9037713
A Lagrangian formulation of Zador's entropy-constrained quantization theorem
Zador's (1963, 1966) 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. The equivalence of the two formulations is shown and the result is proved for source distributions that are absolutely continuous with respect to the Lebesgue measure which satisfy an entropy condition, thereby generalizing the conditions stated by Zador under which the result holds.
3117640
Asymptotic Performance of Vector Quantizers with a Perceptual Distortion Measure
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.
26279535
On Zador's entropy-constrained quantization theorem
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.
1149168
Unsupervised Multiresolution Segmentation for Images with Low Depth of Field
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.
13204199
A source coding approach to classification by vector quantization and the principle of minimum description length
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.
10105
Real-Time Computerized Annotation of Pictures
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.
40615325
Finite element analysis for a nonlinear diffusion model in image processing
Abstract The optimal error estimate O ( h k +1 ) for a popular nonlinear diffusion model widely used in image processing is proved for the standard k th -order ( k ≥ 1) conforming tensor-product finite elements in the L 2 -norm. The optimal L 2 -estimate is obtained by the integral identity technique [1–3] without using the classic Nitsche duality argument [4].
1263346
Accelerating XML Structural Join by Partitioning
Structural join is the core part of XML queries and has a significant impact on the performance of XML queries, several classical structural join algorithms have been proposed such as Stack-tree join and XR-Tree join. In this paper, we consider to answer the problem of structural join by partitioning. We first extend the relationships between nodes to the relationships between partitions in the plane and get some observations. We then propose a new partition-based method P-Join for structural join. Based on P-Join, moreover, we present an enhanced partitioned-based spatial structural join algorithm PSSJ.
4324450
Cycles through subsets with large degree sums
Let G be a 2-connected graph on n vertices and let X V(G). We say that G is X-cyclable if G has an X-cycle, i.e., a cycle containing all vertices of X. We denote by ?(X) the maximum number of pairwise nonadjacent vertices in the subgraph G[X] of G induced by X. If G[X] is not complete, we denote by ?(X) the minimum cardinality of a set of vertices of G separating two vertices of X. By ?(X) we denote the minimum degree (in G) of the vertices of X, and by ?3(X) the minimum value of the degree sum (in G) of any three pairwise nonadjacent vertices of X. Our first main result is the following extension in terms of X-cyclability of a result on hamiltonian graphs by Bauer et al. If ?3(X) n + mingk(X), ?(X), then G is X-cyclable. Our second main result is the following generalization of a result of Fournier. If ?(X) ?(X), then G is X-cyclable. We give a number of extensions of other known results, thereby generalizing some recent results of Veldman.
30686158
Applying Association Rules for Interesting Recommendations Using Rule Templates
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.
2145584
A Comparison and Semi-Quantitative Analysis of Words and Character-Bigrams as Features in Chinese Text Categorization
Words and character-bigrams are both used as features in Chinese text processing tasks, but no systematic comparison or analysis of their values as features for Chinese text categorization has been reported heretofore. We carry out here a full performance comparison between them by experiments on various document collections (including a manually word-segmented corpus as a golden standard), and a semi-quantitative analysis to elucidate the characteristics of their behavior; and try to provide some preliminary clue for feature term choice (in most cases, character-bigrams are better than words) and dimensionality setting in text categorization systems.