Least squares quantization in PCM

1982/03/01 by S. Lloyd, Sheelagh Lloyd · 15,730 citations
Computer Science · Engineering · Mathematics · #Advanced Wireless Communication Techniques #Algorithm #Amplitude #Applied mathematics #Coding theory and cryptography #Combinatorics #Error Correcting Code Techniques #Gaussian #Mathematics #Physics #Quantization (signal processing) #Quantum mechanics #Topology (electrical circuits)

paper · open access · doi:10.1109/tit.1982.1056489

published in IEEE Transactions on Information Theory 28(2), 129-137 (Institute of Electrical and Electronics Engineers)

openalex publication_date 1982/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

It has long been realized that in pulse-code modulation (PCM), with a given ensemble of signals to handle, the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall. It has been shown by Panter and Dite that, in the limit as the number of quanta becomes infinite, the asymptotic fractional density of quanta per unit voltage should vary as the one-third power of the probability density per unit voltage of signal amplitudes. In this paper the corresponding result for any finite number of quanta is derived; that is, necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy. The optimization criterion used is that the average quantization noise power be a minimum. It is shown that the result obtained here goes over into the Panter and Dite result as the number of quanta become large. The optimum quautization schemes for2^bquanta,b=1,2, ⋯, 7, are given numerically for Gaussian and for Laplacian distribution of signal amplitudes.

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• Topological Structure Description for Artcode Detection Using the Shape of Orientation Histogram
• Fast Haar Transforms for Graph Neural Networks
• Learning to Cluster Faces via Transformer
• Characterizing English Variation across Social Media Communities with BERT
• Approximate DBSCAN under Differential Privacy
• Explainable Graph Spectral Clustering For GloVe-like Text Embeddings
• EFU: Enforcing Federated Unlearning via Functional Encryption
• MorphIt: Flexible Spherical Approximation of Robot Morphology for Representation-driven Adaptation
• Summarizing Classed Region Maps with a Disk Choreme
• Clustering in Block Markov Chains
• Error-Bounded and Feature Preserving Surface Remeshing with Minimal Angle Improvement
• Compressive Mining: Fast and Optimal Data Mining in the Compressed Domain
• Go with the Flow: Adaptive Control for Neural ODEs
• Julia Implementation of the Dynamic Distributed Dimensional Data Model
• On the time integration for phase field modeling of grain growth in additive manufacturing
• A Simple PTAS for Weighted k-means and Sensor Coverage
• Mixture of Experts Guided by Gaussian Splatters Matters: A new Approach to Weakly-Supervised Video Anomaly Detection
• Deep Language Geometry: Constructing a Metric Space from LLM Weights
• Exact and Heuristic Algorithms for Constrained Biclustering
• SPaRFT: Self-Paced Reinforcement Fine-Tuning for Large Language Models
• Open-world Point Cloud Semantic Segmentation: A Human-in-the-loop Framework
• Bootstrap Deep Spectral Clustering with Optimal Transport
• Fast and energy-efficient technique for jammed region mapping in wireless sensor networks
• Unsupervised and semi-supervised clustering methods to identify and refine participant experience levels in educational research
• Neighborhood-Preserving Voronoi Treemaps
• Geodesic Centroidal Voronoi Tessellations: Theories, Algorithms and Applications
• Scalable Varied-Density Clustering via Graph Propagation
• Unraveling Hidden Representations: A Multi-Modal Layer Analysis for Better Synthetic Content Forensics
• Finite-State Markov Modeling of Leaky Waveguide Channels in Communication-based Train Control (CBTC) Systems
• Towards Fair Deep Clustering With Multi-State Protected Variables
• On Convergence of Epanechnikov Mean Shift
• Network Anomaly Detection: A Survey and Comparative Analysis of Stochastic and Deterministic Methods
• Differentially private k-means clustering via exponential mechanism and max cover
• FaceGCD: Generalized Face Discovery via Dynamic Prefix Generation
• From Seeing to Experiencing: Scaling Navigation Foundation Models with Reinforcement Learning
• Gossip Coverage Control for Robotic Networks: Dynamical Systems on the Space of Partitions
• Learning to Gridize: Segment Physical World by Wireless Communication Channel
• TDAPNet: Prototype Network with Recurrent Top-Down Attention for Robust Object Classification under Partial Occlusion
• EPTAS for k-means Clustering of Affine Subspaces
• Sketching Datasets for Large-Scale Learning (long version)
• Tree Index: A New Cluster Evaluation Technique
• An ℓ_p theory of PCA and spectral clustering
• Uncertainty quantification and propagation in surrogate-based Bayesian inference
• Semi-discrete unbalanced optimal transport and quantization
• Functional Factorial K-means Analysis
• Fast k-means based on KNN Graph
