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Conference on Image Processing - algorithms and Systems X and Parallel Processing for Imaging Applications II

作者： Vicory, Jared Celebi, M. Emre Louisiana State Univ Dept Comp Sci Shreveport LA 71105 USA

ISBN: (纸本)9780819489425

Gray-level quantization (reduction) is an important operation in image processing and analysis. The lloyd-max algorithm (LMA) is a classic scalar quantization algorithm that can be used for gray-level reduction with minimal mean squared distortion. However, the algorithm is known to be very sensitive to the choice of initial centers. In this paper, we introduce an adaptive and deterministic algorithm to initialize the LMA for gray-level quantization. Experiments on a diverse set of publicly available test images demonstrate that the presented method outperforms the commonly used uniform initialization method.

关键词： Gray-level reduction scalar quantization lloyd-max algorithm center initialization

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Rate-Constrained Quantization for Communication-Efficient Federated Learning

Rate-Constrained Quantization for Communication-Efficient Fe...

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2025 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2025

作者： Hamidi, Shayan Mohajer Bereyhi, Ali ECE Department University of Waterloo Canada ECE Department University of Toronto Canada

ISBN: (纸本)9798350368741

Quantization is a common approach to mitigate the communication cost of federated learning (FL). In practice, the quantized local parameters are further encoded via an entropy coding technique, such as Huffman coding, for efficient data compression. In this case, the exact communication overhead is determined by the bit rate of the encoded gradients. Recognizing this fact, this work deviates from the existing approaches in the literature and develops a novel quantized FL framework, called rate-constrained federated learning (RC-FED), in which we deploy the conventional entropy-constrained scalar quantization technique to quantize the gradients subject to both fidelity and data rate constraints. Particularly, we formulate this scheme, as a joint optimization in which the quantization distortion is minimized while the rate of encoded gradients is kept below a target threshold. This enables for a tunable trade-off between quantization distortion and communication cost. We analyze the convergence behavior of RC-FED, and show its superior performance against baseline quantized FL schemes on several datasets. © 2025 IEEE.

关键词： Federated learning lloyd-max algorithm scalar quantization source coding

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Control Over Gaussian Channels With and Without Source-Channel Separation

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2019年第9期64卷 3690-3705页

作者： Khina, Anatoly Garding, Elias Riedel Pettersson, Gustav M. Kostina, Victoria Hassibi, Babak CALTECH Dept Elect Engn Pasadena CA 91125 USA Tel Aviv Univ Dept Elect Engn Syst IL-6997801 Tel Aviv Israel Univ Cambridge Dept Appl Math & Theoret Phys Ctr Math Sci Cambridge CB3 0WA England KTH Royal Inst Technol Sch Engn Sci SE-10044 Stockholm Sweden

We consider the problem of controlling an unstable linear plant with Gaussian disturbances over an additive white Gaussian noise channel with an average transmit power constraint, where the signaling rate of communication may be different from the sampling rate of the underlying plant. Such a situation is quite common since sampling is done at a rate that captures the dynamics of the plant and that is often lower than the signaling rate of the communication channel. This rate mismatch offers the opportunity of improving the system performance by using coding over multiple channel uses to convey a single control action. In a traditional, separation-based approach to source and channel coding, the analog message is first quantized down to a few bits and then mapped to a channel codeword whose length is commensurate with the number of channel uses per sampled message. Applying the separation-based approach to control meets its challenges: first, the quantizer needs to be capable of zooming in and out to be able to track unbounded system disturbances, and second, the channel code must be capable of improving its estimates of the past transmissions exponentially with time, a characteristic known as anytime reliability. We implement a separated scheme by leveraging recently developed techniques for control over quantized-feedback channels and for efficient decoding of anytime-reliable codes. We further propose an alternative, namely, to perform analog joint source-channel coding, by this avoiding the digital domain altogether. For the case where the communication signaling rate is twice the sampling rate, we employ analog linear repetition as well as Shannon-Kotel'nikov maps to show a significant improvement in stability margins and linear-quadratic costs over separation-based schemes. We conclude that such analog coding performs better than separation, and can stabilize all moments as well as guarantee almost-sure stability.

