arXiv subjects

Rustam Mussabayev

Publications and source records attributed to Rustam Mussabayev.

9 recordsLinked to original sources

arXiv2026

Data-Native Global Optimization for Big Data K-means Clustering

Big data clustering remains challenging: the Minimum Sum-of-Squares Clustering (MSSC) problem underlying K-means is NP-hard, and existing methods either reach poor local minima or require prohibitive metaheuristic hybrids. We target arbitrarily tall data: a fixed feature space may contain arbitrarily many, possibly infinitely many, observations, while the algorithm accesses only finite random samples. We propose Big-means++, an algorithm achieving scalability and global-search quality by curating inputs to MSSC optimization on big data. It orchestrates local K-means refinements into a data-native global search for big data clustering. Rather than optimizing the full-data MSSC objective, Big-means++ traverses sample-induced surrogate landscapes. Each sample defines a distinct empirical MSSC approximation with a perturbed local-optimum structure, turning sample-to-sample variation into a global-search mechanism. Unlike Big-means, a flowing-incumbent strategy propagates centroid state across empirical landscapes through K-means refinements on fresh samples without rollback to a best-so-far solution. This increases mobility and favors stable, high-quality configurations across approximations of the full-data structure. A new shaking mechanism varies sample size geometrically, broadening the surrogate landscapes explored across resolution scales, accounting for cluster imbalance, and improving solution quality. A competitive multi-agent system asynchronously explores independent sampled landscapes, transforming diverse stochastic trajectories into collective search intelligence. Automatic convergence detection stops each agent after attaining a high-quality solution but before further search risks degrading it, while providing a universal speed-quality control. Experiments on 22 datasets against 11 competing algorithms demonstrate the effectiveness, efficiency, and robustness of Big-means++.

cs.LG↗

arXiv2026

MLLM-Microscope: Unlocking Hidden Structure Within Multimodal Large Language Models

This work presents MLLM-Microscope, a novel system designed for analyzing the hidden representations within Multimodal Large Language Models (MLLMs). Our system evaluates the linearity, intrinsic dimension, and anisotropy of multimodal token embeddings across transformer layers. Utilizing the ScienceQA dataset, we evaluate two state-of-the-art MLLMs, LLaVA-NeXT and OmniFusion. We find that both the main and residual streams for tokens of both modalities exhibit highly linear behaviors across transformer layers. However, LLaVA-NeXT's image tokens reveal a slight decline in linearity, whereas OmniFusion's remain consistent. Image token dimensions in OmniFusion remain consistently higher across layers compared to LLaVA-NeXT. Also, the OmniFusion's anisotropy is observed to stay consistently low throughout the layers. These findings suggest that the inner workings of MLLMs highly depend on the nature of modality fusion performed before passing the token sequence into LLM. This and other new potential insights obtainable from our system are surely capable of enhancing our understanding of the inner workings of MLLMs, informing future model design and optimization.

cs.CL↗

arXiv2024

Boosting K-means for Big Data by Fusing Data Streaming with Global Optimization

K-means clustering is a cornerstone of data mining, but its efficiency deteriorates when confronted with massive datasets. To address this limitation, we propose a novel heuristic algorithm that leverages the Variable Neighborhood Search (VNS) metaheuristic to optimize K-means clustering for big data. Our approach is based on the sequential optimization of the partial objective function landscapes obtained by restricting the Minimum Sum-of-Squares Clustering (MSSC) formulation to random samples from the original big dataset. Within each landscape, systematically expanding neighborhoods of the currently best (incumbent) solution are explored by reinitializing all degenerate and a varying number of additional centroids. Extensive and rigorous experimentation on a large number of real-world datasets reveals that by transforming the traditional local search into a global one, our algorithm significantly enhances the accuracy and efficiency of K-means clustering in big data environments, becoming the new state of the art in the field.

cs.LG↗

arXiv2024

Variable Landscape Search: A Novel Metaheuristic Paradigm for Unlocking Hidden Dimensions in Global Optimization

This paper presents the Variable Landscape Search (VLS), a novel metaheuristic designed to globally optimize complex problems by dynamically altering the objective function landscape. Unlike traditional methods that operate within a static search space, VLS introduces an additional level of flexibility and diversity to the global optimization process. It does this by continuously and iteratively varying the objective function landscape through slight modifications to the problem formulation, the input data, or both. The innovation of the VLS metaheuristic stems from its unique capability to seamlessly fuse dynamic adaptations in problem formulation with modifications in input data. This dual-modality approach enables continuous exploration of interconnected and evolving search spaces, significantly enhancing the potential for discovering optimal solutions in complex, multi-faceted optimization scenarios, making it adaptable across various domains. In this paper, one of the theoretical results is obtained in the form of a generalization of the following three alternative metaheuristics, which have been reduced to special cases of VLS: Variable Formulation Search (VFS), Formulation Space Search (FSS), and Variable Search Space (VSS). As a practical application, the paper demonstrates the superior efficiency of a recent big data clustering algorithm through its conceptualization using the VLS paradigm.

