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106
How many bins should be put in a regular histogram
, 2003
"... Given an nsample from some unknown density f on [0, 1], it is easy to construct an histogram of the data based on some given partition of [0, 1], but not so much is known about an optimal choice of the partition, especially when the set of data is not large, even if one restricts to partitions into ..."
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Cited by 45 (9 self)
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Given an nsample from some unknown density f on [0, 1], it is easy to construct an histogram of the data based on some given partition of [0, 1], but not so much is known about an optimal choice of the partition, especially when the set of data is not large, even if one restricts to partitions into intervals of equal length. Existing methods are either rules of thumbs or based on asymptotic considerations and often involve some smoothness properties of f . Our purpose in this paper is to give a fully automatic and simple method to choose the number of bins of the partition from the data. It is based on a nonasymptotic evaluation of the performances of penalized maximum likelihood estimators in some exponential families due to Castellan and heavy simulations which allowed us to optimize the form of the penalty function. These simulations show that the method works quite well for sample sizes as small as 25.
DataBased Choice of Histogram Bin Width
 The American Statistician
, 1996
"... The most important parameter of a histogram is the bin width, since it controls the tradeoff between presenting a picture with too much detail ("undersmoothing ") or too little detail ("oversmoothing") with respect to the true distribution. Despite this importance there has been ..."
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Cited by 35 (0 self)
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The most important parameter of a histogram is the bin width, since it controls the tradeoff between presenting a picture with too much detail ("undersmoothing ") or too little detail ("oversmoothing") with respect to the true distribution. Despite this importance there has been surprisingly little research into estimation of the "optimal" bin width. Default bin widths in most common statistical packages are, at least for large samples, quite far from the optimal bin width. Rules proposed by, for example, Scott (1992) lead to better large sample performance of the histogram, but are not consistent themselves. In this paper we extend the bin width rules of Scott to those that achieve rootn rates of convergence to the L 2 optimal bin width; thereby providing firm scientific justification for their use. Moreover, the proposed rules are simple, easy and fast to compute and perform well in simulations. KEY WORDS: Binning; Data analysis; Density estimation; Kernel functional estimator; S...
Histograms Analysis for Image Retrieval
, 2001
"...  This paper analyzes the use of histograms of low level image features, such as color and luminance, as descriptors for image retrieval purposes. A novel denition of histogram capacity curve taking into account the density distribution of histograms in the corresponding spaces is proposed and used ..."
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Cited by 32 (0 self)
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 This paper analyzes the use of histograms of low level image features, such as color and luminance, as descriptors for image retrieval purposes. A novel denition of histogram capacity curve taking into account the density distribution of histograms in the corresponding spaces is proposed and used to quantify the eectiveness of image descriptors and histogram dissimilarities in image retrieval applications. The results permit the design of scalable image retrieval systems which make optimal use of computational and storage resources. Keywords: image retrieval, histograms, density estimation, distribution comparison. 1. Introduction A currently active line of research and development in the Computer Vision community is the design and development of ecient tools for accessing multimedia material, such as video and still images, using their media specic features. In particular, several research papers and tools have been presented for image retrieval based on low level visual featu...
Using Correlated Surprise to Infer Shared Influence
"... We propose a method for identifying the sources of problems in complex production systems where, due to the prohibitive costs of instrumentation, the data available for analysis may be noisy or incomplete. In particular, we may not have complete knowledge of all components and their interactions. We ..."
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Cited by 18 (5 self)
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We propose a method for identifying the sources of problems in complex production systems where, due to the prohibitive costs of instrumentation, the data available for analysis may be noisy or incomplete. In particular, we may not have complete knowledge of all components and their interactions. We define influences as a class of component interactions that includes direct communication and resource contention. Our method infers the influences among components in a system by looking for pairs of components with timecorrelated anomalous behavior. We summarize the strength and directionality of shared influences using a StructureofInfluence Graph (SIG). This paper explains how to construct a SIG and use it to isolate system misbehavior, and presents both simulations and indepth case studies with two autonomous vehicles and a 9024node production supercomputer. 1
An outlierbased data association method for linking criminal incidents
 In Proceedings of 3rd SIAM Data Mining Conference
, 2003
"... Data association is an important datamining task and it has various applications. In crime analysis, data association means to link criminal incidents committed by the same person. It helps to discover crime patterns and catch the criminal. In this paper, we present an outlierbased data associatio ..."