关键词： Channel coding combined source-channel coding Gaussian channel lloyd-max algorithm networked control systems quantization tree codes

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ON THE DESIGN OF AN OPTIMAL QUANTIZER

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IEEE TRANSACTIONS ON INFORMATION THEORY 1993年第4期39卷 1180-1194页

作者： TRUSHKIN, AV Institute for Problems of Information Transmission Russian Academy of Science Moscow Russia

The problem of designing an optimal quantizer with a fixed number of levels for a wide class of error weighting functions and an arbitrary distribution function is discussed. The existence of an optimal quantizer is proved and a two-stage algorithm for its design is suggested. In this algorithm, at the first stage, lloyd's iterative Method I is applied for reducing the region where, at the second stage, the search for an optimal quantizer is performed, using a hybrid of the dynamic programming algorithm and the lloyd-max algorithm, which achieves the absolute optimality of dynamic programming with much less computational effort. And for a continuous distribution with log-concave density and an increasing convex weighting function of the absolute quantization error, a reliable method is presented for computing the parameters of the optimal quantizer with a known precision, using a generalization either of lloyd's Method I or of the lloyd-max algorithm.

关键词： OPTIMAL QUANTIZER DYNAMIC PROGRAMMING lloyd METHOD-I lloyd-max algorithm

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k-Vectors: An Alternating Minimization algorithm for Learning Regression Functions

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IEEE TRANSACTIONS ON INFORMATION THEORY 2020年第11期66卷 7196-7221页

作者： Weinberger, Nir Feder, Meir MIT IDSS 77 Massachusetts Ave Cambridge MA 02139 USA MIT LIDS 77 Massachusetts Ave Cambridge MA 02139 USA Tel Aviv Univ Sch Elect Engn IL-69978 Tel Aviv Israel

The k-vectors algorithm for learning regression functions proposed here is akin to the well-known k-means algorithm. Both algorithms partition the feature space, but unlike the k-means algorithm, the k-vectors algorithm aims to reconstruct the response rather than the feature. The partitioning rule of the algorithm is based on maximizing the correlation (inner product) of the feature vector with a set of k vectors, and generates polyhedral cells, similar to the ones generated by the nearest-neighbor rule of the k-means algorithm. Similarly to k-means, the learning algorithm alternates between two types of steps. In the first type of steps, k labels are determined via a centroid-type rule (in the response space), which uses a surrogate hinge-type loss function to the mean squared error loss function. In the second type of steps, the k vectors which determine the partition are updated according to a multiclass classification rule, in the spirit of support vector machines. It is proved that both steps of the algorithm only require solving convex optimization problems, and that the algorithm is empirically consistent - as the length of the training sequence increases to infinity, fixedpoints of the empirical version of the algorithm tend to fixed points of the population version of the algorithm. Learnability of the predictor class posit by the algorithm is also established.

关键词： Alternating minimization clustering convergence rates global convergence k-means lloyd-max algorithm nonparametric regression partitioning estimates quantization supervised learning support vector machines

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DISTRIBUTED ESTIMATION AND QUANTIZATION

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IEEE TRANSACTIONS ON INFORMATION THEORY 1993年第4期39卷 1456-1459页

作者： GUBNER, JA Department of Electrical and Computer Engineering University of Wisconsin Madison Madison WI USA

An algorithm is developed for the design of a nonlinear, n-sensor, distributed estimation system subject to communication and computation constraints. The algorithm uses only bivariate probability distributions and yields locally optimal estimators that satisfy the required system constraints. It is shown that the algorithm is a generalization of the classical lloyd-max results.

关键词： NONLINEAR ESTIMATION DISTRIBUTED ESTIMATION SENSOR FUSION lloyd-max algorithm

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NQFL: Nonuniform Quantization for Communication Efficient Federated Learning

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IEEE COMMUNICATIONS LETTERS 2024年第2期28卷 332-336页

作者： Chen, Guojun Xie, Kaixuan Tu, Yuheng Song, Tiecheng Xu, Yinfei Hu, Jing Xin, Lun Southeast Univ Sch Informat Sci & Engn Nanjing 210096 Peoples R China Natl Mobile Commun Res Lab Nanjing 210096 Peoples R China China Mobile Res Inst Beijing 100053 Peoples R China

Federated learning (FL), as a potential machine learning framework for privacy preservation, has gained significant attention. However, the considerable communication overhead associated with FL remains a prominent challenge. To mitigate this issue, a nonuniform quantization scheme based on lloyd-max algorithm is introduced in this letter. By employing this approach, less communication resources are consumed to achieve the same performance. Through performance analysis and numerical simulations, we verify the convergence and effectiveness of the proposed algorithm. It demonstrates the potential of our approach in reducing communication overhead while maintaining reliable performance in FL systems.

