.

Information-theoretic quantities play a crucial role in understanding non-linear relationships between random variables and are widely used across scientific disciplines. However, estimating these quantities remains an open problem, particularly in the case of high-dimensional discrete distributions. Current approaches typically rely on embedding discrete data into a continuous space and applying neural estimators originally designed for continuous distributions, a process that may not fully capture the discrete nature of the underlying data. We consider Continuous-Time Markov Chains (CTMCs), stochastic processes on discrete state-spaces which have gained popularity due to their generative modeling applications. In this work, we introduce INFO-SEDD, a novel method for estimating information-theoretic quantities of discrete data, including mutual information and entropy. Our approach requires the training of a single parametric model, offering significant computational and memory advantages. Additionally, it seamlessly integrates with pretrained networks, allowing for efficient reuse of pretrained generative models. To evaluate our approach, we construct a challenging synthetic benchmark. Our experiments demonstrate that INFO-SEDD is robust and outperforms neural competitors that rely on embedding techniques. Moreover, we validate our method on a real-world task: estimating the entropy of an Ising model. Overall, INFO-SEDD outperforms competing methods and shows scalability to high-dimensional scenarios, paving the way for new applications where estimating MI between discrete distribution is the focus. The promising results in this complex, high-dimensional scenario highlight INFO-SEDD as a powerful new estimator in the toolkit for information-theoretical analysis.