math.OC↗

arXiv2024

Superior Parallel Big Data Clustering through Competitive Stochastic Sample Size Optimization in Big-means

This paper introduces a novel K-means clustering algorithm, an advancement on the conventional Big-means methodology. The proposed method efficiently integrates parallel processing, stochastic sampling, and competitive optimization to create a scalable variant designed for big data applications. It addresses scalability and computation time challenges typically faced with traditional techniques. The algorithm adjusts sample sizes dynamically for each worker during execution, optimizing performance. Data from these sample sizes are continually analyzed, facilitating the identification of the most efficient configuration. By incorporating a competitive element among workers using different sample sizes, efficiency within the Big-means algorithm is further stimulated. In essence, the algorithm balances computational time and clustering quality by employing a stochastic, competitive sampling strategy in a parallel computing setting.

cs.LG↗

arXiv2023

High-Performance Hybrid Algorithm for Minimum Sum-of-Squares Clustering of Infinitely Tall Data

This paper introduces a novel formulation of the clustering problem, namely the Minimum Sum-of-Squares Clustering of Infinitely Tall Data (MSSC-ITD), and presents HPClust, an innovative set of hybrid parallel approaches for its effective solution. By utilizing modern high-performance computing techniques, HPClust enhances key clustering metrics: effectiveness, computational efficiency, and scalability. In contrast to vanilla data parallelism, which only accelerates processing time through the MapReduce framework, our approach unlocks superior performance by leveraging the multi-strategy competitive-cooperative parallelism and intricate properties of the objective function landscape. Unlike other available algorithms that struggle to scale, our algorithm is inherently parallel in nature, improving solution quality through increased scalability and parallelism, and outperforming even advanced algorithms designed for small and medium-sized datasets. Our evaluation of HPClust, featuring four parallel strategies, demonstrates its superiority over traditional and cutting-edge methods by offering better performance in the key metrics. These results also show that parallel processing not only enhances the clustering efficiency, but the accuracy as well. Additionally, we explore the balance between computational efficiency and clustering quality, providing insights into optimal parallel strategies based on dataset specifics and resource availability. This research advances our understanding of parallelism in clustering algorithms, demonstrating that a judicious hybridization of advanced parallel approaches yields optimal results for MSSC-ITD. Experiments on synthetic data further confirm HPClust's exceptional scalability and robustness to noise.

cs.DC↗

arXiv2023

Comparative Analysis of Optimization Strategies for K-means Clustering in Big Data Contexts: A Review

This paper presents a comparative analysis of different optimization techniques for the K-means algorithm in the context of big data. K-means is a widely used clustering algorithm, but it can suffer from scalability issues when dealing with large datasets. The paper explores different approaches to overcome these issues, including parallelization, approximation, and sampling methods. The authors evaluate the performance of various clustering techniques on a large number of benchmark datasets, comparing them according to the dominance criterion provided by the "less is more" approach (LIMA), i.e., simultaneously along the dimensions of speed, clustering quality, and simplicity. The results show that different techniques are more suitable for different types of datasets and provide insights into the trade-offs between speed and accuracy in K-means clustering for big data. Overall, the paper offers a comprehensive guide for practitioners and researchers on how to optimize K-means for big data applications.

cs.LG↗

arXiv2022

How to Use K-means for Big Data Clustering?

K-means plays a vital role in data mining and is the simplest and most widely used algorithm under the Euclidean Minimum Sum-of-Squares Clustering (MSSC) model. However, its performance drastically drops when applied to vast amounts of data. Therefore, it is crucial to improve K-means by scaling it to big data using as few of the following computational resources as possible: data, time, and algorithmic ingredients. We propose a new parallel scheme of using K-means and K-means++ algorithms for big data clustering that satisfies the properties of a ``true big data'' algorithm and outperforms the classical and recent state-of-the-art MSSC approaches in terms of solution quality and runtime. The new approach naturally implements global search by decomposing the MSSC problem without using additional metaheuristics. This work shows that data decomposition is the basic approach to solve the big data clustering problem. The empirical success of the new algorithm allowed us to challenge the common belief that more data is required to obtain a good clustering solution. Moreover, the present work questions the established trend that more sophisticated hybrid approaches and algorithms are required to obtain a better clustering solution.

cs.LG↗

arXiv2020

Neural Named Entity Recognition for Kazakh

We present several neural networks to address the task of named entity recognition for morphologically complex languages (MCL). Kazakh is a morphologically complex language in which each root/stem can produce hundreds or thousands of variant word forms. This nature of the language could lead to a serious data sparsity problem, which may prevent the deep learning models from being well trained for under-resourced MCLs. In order to model the MCLs' words effectively, we introduce root and entity tag embedding plus tensor layer to the neural networks. The effects of those are significant for improving NER model performance of MCLs. The proposed models outperform state-of-the-art including character-based approaches, and can be potentially applied to other morphologically complex languages.

cs.IR↗