• RoD-TAL: A Benchmark for Answering Questions in Romanian Driving License Exams
• k-sums: another side of k-means
• GMM-Based Time-Varying Coverage Control
• Unsupervised Learning of GMM with a Uniform Background Component
• Balancing the Communication Load of Asynchronously Parallelized Machine Learning Algorithms
• Dilation, smoothed distance, and minimization diagrams of convex functions
• Clustering is semidefinitely not that hard: Nonnegative SDP for manifold disentangling
• Probabilistic Structure Learning for EEG/MEG Source Imaging with Hierarchical Graph Prior
• Asymmetric Co-Teaching for Unsupervised Cross Domain Person Re-Identification
• Density Adaptive Parallel Clustering
• clusterNOR: A NUMA-Optimized Clustering Framework
• Hierarchical Manifold Clustering on Diffusion Maps for Connectomics (MIT 18.S096 final project)
• Mining for Spatially-Near Communities in Geo-Located Social Networks
• Scaling Up Graph Neural Networks Via Graph Coarsening
• Rk-means: Fast Clustering for Relational Data
• Alignment of color discrimination in humans and image segmentation networks
• C2FNAS: Coarse-to-Fine Neural Architecture Search for 3D Medical Image Segmentation
• Random projection trees for vector quantization
• Machine learning in geo- and environmental sciences: From small to large scale
• Discovering Communities of Malapps on Android-based Mobile Cyber-physical Systems
• An efficient K-means algorithm for Massive Data
• Learned Sectors: A fundamentals-driven sector reclassification project
• A Virtual Processor brings back the Free Lunch
• Towards human-interpretable, automated learning of feedback control for the mixing layer
• An Algorithmic Pipeline for Analyzing Multi-parametric Flow Cytometry Data
• Cluster-based Wireless Energy Transfer for Low Complex Energy Receivers
• Multi-Robot Gaussian Process Estimation and Coverage: A Deterministic Sequencing Algorithm and Regret Analysis
• Learning Manifolds with K-Means and K-Flats
• Time-Series Analysis via Low-Rank Matrix Factorization Applied to Infant-Sleep Data
• On the Centroids of Symmetrized Bregman Divergences
• Revisiting Training Strategies and Generalization Performance in Deep Metric Learning
• Anomaly Detection in Bitcoin Network Using Unsupervised Learning Methods
• Optimal Shape-Gain Quantization for Multiuser MIMO Systems with Linear Precoding
• A Dynamic Algorithm for Facilitated Charging of Plug-In Electric Vehicles
• Graph-Community Detection for Cross-Document Topic Segment Relationship Identification
• Strong Black-box Adversarial Attacks on Unsupervised Machine Learning Models
• Interpretable Image Clustering via Diffeomorphism-Aware K-Means
• A Deep Factorization of Style and Structure in Fonts
• Learning clusters of partially observed linear dynamical systems
• FedChip: Federated LLM for Artificial Intelligence Accelerator Chip Design
• Breaking the Communication-Privacy-Accuracy Trilemma
• Weight-of-evidence 2.0 with shrinkage and spline-binning
• Polynomial Time Algorithm for 2-Stable Clustering Instances
• A constant FPT approximation algorithm for hard-capacitated k-means
• Clustering with Spectral Norm and the k-means Algorithm
• A computationally efficient framework for vector representation of persistence diagrams
• Identifying Signatures of Image Phenotypes to Track Treatment Response in Liver Disease
• Regularized k-POD: Sparse k-means clustering for high-dimensional missing data
• A Practical Algorithm for Distributed Clustering and Outlier Detection
• Adaptive Clustering through Semidefinite Programming
• Sensitive Information Detection: Recursive Neural Networks for Encoding Context
• Learning in High-Dimensional Multimedia Data: The State of the Art
• Data Stability in Clustering: A Closer Look
• Computer-Assisted Analysis of Biomedical Images
• Semi-supervised K-means++
• S2SD: Simultaneous Similarity-based Self-Distillation for Deep Metric Learning
• K-Deep Simplex: Deep Manifold Learning via Local Dictionaries
• Spatial-Temporal Cluster Relations -- A Foundation for Trajectory Cluster Lifetime Analysis
• Outliers Detection Is Not So Hard: Approximation Algorithms for Robust Clustering Problems Using Local Search Techniques
• Nonlinear Dimensionality Reduction on Graphs
• Unsupervised Continual Learning Via Pseudo Labels
• Simultaneous Clustering and Optimization for Evolving Datasets
• Graph-SIM: A Graph-based Spatiotemporal Interaction Modelling for Pedestrian Action Prediction
• Certifying Global Optimality of Graph Cuts via Semidefinite Relaxation: A Performance Guarantee for Spectral Clustering
• Massive Data Clustering in Moderate Dimensions from the Dual Spaces of Observation and Attribute Data Clouds
• Alleviating Textual Reliance in Medical Language-guided Segmentation via Prototype-driven Semantic Approximation
• Bonsai -- Diverse and Shallow Trees for Extreme Multi-label Classification
• Integration of Old and New Knowledge for Generalized Intent Discovery: A Consistency-driven Prototype-Prompting Framework