关键词： Servers Quantization (signal) Computational modeling Data models Standards Costs Iterative methods Federated learning communication efficiency nonuniform quantizer lloyd-max algorithm

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Signaling Games for Log-Concave Distributions: Number of Bins and Properties of Equilibria

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IEEE TRANSACTIONS ON INFORMATION THEORY 2022年第3期68卷 1731-1757页

作者： Kazikli, Ertan Saritas, Serkan Gezici, Sinan Linder, Tamas Yuksel, Serdar Queens Univ Dept Math & Stat Kingston ON K7L 3N6 Canada Middle East Tech Univ METU Dept Elect & Elect Engn TR-06800 Ankara Turkey Bilkent Univ Dept Elect & Elect Engn TR-06800 Ankara Turkey

We investigate the equilibrium behavior for the decentralized cheap talk problem for real random variables and quadratic cost criteria in which an encoder and a decoder have misaligned objective functions. In prior work, it has been shown that the number of bins in any equilibrium has to be countable, generalizing a classical result due to Crawford and Sobel who considered sources with density supported on [0, 1]. In this paper, we first refine this result in the context of log-concave sources. For sources with two-sided unbounded support, we prove that, for any finite number of bins, there exists a unique equilibrium. In contrast, for sources with semi-unbounded support, there may be a finite upper bound on the number of bins in equilibrium depending on certain conditions stated explicitly. Moreover, we prove that for log-concave sources, the expected costs of the encoder and the decoder in equilibrium decrease as the number of bins increases. Furthermore, for strictly log-concave sources with two-sided unbounded support, we prove convergence to the unique equilibrium under best response dynamics which starts with a given number of bins, making a connection with the classical theory of optimal quantization and convergence results of lloyd's method. In addition, we consider more general sources which satisfy certain assumptions on the tail(s) of the distribution and we show that there exist equilibria with infinitely many bins for sources with two-sided unbounded support. Further explicit characterizations are provided for sources with exponential, Gaussian, and compactly-supported probability distributions.

关键词： Decoding Quantization (signal) Costs Games Upper bound Nash equilibrium Linear programming Cheap talk signaling games Nash equilibrium optimal quantization lloyd-max algorithm payoff dominant equilibria

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VARIANCE-CUT: A FAST COLOR QUANTIZATION METHOD BASED ON HIERARCHICAL CLUSTERING

VARIANCE-CUT: A FAST COLOR QUANTIZATION METHOD BASED ON HIER...

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10th International Conference on Electronics, Computer and Computation (ICECCO)

作者： Celebi, M. Emre Wen, Quan Louisiana State Univ Dept Comp Sci Shreveport LA 71105 USA Univ Elect Sci & Technol China Sch Engn & Comp Sci Chengdu Peoples R China

ISBN: (纸本)9781479933433

Color quantization is an important operation with many applications in graphics and image processing. Clustering algorithms have been extensively applied to this problem. In this paper, we propose a simple yet effective color quantization method based on divisive hierarchical clustering. Our method utilizes the commonly used binary splitting strategy along with several carefully selected heuristics that ensure a good balance between effectiveness and efficiency. We also propose a slightly computationally expensive variant of this method that employs local optimization using the lloyd-max algorithm. Experiments on publicly available test images demonstrate that the proposed method outperforms some of the most popular quantizers in the literature.

关键词： Color quantization divisive hierarchical clustering binary splitting lloyd-max algorithm

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Unsupervised Joint Feature Discretization and Selection

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5th Iberian Conference on Pattern Recognition and Image Analysis (IbPRIA)

作者： Ferreira, Artur Figueiredo, Mario Inst Super Engn Lisboa Lisbon Portugal Inst Super Tecn Lisbon Portugal Inst Telecommun Lisbon Portugal

ISBN: (纸本)9783642212567;9783642212574

In many applications, we deal with high dimensional datasets with different types of data. For instance, in text classification and information retrieval problems, we have large collections of documents. Each text is usually represented by a bag-of-words or similar representation, with a large number of features (terms). Many of these features may be irrelevant (or even detrimental) for the learning tasks. This excessive number of features carries the problem of memory usage in order to represent and deal with these collections, clearly showing the need for adequate techniques for feature representation, reduction, and selection, to both improve the classification accuracy and the memory requirements. In this paper, we propose a combined unsupervised feature discretization and feature selection technique. The experimental results on standard datasets show the efficiency of the proposed techniques as well as improvement over previous similar techniques.

关键词： Feature discretization feature selection feature reduction lloyd-max algorithm sparse data text classification support vector machines naive Bayes

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