A new Mallows distance based metric for comparing clusterings
Despite of the large number of algorithms developed for clustering, the study on comparing clustering results is limited. In this paper, we propose a measure for comparing clustering results to tackle two issues insufficiently addressed or even overlooked by existing methods: (a) taking into account the distance between cluster representatives when assessing the similarity of clustering results; (b) constructing a unified framework for defining a distance based on either hard or soft clustering and ensuring the triangle inequality under the definition. Our measure is derived from a complete and globally optimal matching between clusters in two clustering results. It is shown that the distance is an instance of the Mallows distance---a metric between probability distributions in statistics. As a result, the defined distance inherits desirable properties from the Mallows distance. Experiments show that our clustering distance measure successfully handles cases difficult for other measures.

title: Real-Time Computerized Annotation of Pictures
abstract: Developing effective methods for automated annotation of digital pictures continues to challenge computer scientists. The capability of annotating pictures by computers can lead to breakthroughs in a wide range of applications, including Web image search, online picture-sharing communities, and scientific experiments. In this work, the authors developed new optimization and estimation techniques to address two fundamental problems in machine learning. These new techniques serve as the basis for the automatic linguistic indexing of pictures - real time (ALIPR) system of fully automatic and high-speed annotation for online pictures. In particular, the D2-clustering method, in the same spirit as K-Means for vectors, is developed to group objects represented by bags of weighted vectors. Moreover, a generalized mixture modeling technique (kernel smoothing as a special case) for nonvector data is developed using the novel concept of hypothetical local mapping (HLM). ALIPR has been tested by thousands of pictures from an Internet photo-sharing site, unrelated to the source of those pictures used in the training process. Its performance has also been studied at an online demonstration site, where arbitrary users provide pictures of their choices and indicate the correctness of each annotation word. The experimental results show that a single computer processor can suggest annotation terms in real time and with good accuracy.

title: A source coding approach to classification by vector quantization and the principle of minimum description length
abstract: An algorithm for supervised classification using vector quantization and entropy coding is presented. The classification rule is formed from a set of training data {(X/sub i/, Y/sub i/)}/sub i=1//sup n/, which are independent samples from a joint distribution P/sub XY/. Based on the principle of minimum description length (MDL), a statistical model that approximates the distribution P/sub XY/ ought to enable efficient coding of X and Y. On the other hand, we expect a system that encodes (X, Y) efficiently to provide ample information on the distribution P/sub XY/. This information can then be used to classify X, i.e., to predict the corresponding Y based on X. To encode both X and Y, a two-stage vector quantizer is applied to X and a Huffman code is formed for Y conditioned on each quantized value of X. The optimization of the encoder is equivalent to the design of a vector quantizer with an objective function reflecting the joint penalty of quantization error and misclassification rate. This vector quantizer provides an estimation of the conditional distribution of Y given X, which in turn yields an approximation to the Bayes classification rule. This algorithm, namely discriminant vector quantization (DVQ), is compared with learning vector quantization (LVQ) and CART/sup R/ on a number of data sets. DVQ outperforms the other two on several data sets. The relation between DVQ, density estimation, and regression is also discussed.

title: On Zador's entropy-constrained quantization theorem
abstract: Zador's classic result for the asymptotic high-rate behavior of entropy-constrained vector quantization is recast in a Lagrangian form which better matches the Lloyd algorithm used to optimize such quantizers. A proof that the result holds for a general class of distributions is sketched.

title: Asymptotic Performance of Vector Quantizers with a Perceptual Distortion Measure
abstract: Gersho's (1979) bounds on the asymptotic performance of vector quantizers are valid for vector distortions which are powers of the Euclidean norm. Yamada, Tazaki, and Gray (1980) generalized the results to distortion measures that are increasing functions of the norm of their argument. In both cases, the distortion is uniquely determined by the vector quantization error, i.e., the Euclidean difference between the original vector and the codeword into which it is quantized. We generalize these asymptotic bounds to input-weighted quadratic distortion measures and measures that are approximately output-weighted-quadratic when the distortion is small, a class of distortion measures often claimed to be perceptually meaningful. An approximation of the asymptotic distortion based on Gersho's conjecture is derived as well. We also consider the problem of source mismatch, where the quantizer is designed using a probability density different from the true source density. The resulting asymptotic performance in terms of distortion increase in decibels is shown to be linear in the relative entropy between the true and estimated probability densities.