• The effects of heat treatment on the response of WE43 Mg alloy: crystal plasticity finite element simulation and SEM-DIC experiment
• Gradient boosted multi-population mortality modelling with high-frequency data
• Adaptive Algorithms for Coverage Control and Space Partitioning in Mobile Robotic Networks
• Compute SNR-Optimal Analog-to-Digital Converters for Analog In-Memory Computing
• Computing Optimal Assignments in Linear Time for Approximate Graph\n Matching
• Unsupervised Feature Learning Architecture with Multi-clustering Integration RBM
• CoreSPECT: Enhancing Clustering Algorithms via an Interplay of Density and Geometry
• Community Detection in the Hyperbolic Space
• Toward Metric Indexes for Incremental Insertion and Querying
• Beyond Feature and Structure Alignment: Learning Transferable Propagation Knowledge for Graph Foundation Models
• Feed-Forward SceneDINO for Unsupervised Semantic Scene Completion
• Compressing Colour Images with Joint Inpainting and Prediction
• Data Compressibility Quantifies LLM Memorization
• Coresets for Clustering with Fairness Constraints
• Assign Hysteresis Parameter For Ericsson BTS Power Saving Algorithm Using Unsupervised Learning
• any4: Learned 4-bit Numeric Representation for LLMs
• Modeling and Predicting Trust Dynamics in Human-Robot Teaming: A Bayesian Inference Approach
• Integrating Categorical Semantics into Unsupervised Domain Translation
• Parsimonious Gaussian mixture models with piecewise-constant eigenvalue profiles
• Time-Varying Coverage Control: A Distributed Tracker-Planner MPC Framework
• Structures of Spurious Local Minima in k-means
• DiGA3D: Coarse-to-Fine Diffusional Propagation of Geometry and Appearance for Versatile 3D Inpainting
• Revisiting Role Discovery in Networks: From Node to Edge Roles
• Quantitative characterization of tissue states using multiomics and ecological spatial analysis
• Sanitizing Manufacturing Dataset Labels Using Vision-Language Models
• LOGAN: Local Group Bias Detection by Clustering
• Minimal Learning Machine: Theoretical Results and Clustering-Based Reference Point Selection
• Adaptable Non-parametric Approach for Speech-based Symptom Assessment: Isolating Private Medical Data in a Retrieval Datastore
• Fiber-induced nonlinearity compensation in coherent optical systems by affinity propagation soft-clustering
• CN-SBM: Categorical Block Modelling For Primary and Residual Copy Number Variation
• Recomposed realities: animating still images via patch clustering and randomness
• Improved seeding strategies for k-means and k-GMM
• GANE: A Generative Adversarial Network Embedding
• Schrödinger-Föllmer Sampler: Sampling without Ergodicity
• Finding Clustering Algorithms in the Transformer Architecture
• Recovery and Generalization in Over-Realized Dictionary Learning
• Ukiyo-e Analysis and Creativity with Attribute and Geometry Annotation
• Optimal dual quantizers of 1D log-concave distributions: uniqueness and Lloyd like algorithm
• Quantizing for Noisy Flash Memory Channels
• One-class classification with application to forensic analysis
• Differentially Private k-Means Clustering
• A General Framework for Linking Free and Forced Fluctuations via Koopmanism
• Model Fusion via Retrofitting
• RadarSeq: A Temporal Vision Framework for User Churn Prediction via Radar Chart Sequences
• Language-Grounded Hierarchical Planning and Execution with Multi-Robot 3D Scene Graphs
• Energy Efficient Node Deployment in Wireless Ad-hoc Sensor Networks
• A robust and sparse K-means clustering algorithm
• PCS Workflow for Veridical Data Science in the Age of AI
• Full MIMO Channel Estimation Using A Simple Adaptive Partial Feedback Method
• Particle Gaussian Mixture (PGM) Filters
• BinaryRelax: A Relaxation Approach For Training Deep Neural Networks With Quantized Weights
• A Parallel Direct Eigensolver for Sequences of Hermitian Eigenvalue Problems with No Tridiagonalization
• Machine learning approaches for automatic cleaning of investigative drilling data
• An Observation on Lloyd's k-Means Algorithm in High Dimensions
• Identifying transient and variable sources in radio images
• Dimensionality Reduction for k-Means Clustering and Low Rank Approximation
• Quantized local reduced-order modeling in time (ql-ROM)
• Anomaly Detection in the Bitcoin System - A Network Perspective
• Learning Augmented Graph k-Clustering
• Complex networks for event detection in heterogeneous high volume news streams
• On the Performance of Cooperative Spectrum Sensing under Quantization
• Modified K-means Algorithm with Local Optimality Guarantees
• Relative Error Fair Clustering in the Weak-Strong Oracle Model
• Neuromorphic Online Clustering and Its Application to Spike Sorting
• Learning Overspecified Gaussian Mixtures Exponentially Fast with the EM Algorithm
• Unsupervised Document and Template Clustering using Multimodal Embeddings
• Random Projections for k-means Clustering
• Clustering via Boundary Erosion
• How do Probabilistic Graphical Models and Graph Neural Networks Look at Network Data?