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Cited by 18 (0 self)
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Data association is an important datamining task and it has various applications. In crime analysis, data association means to link criminal incidents committed by the same person. It helps to discover crime patterns and catch the criminal. In this paper, we present an outlierbased data association method. An outlier score function is defined to measure the extremeness of an observation, and the data association method is developed based upon the outlier score function. We apply this method to the robbery data from Richmond, Virginia, and compare the result with a similaritybased association method. Result shows that the outlierbased data association method is promising.
Information theoretic feature extraction for audiovisual speech recognition
 IEEE TRANSACTIONS ON SIGNAL PROCESSING
, 2009
"... The problem of feature selection has been thoroughly analyzed in the context of pattern classification, with the purpose of avoiding the curse of dimensionality. However, in the context of multimodal signal processing, this problem has been studied less. Our approach to feature extraction is based ..."
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Cited by 11 (1 self)
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The problem of feature selection has been thoroughly analyzed in the context of pattern classification, with the purpose of avoiding the curse of dimensionality. However, in the context of multimodal signal processing, this problem has been studied less. Our approach to feature extraction is based on information theory, with an application on multimodal classification, in particular audio–visual speech recognition. Contrary to previous work in information theoretic feature selection applied to multimodal signals, our proposed methods penalize features for their redundancy, achieving more compact feature sets and better performance. We propose two greedy selection algorithms, one that penalizes a proportion of feature redundancy, while the other uses conditional mutual information as an evaluation measure, for the selection of visual features for audio–visual speech recognition. Our features perform better than linear discriminant analysis, the most usual transform for dimensionality reduction in the field, across a wide range of dimensionality values and combined with audio at different quality levels.
The problem with sturges rule for constructing histograms
, 1995
"... Abstract Most statistical packages use Sturges ’ rule (or an extension of it) for selecting the number of classes when constructing a histogram. Sturges ’ rule is also widely recommended in introductory statistics textbooks. It is known that Sturges ’ rule leads to oversmoothed histograms, but Sturg ..."
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Cited by 7 (0 self)
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Abstract Most statistical packages use Sturges ’ rule (or an extension of it) for selecting the number of classes when constructing a histogram. Sturges ’ rule is also widely recommended in introductory statistics textbooks. It is known that Sturges ’ rule leads to oversmoothed histograms, but Sturges ’ derivation of his rule has never been questioned. In this note, I point out that the argument leading to Sturges ’ rule is wrong. Key words: Histogram, binwidth selection, statistical computer packages. Herbert Sturges (1926) considered an idealised frequency histogram with k bins where the ith bin count is the binomial coefficient ( k−1) i, i = 0, 1,..., k − 1. As k increases, this ideal frequency histogram approaches the shape of a normal density. The total sample size is k−1 ∑ k − 1 n = i i=0 = (1 + 1) k−1 = 2 k−1 by the binomial expansion. So the number of classes to choose when constructing a
Dot plots
 The American Statistician
, 1999
"... Dot plots represent individual observations in a batch of data with symbols, usually circular dots. They have been used for more than a hundred years to depict distributions in detail. Handdrawn examples show their authors ’ efforts to arrange symbols so that they are as near as possible to their pr ..."
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Cited by 5 (1 self)
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Dot plots represent individual observations in a batch of data with symbols, usually circular dots. They have been used for more than a hundred years to depict distributions in detail. Handdrawn examples show their authors ’ efforts to arrange symbols so that they are as near as possible to their proper locations on a scale without overlapping enough to obscure each other. Recent computer programs that attempt to reproduce these historical plots have unfortunately resorted to simple histogram binning instead of using methods that follow the rules for the handdrawn examples. This paper introduces an algorithm that more accurately represents the dot plots cited in the literature.