title: Unsupervised Multiresolution Segmentation for Images with Low Depth of Field
abstract: Unsupervised segmentation of images with low depth of field (DOF) is highly useful in various applications. This paper describes a novel multiresolution image segmentation algorithm for low DOF images. The algorithm is designed to separate a sharply focused object-of-interest from other foreground or background objects. The algorithm is fully automatic in that all parameters are image independent. A multi-scale approach based on high frequency wavelet coefficients and their statistics is used to perform context-dependent classification of individual blocks of the image. Unlike other edge-based approaches, our algorithm does not rely on the process of connecting object boundaries. The algorithm has achieved high accuracy when tested on more than 100 low DOF images, many with inhomogeneous foreground or background distractions. Compared with he state of the art algorithms, this new algorithm provides better accuracy at higher speed.

title: Introducing a Rule Importance Measure
abstract: Association rule algorithms often generate an excessive number of rules, many of which are not significant. It is difficult to determine which rules are more useful, interesting and important. We introduce a rough set based Rule Importance Measure to select the most important rules. We use ROSETTA software to generate multiple reducts. Apriori association rule algorithm is then applied to generate rule sets for each data set based on each reduct. Some rules are generated more frequently than the others among the total rule sets. We consider such rules as more important. We define rule importance as the frequency of an association rule generated across all the rule sets. Rule importance is different from either rule interestingness measures or rule quality measures because of their application tasks, the processes where the measures are applied and the contents they measure. The experimental results from an artificial data set, UCI machine learning datasets and an actual geriatric care medical data set show that our method reduces the computational cost for rule generation and provides an effective measure of how important is a rule.

title: Compression of the layered depth image
abstract: A layered depth image (LDI) is a new popular representation and rendering method for objects with complex geometries. Similar to a 2D image, the LDI consists of an array of pixels. However, unlike the 2D image, an LDI pixel has depth information, and there are multiple layers at a pixel location. In this paper, we develop a novel LDI compression algorithm that handles the multiple layers and the depth coding. The algorithm records the number of LDI layers at each pixel location, and compresses LDI color and depth components separately. For LDI layer with sparse pixels, the data is aggregated and then encoded. An empirical rate-distortion model is used to optimally allocate bits among different components. Compared with benchmark compression tools such as JPEG-2000 and MPEG-4, our scheme improves the compression performance significantly.

title: Hierarchical land cover information retrieval in object-oriented remote sensing image databases with native queries
abstract: Classification and change detection of land cover types in the remotely sensed images is one of the major applications in remote sensing. This paper presents a hierarchical framework for land cover information storage and retrieval from object-oriented (OO) remote sensing image databases. Multi-spectral (band) remotely sensed images are classified by an optimized k-means clustering algorithm. The land cover maps are then decomposed and indexed with region quad-tree data structure stored in an OO database. Native queries (NQs), which use the semantics of the OO programming language for query composition, are developed to retrieve land cover distribution information and detect the changes of each land cover type at multi levels. A prototype system was implemented and the experiments were conducted on a time series Landsat Thematic Mapper (TM) images. The results show the effectiveness of the framework and the potentials in other remote sensing applications like urban planning and drought monitoring.

title: Applying Association Rules for Interesting Recommendations Using Rule Templates
abstract: In this paper, we propose a new method of applying association rules for recommendation systems. Association rule algorithms are used to discover associations among items in transaction datasets. However, applying association rule algorithms directly to make recommendations usually generates too many rules; thus, it is difficult to find interesting recommendations for users among so many rules. Rule templates define certain types of rules; therefore, they are one of the interestingness measures that reduce the number of rules that do not interest users. We describe a new method. By defining more appropriate rule templates, we are able to extract interesting rules for users in a recommendation system. Experimental results show that our method increases the accuracy of recommendations.

title: Computationally efficient parameter estimation for harmonic sinusoidal signals
abstract: A Markov-like weighted least squares (WLS) estimator is presented herein for harmonic sinusoidal parameter estimation. The estimator involves two distinct steps whereby it first obtains a set of in ...