• Hybrid approach to reconstruct nanoscale grating dimensions using scattering and fluorescence with soft X-rays
• On Ray Reordering Techniques for Faster GPU Ray Tracing
• Complexity of Single-Swap Heuristics for Metric Facility Location and Related Problem
• A Robust Optimization Framework for Flexible Industrial Energy Scheduling: Application to a Cement Plant with Market Participation
• Prompts to Summaries: Zero-Shot Language-Guided Video Summarization with Large Language and Video Models
• Fast Noise Removal for k-Means Clustering
• Improving distribution and flexible quantization for DCT coefficients
• Community Detection for Power Systems Network Aggregation Considering Renewable Variability
• The Role of Global Labels in Few-Shot Classification and How to Infer Them
• Learning Robust Heterogeneous Graph Representations via Contrastive-Reconstruction under Sparse Semantics
• CO-VADA: A Confidence-Oriented Voice Augmentation Debiasing Approach for Fair Speech Emotion Recognition
• Robust Precoding Design for Coarsely Quantized MU-MIMO Under Channel Uncertainties
• Neural Visibility Cache for Real-Time Light Sampling
• A Low-Complexity Soft-Output wMD Decoding for Uplink MIMO Systems with One-Bit ADCs
• Discrete Knowledge Graph Embedding based on Discrete Optimization
• Linear signal recovery from b-bit-quantized linear measurements: precise analysis of the trade-off between bit depth and number of measurements
• Introduction to Coresets: Approximated Mean
• PCDVQ: Enhancing Vector Quantization for Large Language Models via Polar Coordinate Decoupling
• Urania: Differentially Private Insights into AI Use
• Winner-takes-all for Multivariate Probabilistic Time Series Forecasting
• A Digital Quantum Algorithm for Jet Clustering in High-Energy Physics
• When Models Know More Than They Can Explain: Quantifying Knowledge Transfer in Human-AI Collaboration
• Kernel k-Medoids as General Vector Quantization
• Nearly Optimal Dynamic k-Means Clustering for High-Dimensional Data
• Joint Detection of Fraud and Concept Drift inOnline Conversations with LLM-Assisted Judgment
• WIR3D: Visually-Informed and Geometry-Aware 3D Shape Abstraction
• Learning Mixtures of Gaussians using the k-means Algorithm
• Human-like Clustering with Deep Convolutional Neural Networks
• The Importance of Good Starting Solutions in the Minimum Sum of Squares Clustering Problem
• A Tutorial on Discriminative Clustering and Mutual Information
• Data-Driven Clustering via Parameterized Lloyd's Families
• ε-Coresets for Clustering (with Outliers) in Doubling Metrics
• Stochastic Wasserstein Barycenters
• GPU Methodologies for Numerical Partial Differential Equations
• SELECT: A Submodular Approach for Active LiDAR Semantic Segmentation
• RAPIDNN: In-Memory Deep Neural Network Acceleration Framework
• Point-Set Anchors for Object Detection, Instance Segmentation and Pose Estimation
• A Generic Distributed Clustering Framework for Massive Data
• Deep TEN: Texture Encoding Network
• Data Pruning by Information Maximization
• Your Interface, Your Control: Adapting Takeover Requests for Seamless Handover in Semi-Autonomous Vehicles
• WishGI: Lightweight Static Global Illumination Baking via Spherical Harmonics Fitting
• Unconditional CNN denoisers contain sparse semantic representation of images
• Variational Bayesian Quantization
• Interpolative Separable Density Fitting through Centroidal Voronoi Tessellation With Applications to Hybrid Functional Electronic Structure Calculations
• Creativity: Generating Diverse Questions using Variational Autoencoders
• Fusion of an Ensemble of Augmented Image Detectors for Robust Object Detection
• ARIA: Training Language Agents with Intention-Driven Reward Aggregation
• Mobile App Tasks with Iterative Feedback (MoTIF): Addressing Task Feasibility in Interactive Visual Environments
• Segment-Based Credit Scoring Using Latent Clusters in the Variational Autoencoder
• Semismooth Newton Augmented Lagrangian Algorithm for Adaptive Lasso Penalized Least Squares in Semiparametric Regression
• A novel sensitivity analysis method for agent-based models stratifies in-silico tumor spheroid simulations
• Zoom: SSD-based Vector Search for Optimizing Accuracy, Latency and Memory
• Medoids in almost linear time via multi-armed bandits
• LKD-KGC: Domain-Specific KG Construction via LLM-driven Knowledge Dependency Parsing
• A Channelized Binning Method for Extraction of Dominant Color Pixel Value
• GARLIC: GAussian Representation LearnIng for spaCe partitioning
• Representational Difference Explanations
• Number of Clusters in a Dataset: A Regularized K-means Approach
• A Computational Approach to Improving Fairness in K-means Clustering
• A Short Note on Analyzing Sequence Complexity in Trajectory Prediction Benchmarks
• Team Formation for Scheduling Educational Material in Massive Online Classes
• Deep Embedded K-Means Clustering
• Online Clustering by Penalized Weighted GMM
• End-to-End Learned Image Compression with Quantized Weights and Activations
• Commuting with Autonomous Vehicles: A Branch and Cut Algorithm with Redundant Modeling
• Efficient feature matching for UAV images based on compact GPU data scheduling
• Deep Learning with Low Precision by Half-wave Gaussian Quantization
• Multi-Target Domain Adaptation via Unsupervised Domain Classification for Weather Invariant Object Detection
• Multi-Agent Control Using Coverage Over Time-Varying Domains
