Christine D. Piatko

An efficient k-means clustering algorithm: analysis and implementation

In k-means clustering, we are given a set of n data points in d-dimensional space R/sup d/ and an integer k and the problem is to determine a set of k points in Rd, called centers, so as to minimize the mean squared distance from each data point to its nearest center. A popular heuristic for k-means clustering is Lloyds (1982) algorithm. We present a simple and efficient implementation of Lloyds k-means clustering algorithm, which we call the filtering algorithm. This algorithm is easy to implement, requiring a kd-tree as the only major data structure. We establish the practical efficiency of the filtering algorithm in two ways. First, we present a data-sensitive analysis of the algorithms running time, which shows that the algorithm runs faster as the separation between clusters increases. Second, we present a number of empirical studies both on synthetically generated data and on real data sets from applications in color quantization, data compression, and image segmentation.

A local search approximation algorithm for k-means clustering

In k-means clustering we are given a set of n data points in d-dimensional space Rd and an integer k, and the problem is to determine a set of k points in ÓC;d, called centers, to minimize the mean squared distance from each data point to its nearest center. No exact polynomial-time algorithms are known for this problem. Although asymptotically efficient approximation algorithms exist, these algorithms are not practical due to the extremely high constant factors involved. There are many heuristics that are used in practice, but we know of no bounds on their performance.We consider the question of whether there exists a simple and practical approximation algorithm for k-means clustering. We present a local improvement heuristic based on swapping centers in and out. We prove that this yields a (9+ε)-approximation algorithm. We show that the approximation factor is almost tight, by giving an example for which the algorithm achieves an approximation factor of (9-ε). To establish the practical value of the heuristic, we present an empirical study that shows that, when combined with Lloyds algorithm, this heuristic performs quite well in practice.

The analysis of a simple k -means clustering algorithm

Abstract : K-means clustering is a very popular clustering technique which is used in numerous applications. Given a set of n data points in R(exp d) and an integer k, the problem is to determine a set of k points R(exp d), called centers, so as to minimize the mean squared distance from each data point to its nearest center. A popular heuristic for k-means clustering is Lloyds algorithm. In this paper, we present a simple and efficient implementation of Lloyds k-means clustering algorithm, which we call the filtering algorithm. This algorithm is very easy to implement. It differs from most other approaches in that it precomputes a kd-tree data structure for the data points rather than the center points. We establish the practical efficiency of the filtering algorithm in two ways. First, we present a data-sensitive analysis of the algorithms running time. Second, we have implemented the algorithm and performed a number of empirical studies, both on synthetically generated data and on real data from applications in color quantization, compression, and segmentation.

Comparing Real and Synthetic Images: Some Ideas About Metrics

This paper explores numerical techniques for comparing real and synthetic luminance images. We introduce components of a perceptually based metric using ideas from the image compression literature. We apply a series of metrics to a set of real and synthetic images, and discuss their performance. Finally, we conclude with suggestions for future work in formulating image metrics and incorporating them into new image synthesis methods.

Named entity recognition using hundreds of thousands of features

We present an approach to named entity recognition that uses support vector machines to capture transition probabilities in a lattice. The support vector machines are trained with hundreds of thousands of features drawn from the CoNLL-2003 Shared Task training data. Margin outputs are converted to estimated probabilities using a simple static function. Performance is evaluated using the CoNLL-2003 Shared Task test set; Test B results were Fβ=1 = 84.67 for English, and Fβ=1 = 69.96 for German.

A visibility matching tone reproduction operator for high dynamic range scenes

The authors present a tone reproduction operator that preserves visibility in high dynamic range scenes. The method introduces a new histogram adjustment technique, based on the population of local adaptation luminances in a scene. To match subjective viewing experience, the method incorporates models for human contrast sensitivity, glare, spatial acuity and color sensitivity. They compare the results to previous work and present examples the techniques applied to lighting simulation and electronic photography.

Minimum-link watchman tours

We consider the problem of computing a watchman route in a polygon with holes. We show that the problem of finding a minimum-link watchman route is NP-complete, even if the holes are all convex. The proof is based on showing that the related problem of finding a minimum-link tour on a set of points in the plane is NP-complete. We provide a provably good approximation algorithm that achieves an approximation factor of O(log n ).

Perceptual Issues in Substituting Texture for Geometry

An important goal in interactive computer graphics is to allow the user to interact dynamically with three-dimensional objects. The computing resources required to represent, transmit and display a three dimensional object depends on the number of polygons used to represent it. Many geometric simplification algorithms have been developed to represent the geometry with as few polygons as possible, without substantially changing the appearance of the rendered object. A popular method for achieving geometric simplification is to replace fine scale geometric detail with texture images mapped onto the simplified geometry. However the effectiveness of replacing geometry with texture has not been explored experimentally. In this paper we describe a visual experiment in which we examine the perceived quality of various representations of textured, geometric objects, viewed under direct and oblique illumination. We used a pair of simple large scale objects with different fine-scale geometric detail. For each object we generated many representations, varying the resources allocated to geometry and texture. The experimental results show that while replacing geometry with texture can be very effective, in some cases the addition of texture does not improve perceived quality, and can sometimes reduce the perceived quality.

Supporting insight-based information exploration in intelligence analysis

Capturing the exploratory search process can help represent analytical insight.

A Language-Independent Approach to European Text Retrieval

We present an approach to multilingual information retrieval that does not depend on the existence of specific linguistic resources such as stemmers or thesauri. Using the HAIRCUT system we participated in the monolingual, bilingual, and multilingual tasks of the CLEF-2000 evaluation. Our approach, based on combining the benefits of words and character n-grams, was effective for both language-independent monolingual retrieval as well as for cross-language retrieval using translated queries. After describing our monolingual retrieval approach we compare a translation method using aligned parallel corpora to commercial machine translation software.