This paper describes four recent papers on clustering, each of which approaches the clustering problem from a different perspective and with different goals. It analyzes the strengths and weaknesses of each approach and describes how a user could could decide which algorithm to use for a given clustering application. Finally, it concludes with ideas that could make the selection and use of clustering algorithms for data analysis less difficult.

Abstract — In this paper, we study a clustering technique for the hierarchical traffic grooming approach in WDM mesh networks. The objective is to minimize the cost of electronic ports, as well as the wavelength requirement of the solution. In the hierarchical grooming approach we have presented in previous work, the first phase is to partition a large mesh network into clusters of nodes. The clustering phase is very important for the final grooming result. Various clustering approaches have been considered in literature; however, not all are suitable for traffic grooming application because they do not take grooming goals into account. In this work, we select a suitable existing clustering algorithm, developed for the K-Center problem, and study its performance as a clustering algorithm for hierarchical grooming. We then improve the algorithm, adapting it specifically for the traffic grooming problem. Experimental results show that the improved version generally provides better solutions than the original algorithm, on various traffic patterns, for the general topology grooming problem instances. I.

We propose a method for choosing the number of colors, or true gray levels, in an image. This is motivated by medical and satellite image segmentation, and may also be useful for color and gray scale image quantization, the display and storage of computer-generated holograms, and the use of cooccurrence matrices for assessing texture in images. Our underlying probability model is a hidden Markov random field. Each number of colors considered is viewed as corresponding to a statistical model for the image, and the resulting models are compared via approximate Bayes factors. The Bayes factors are approximated using BIC, where the required maximized likelihood is approximated by the Qian-Titterington pseudo- likelihood. We call the resulting criterion PLIC (Pseudolikelihood Information Criterion). We also discuss a simpler approximation, MMIC (Marginal Mixture Information Criterion), which is based only on the marginal distribution of pixel values. This turns out to be useful for initialization, and also to have moderately good, albeit suboptimal, performance in its own right. We apply PLIC to three examples: a simulated two-band image, a medical segmentation problem, and a satellite image, and in each case it gives good results in practice. Keywords: BIC; Color image quantization; Cooccurrence matrix; Hologram; ICM algorithm; Image segmentation; Markov Random Field; Medical image; Mixture model; Posterior model probability; Pseudolikelihood; Satellite image.

On the WWW, the transmission time for videos and images impacts the performance of a web site. In order to reduce the bandwidth that is used to transmit images over the Internet, most image formats adopt only a limited number of colors used simultaneously to display color images on a video monitor. Hence, generating a good color palette for a color digitized image is an important task for Internet applications. In general, the Linde-Buzo-Gray (LBG) algorithm can be used to cluster a color digitized image in which each pixel is considered as a 3-dimension vector in an RGB color space for generating a color palette. The codebook generated by the LBG algorithm can be considered as the color palette for the color image. In order to obtain a good color palette, the LBG algorithm needs a large amount of computation time. In this paper, we propose a color finite-state LBG (CFSLBG) algorithm that reduces the computation time by exploiting the correlations of palette entries between the current and previous iterations. Instead of searching the whole color palette, the CFSLBG algorithm searches only a small number of colors that are very close to the training vector. Thus, the computation time for color quantization is reduced. The proposed approach generates RGB palettes efficiently with little sacrifice of quantized image quality. This paper describes the implementation of this work and simulation results.

The maximum intercluster distance and the maximum quantization error that are minimized by the MinMax algorithm are shown to be inappropriate error measures for color image quantization. A fast and effective (improves image quality) method for generalizing activity weighting to any histogram-based color quantization algorithm is presented. A new non-hierarchical color quantization technique called weighted MinMax that is a hybrid between the MinMax and Linde-Buzo-Gray (LBG) algorithms is also described. The weighted MinMax algorithm incorporates activity weighting and seeks to minimize WRMSE, whereby obtaining high quality quantized images with significantly less visual distortion than the MinMax algorithm. Key words and phrases: color image quantization, minimizing maximum intercluster distance, nonhierarchical clustering, image compression. 1. INTRODUCTION In color quantization a truecolor image is irreversibly transformed into a color-mapped image consisting of K carefully select...

Abstract — Color quantization is an important operation with many applications in graphics and image processing. Most quantization methods are essentially based on data clustering algorithms one which is the popular k-means algorithm. A common drawback of many conventional clustering algorithms is the generation of empty clusters (dead units). In this paper, we apply Uchiyama and Arbib’s competitive learning algorithm [1] to the problem of color quantization. In contrast to the conventional batch k-means algorithm, this competitive learning algorithm requires no cluster center initialization. In addition, it effectively avoids the dead unit problem by utilizing a simple cluster splitting rule. Experiments on commonly used test images demonstrate that the presented method outperforms various stateof-the-art methods in terms of quantization effectiveness.

Steganography is the art of writing hidden messages in such a way that no one; apart from the sender and intended recipient even understand there is a hidden message. Steganography includes the concealment of information within computer files. One of the most common methods of implementation is Least Significant Bit Insertion, in which the least significant bit of every byte is altered to form the bit-string representing the embedded file. Altering the LSB will only cause minor changes in color. While this technique works well for 24-bit color image files, steganography has not been as successful when using an 8-bit color image file, due to limitations in color variations and the use of a color table. Color table is organized as- the first three bytes correspond to RGB components and the last byte is reserved or unused. The proposed technique is to generate the image from a 24-bit bitmap to an 8-bit bitmap using color quantization resulted in minor variations in the image, which are barely noticeable to the human eye. However, these slight variations aid in hiding the data.

A new class of digital halftoning algorithms is introduced. Anti-correlation digital halftoning (ACDH) combines the idea of a well-known game, Russian roulette, with the statistical approach to bilevel quantization of digital images. A representative ofthe class, serpentine anticorrelation digital halftoning, is described and compared to error di usion, ordered dither, and other important digital halftoning techniques. Serpentine ACDH causes fewer unpleasant correlated artifacts and less contouring than the benchmark algorithms. The quantization noise spectra associated with serpentine ACDH possess bene cial characteristics related to properties of the vision system. The term \violet noise " is proposed to describe quantization noise with stronger bias in favor of high-frequency components than that of blue noise. Novel techniques for color visualization of the noise spectra and the corresponding phase spectra are introduced, and the relative signi cance of the magnitudes and phases of the discrete Fourier transform of the quantization noise is studied. Unlike popular algorithms based on error di usion, serpentine ACDH does not enhance edges. This is good for applications to digital holography and medical imaging. A simple input preprocessing technique allowsonetointroduce edge enhancement if desired, while keeping it more isotropic than that of error di usion. The relation between unwanted transient boundary e ects and edge enhancement accompanying error di usion is examined, and approaches to reduction of boundary e ects are considered. Serpentine ACDH does not cause signi cant boundary e ects. The average intensity representation by di erent algorithms is studied for constant input levels (serpentine ACDH does remarkably well). Prospects for ACDH research are discussed.