• PhD Dissertation: Generalized Independent Components Analysis Over Finite Alphabets
• LASER: Stratified Selective Sampling for Instruction Tuning with Dedicated Scoring Strategy
• AspeRa: Aspect-based Rating Prediction Model
• Identifying and Exploiting Structures for Reliable Deep Learning
• Convergent Functions, Divergent Forms
• Simple yet Effective Graph Distillation via Clustering
• Radio: Rate-Distortion Optimization for Large Language Model Compression
• Linear Time Clustering for High Dimensional Mixtures of Gaussian Clouds
• Neural networks behave as hash encoders: An empirical study
• The Avengers: A Simple Recipe for Uniting Smaller Language Models to Challenge Proprietary Giants
• Machine learning-driven prediction of catamaran resistance via a GA-optimised ANN surrogate model for hydrodynamic flow regime delineation
• Too Much Information Kills Information: A Clustering Perspective
• Lightweight Embeddings with Graph Rewiring for Collaborative Filtering
• A Comparison of Clustering and Missing Data Methods for Health Sciences
• Submodular Hamming Metrics
• Regularized Non-negative Spectral Embedding for Clustering
• A Hybrid Algorithm Based Robust Big Data Clustering for Solving Unhealthy Initialization, Dynamic Centroid Selection and Empty clustering Problems with Analysis
• C3R: Channel Conditioned Cell Representations for unified evaluation in microscopy imaging
• Intelligent User Clustering and Robust Beamforming Design for UAV-NOMA Downlink
• Using Centroidal Voronoi Tessellations to Scale Up the Multi-dimensional Archive of Phenotypic Elites Algorithm
• Automated detection and classification of cryptographic algorithms in binary programs through machine learning
• Scalable Continual Top-k Keyword Search in Relational Databases
• Experiments on Open-Set Speaker Identification with Discriminatively Trained Neural Networks
• On the Uniqueness of Binary Quantizers for Maximizing Mutual Information
• Learning over inherently distributed data
• Unsupervised Clustering for Fault Analysis in High-Voltage Power Systems Using Voltage and Current Signals
• Non-asymptotic convergence bounds for Wasserstein approximation using point clouds
• Iterative Source-Channel Coding Approach to Witsenhausen's Counterexample
• Routing with Self-Attention for Multimodal Capsule Networks
• Temporal Hierarchical Clustering
• LocalKMeans: Convergence of Lloyd's Algorithm with Distributed Local Iterations
• Causal Links Between US Economic Sectors
• BP-Seg: A graphical model approach to unsupervised and non-contiguous text segmentation using belief propagation
• A bi-criteria approximation algorithm for k Means
• Ranking labs-of-origin for genetically engineered DNA using Metric Learning
• Jet Substructure Probe on Scalar Leptoquark Models via Top Polarization
• Quantization
• Native Segmentation Vision Transformers
• Principal Patterns on Graphs: Discovering Coherent Structures in Datasets
• AccD: A Compiler-based Framework for Accelerating Distance-related Algorithms on CPU-FPGA Platforms
• Refining Neural Activation Patterns for Layer-Level Concept Discovery in Neural Network-Based Receivers
• Bayesian Optimization with Approximate Set Kernels
• Unsupervised deep learning for grading of age-related macular degeneration using retinal fundus images
• Relationship Analysis of Image-Text Pair in SNS Posts
• EmoGist: Efficient In-Context Learning for Visual Emotion Understanding
• Mitigating Subgroup Disparities in Multi-Label Speech Emotion Recognition: A Pseudo-Labeling and Unsupervised Learning Approach
• D4+: Emergent Adversarial Driving Maneuvers with Approximate Functional Optimization
• Learning a Single Tucker Decomposition Network for Lossy Image Compression with Multiple Bits-Per-Pixel Rates
• High-dimensional clustering via Random Projections
• Adversarially Robust Low Dimensional Representations
• A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data
• Attention-based clustering
• Relax, no need to round: integrality of clustering formulations
• Optimal Formats for Weight Quantisation
• CATS: Clustering-Aggregated and Time Series for Business Customer Purchase Intention Prediction
• A numerical algorithm for L₂ semi-discrete optimal transport in 3D
• A Novel and Efficient Vector Quantization Based CPRI Compression Algorithm
• Nonuniform Quantized Decoder for Polar Codes with Minimum Distortion Quantizer
• ProMi: An Efficient Prototype-Mixture Baseline for Few-Shot Segmentation with Bounding-Box Annotations
• Towards Clustering-friendly Representations: Subspace Clustering via Graph Filtering
• An Information-Theoretic Framework for Receiver Quantization in Communication
• A Unified Benchmark for Privacy-preserving Vector Search
• A Case for Library-Level k-Means Binning in Histogram Gradient-Boosted Trees
• K*-Means: A Parameter-free Clustering Algorithm
• Responsible AI: Gender bias assessment in emotion recognition
• Purchase intention and actual purchase of cargo cycles: Influencing factors and policy insights
• Theoretical Analysis of the k-Means Algorithm - A Survey
• Higher-dimensional power diagrams for semi-discrete optimal transport
• Restricted Boltzmann Machines with Gaussian Visible Units Guided by Pairwise Constraints
• Blind Source Separation Can Distort Behavior and Connectivity Analyses of Calcium Transients
• Algorithmic Probability-guided Supervised Machine Learning on Non-differentiable Spaces
• Is Supervised Learning Really That Different from Unsupervised?
• Distributed Navigation of Multi-Robot Systems For Sensing Coverage
• A provable SVD-based algorithm for learning topics in dominant admixture corpus
• An Algorithm for Online K-Means Clustering
• Absorption function loss due to the history of previous ankle sprain explored by unsupervised machine learning
• Task Guided Compositional Representation Learning for ZDA
• Signaling Games for Log-Concave Distributions: Number of Bins and\n Properties of Equilibria
• Robust Federated Learning with Confidence-Weighted Filtering and GAN-Based Completion under Noisy and Incomplete Data
• Fair Clustering via Alignment
• Visualization tools for parameter selection in cluster analysis
• MC-Swarm: Minimal-Communication Multi-Agent Trajectory Planning and Deadlock Resolution for Quadrotor Swarm
• Isolation Forest in Novelty Detection Scenario
• Community detection in graphs
• Solving k-means on High-dimensional Big Data
• 4TaStiC: Time and trend traveling time series clustering for classifying long-term type 2 diabetes patients
• No Query, No Access
• Learning Hierarchical Graph Neural Networks for Image Clustering
• Coresets for Clustering in Euclidean Spaces: Importance Sampling is Nearly Optimal
• GuidedQuant: Large Language Model Quantization via Exploiting End Loss Guidance
• GPrune-LLM: Generalization-Aware Structured Pruning for Large Language Models
• Improving Block-Wise LLM Quantization by 4-bit Block-Wise Optimal Float (BOF4): Analysis and Variations
• Towards time series aggregation with exact error quantification for optimization of energy systems
• Robust Unsupervised Learning of Temporal Dynamic Interactions
• An efficient K -means clustering algorithm for massive data
• Online Decomposition of Compressive Streaming Data Using n-ℓ₁ Cluster-Weighted Minimization
• Temporal Phase Shifts in SCADA Networks
• GB-CosFace: Rethinking Softmax-based Face Recognition from the Perspective of Open Set Classification
• GraphComp: Extreme Error-bounded Compression of Scientific Data via Temporal Graph Autoencoders
• Hierarchically Clustered Representation Learning
• Linear time DBSCAN for sorted 1D data and laser range scan segmentation
• (Machine) learning to do more with less
• Context-Aware Online Conformal Anomaly Detection with Prediction-Powered Data Acquisition
• Act Natural! Extending Naturalistic Projection to Multimodal Behavior Scenarios
• Fair Clustering with Clusterlets
• A simple D²-sampling based PTAS for k-means and other Clustering Problems
• RWKVQuant: Quantizing the RWKV Family with Proxy Guided Hybrid of Scalar and Vector Quantization
• Hanson-Wright inequality in Hilbert spaces with application to K-means clustering for non-Euclidean data
• K-Means Kernel Classifier
• Quantized Compressive Sensing
• TurboESM: Ultra-Efficient 3-Bit KV Cache Quantization for Protein Language Models with Orthogonal Rotation and QJL Correction
• Comparing Clusterings by the Variation of Information
• Distance Metric Learning through Minimization of the Free Energy
• Learning to Cluster Faces via Confidence and Connectivity Estimation
• Free Energy Node Embedding via Generalized Skip-gram with Negative Sampling
• Fuzzy Clustering with Similarity Queries
• Shape Representation using Gaussian Process mixture models
• K-sets+: a Linear-time Clustering Algorithm for Data Points with a Sparse Similarity Measure
• RolX
• Social Network Analysis and Mining for Business Applications
• Sketching and Clustering Metric Measure Spaces
• How Sample Completeness Affects Gamma‐Ray Burst Classification
• Adaptive spatial binning of integral-field spectroscopic data using Voronoi tessellations
• Top 10 algorithms in data mining
• A PTAS for k-means clustering based on weak coresets
• From Persistent Homology to Reinforcement Learning with Applications for Retail Banking
• A Stochastic Alternating Balance k-Means Algorithm for Fair Clustering
• The (black) art of runtime evaluation: Are we comparing algorithms or implementations?
• Optimal estimation of Gaussian mixtures via denoised method of moments
• Determining the three-dimensional atomic structure of a metallic glass
• Cutoff for exact recovery of Gaussian mixture models
• ParamMem: Augmenting Language Agents with Parametric Reflective Memory
• Entropy Density and Mismatch in High-Rate Scalar Quantization with Renyi\n Entropy Constraint
• Improving the performance of k-means for color quantization
• Protecting the Undeleted in Machine Unlearning
• d-HNSW: A High-performance Vector Search Engine on Disaggregated Memory
• ActQuant: Sub-4-bit Action-Guided Quantization for Vision-Language-Action Models
• Stable Trajectory Clustering: An Efficient Split and Merge Algorithm
• Towards the Automatic Classification of Avian Flight Calls for Bioacoustic Monitoring
• Provably faster randomized and quantum algorithms for k-means clustering via uniform sampling
• Sequential Bayesian Experimental Design for Prediction in Physical Experiments Informed by Computer Models
• Communication-Avoiding Linear Algebraic Kernel K-Means on GPUs
• MINT: Multi-Vector Search Index Tuning
• VCM: Vision Concept Modeling Based on Implicit Contrastive Learning with Vision-Language Instruction Fine-Tuning
• Formal Verification of TurboQuant: Machine-Checked Proofs and Gap Closures
• Polarization and Integration in Global AI Research
• What is Machine Learning? A Primer for the Epidemiologist
• Distributed Lloyd-Based algorithm for uncertainty-aware multi-robot under-canopy flocking
• Leveraging Subjective Human Annotation for Clustering Historic Newspaper\n Articles
• Mosaic: Cross-Modal Clustering for Efficient Video Understanding
• Fundamental physical cellular constraints drive self‐organization of tissues
• Solar Wind Classifications at Mars using Machine Learning Techniques
• Graph Kernels: State-of-the-Art and Future Challenges
• Compact Lattice-Coded (Multi-Recipient) Kyber without CLT Independence Assumption
• DigitCode: Symbolic Tokenization of Hand Motion by Anatomical Units
• One Knob to Rule Them All: A Unified Optimal Transport View of Cold-Start Active Learning
• Shock finding on a moving mesh – I. Shock statistics in non-radiative cosmological simulations
• K-MLE: A fast algorithm for learning statistical mixture models
• Data clustering: 50 years beyond K-means
• Granular Computing Techniques for Bioinformatics Pattern Recognition Problems in Non-metric Spaces
• AnchorKV: Anchor-Residual KV Cache Compression
• Planar Voronoi Diagrams for Sums of Convex Functions, Smoothed Distance and Dilation
• Grid generation and optimization based on centroidal Voronoi tessellations
• Convergence of the Lloyd Algorithm for Computing Centroidal Voronoi Tessellations
• Nondegeneracy and Weak Global Convergence of the Lloyd Algorithm in ℝ^d
• Simulating decorative mosaics
• Automatic analysis of artistic paintings using information-based measures
• Breath to Pair (B2P): Respiration-Based Pairing Protocol for Wearable Devices
• Occam’s Razor for Big Data? On Detecting Quality in Large Unstructured Datasets
• Dimensionality Reduction for k-means Clustering
• Fuzzy Clustering Data Given on the Ordinal Scale Based on Membership and Likelihood Functions Sharing
• Data-driven approach for synchrotron X-ray Laue microdiffraction scan analysis
• Spend Bits Where Queries Look: KV Cache Vector Quantization with Attention-Preserving Transforms
• Capturing 3D atomic defects and phonon localization at the 2D heterostructure interface
• How Effective Are NPM Malicious Package Detectors? A Large-Scale Empirical Study
• Hierarchical Maximum-Margin Clustering
• An overview of cluster-based image search result organization: background, techniques, and ongoing challenges
• ZeroED: Hybrid Zero-shot Error Detection through Large Language Model Reasoning
• A Density-Driven Method for the Placement of Biological Cells Over Two-Dimensional Manifolds
• Optimal Clustering in Anisotropic Gaussian Mixture Models
• Load estimation in unsteady flows from sparse pressure measurements: Application of transition networks to experimental data
• Simple and Scalable Sparse k-means Clustering via Feature Ranking
• Generalized mean shift with triangular kernel profile
• The Effect of Hydration and Dynamics on the Mass Density of Single Proteins
• Defining and finding lifelike entities with a lazy filter
• Sketch and shift: a robust decoder for compressive clustering
• Evaluating BERTopic on Open-Ended Data: A Case Study with Belgian Dutch Daily Narratives
• Deep Learning for Inferring the Surface Solar Irradiance from Sky Imagery
• Convergence of distributed asynchronous learning vector quantization algorithms
• Community detection in sparse time-evolving graphs with a dynamical Bethe-Hessian
• Workspace Partitioning and Topology Discovery Algorithms for Heterogeneous Multiagent Networks
• k-means as a variational EM approximation of Gaussian mixture models
• Deriving a representative vector for ontology classes with instance word vector embeddings
• Slice and Dice: A Physicalization Workflow for Anatomical Edutainment
• Deep Learning Meets Projective Clustering
• Convolutional Neural Networks with Transformed Input based on Robust Tensor Network Decomposition
• Streaming k-Means Clustering with Fast Queries
• An Approximate Message Passing Framework for Side Information
• Cooperative Multi-Agent Reinforcement Learning for Low-Level Wireless Communication
• Semi-Supervised and Active Few-Shot Learning with Prototypical Networks
• Inversion of the radiative transfer equation for polarized light
• Tree-Structured Random Vector Quantization for Limited-Feedback Wireless Channels
• Cluster-based control of nonlinear dynamics
• Development of Machine Learning in Organic Photovoltaic Cells †
• Simulating TeV gamma-ray morphologies of shell-type supernova remnants
• Supervised Metric Learning with Generalization Guarantees
• Open-Ended Learning Leads to Generally Capable Agents
• On the Benefits of Partial Channel State Information for Repetition Protocols in Block Fading Channels
• Linear stability analysis of morphodynamics during tissue regeneration in plants
• A critical comparison of Lagrangian methods for coherent structure detection
• Hierarchical Means Clustering
• Throughput Analysis of Massive MIMO Uplink With Low-Resolution ADCs
• Local Aggregation for Unsupervised Learning of Visual Embeddings
• Bregman Voronoi Diagrams
• Regularized K-means through hard-thresholding
• Object-aware guidance for autonomous scene reconstruction
• Dynamic time series clustering via volatility change-points
• Binary Companions of Evolved Stars in APOGEE DR14: Search Method and Catalog of ∼5000 Companions
• Variational Bayes Inference in Digital Receivers
• Efficient sparse spherical k-means for document clustering
• A new diffusion-based multilevel algorithm for computing graph partitions
• A Survey on Archetypal Analysis
• Why the Third Axis Is Freedom
• Crystal nucleation and growth in high-entropy alloys revealed by atomic electron tomography
• Extrapolation method to optimize linear-ramp QAOA parameters: Evaluation of QAOA runtime scaling
• Exploring hyperspectral imaging data sets with topological data analysis
• Deep Learning Meets Teleconnections: Improving S2S Predictions for European Winter Weather
• Privacy-Preserving Vertical K-Means Clustering
• Semantically Encoding Activity Labels for Context-Aware Human Activity Recognition
• Low-temperature statistical mechanics of the Quantizer problem: Fast quenching and equilibrium cooling of the three-dimensional Voronoi liquid
• Pseudometrically constrained centroidal voronoi tessellations: Generating uniform antipodally symmetric points on the unit sphere with a novel acceleration strategy and its applications to diffusion and three‐dimensional radial MRI
• Multi-Sense Embeddings for Language Models and Knowledge Distillation
• Lloyd's algorithm [wikipedia]
• Mayday--integrative analytics for expression data. [europepmc]
• Automatic generation of absolute myocardial blood flow images using [15O]H2O and a clinical PET/CT scanner. [europepmc]
• Variational cross-validation of slow dynamical modes in molecular kinetics. [europepmc]
• Kernel regression based segmentation of optical coherence tomography images with diabetic macular edema. [europepmc]
• Conservation of immune gene signatures in solid tumors and prognostic implications. [europepmc]
• Machine learning and systems genomics approaches for multi-omics data. [europepmc]
• Effects of Aging on Cortical Neural Dynamics and Local Sleep Homeostasis in Mice. [europepmc]
• Atomic resolution mechanism of ligand binding to a solvent inaccessible cavity in T4 lysozyme. [europepmc]
• Scutoids are a geometrical solution to three-dimensional packing of epithelia. [europepmc]
• Machine Learning in Agriculture: A Review. [europepmc]
• Correspondence between cerebral glucose metabolism and BOLD reveals relative power and cost in human brain. [europepmc]
• Long non-coding RNAs discriminate the stages and gene regulatory states of human humoral immune response. [europepmc]
• Meta-Analytic Methodology for Basic Research: A Practical Guide. [europepmc]
• The Application of Deep Learning in Cancer Prognosis Prediction. [europepmc]
• DNA Methylation Profiling of Human Hepatocarcinogenesis. [europepmc]
• Unsupervised Learning Methods for Molecular Simulation Data. [europepmc]
• miQC: An adaptive probabilistic framework for quality control of single-cell RNA-sequencing data. [europepmc]
• Cardiac radiotherapy induces electrical conduction reprogramming in the absence of transmural fibrosis. [europepmc]
• Markov State Models to Study the Functional Dynamics of Proteins in the Wake of Machine Learning. [europepmc]
• Statistical power for cluster analysis. [europepmc]
• QMugs, quantum mechanical properties of drug-like molecules. [europepmc]
• Linker-Dependent Folding Rationalizes PROTAC Cell Permeability. [europepmc]
• Interpretable deep learning translation of GWAS and multi-omics findings to identify pathobiology and drug repurposing in Alzheimer's disease. [europepmc]
• Review of single-cell RNA-seq data clustering for cell-type identification and characterization. [europepmc]
• Toward universal cell embeddings: integrating single-cell RNA-seq datasets across species with SATURN. [europepmc]

Related

• Low-Resolution Quantization in Phase Modulated Systems: Optimum Detectors and Error Rate Analysis
• The lower bound of the PCM quantization error in high dimension
• The Performance of PCM Quantization Under Tight Frame Representations
• Performance of quantum data transmission systems in the presence of thermal noise
• Optimal Quantization of Signals for System Identification