The Visual Design and Control of Trellis Display

Abstract

Trellis display is a framework for the visualization of data. Its most prominent aspect is an overall visual design, reminiscent of a garden trelliswork, in which panels are laid out into rows, columns, and pages. On each panel of the trellis, a subset of the data is graphed by a display method such as a scatterplot, curve plot, boxplot, 3-D wireframe, normal quantile plot, or dot plot. Each panel shows the relationship of certain variables conditional on the values of other variables. A number of display methods employed in the visual design of Trellis display enable it to succeed in uncovering the structure of data even when the structure is quite complicated. For example, Trellis display provides a powerful mechanism for understanding interactions in studies of how a response depends on explanatory variables. Three examples demonstrate this; in each case, we make important discoveries not appreciated in the original analyses. Several control methods are also essential to Trellis display. A control method is a technique for specifying information so that a display can be drawn. The control methods of Trellis display form a basic conceptual framework that can be used in designing software. We have demonstrated the viability of the control methods by implementing them in the S/S-PLUS system for graphics and data analysis, but they can be implemented in any software system with a basic capability for drawing graphs.     

一种基于多级查找表的高效Huffman编码算法

本文研究了适用于数字信号处理器的一种高效的Huffman编码算法的问题.利用多级查找表建立规则,并将Huffman树分割为若干子树且为分割后的所有子树建立一个统一的查找表的方法,获得了可用较小的查找表来存储Huffman树且能对比特流进行快速解码的结果.     

A simulation study of IT outsourcing in the credit card business

The use of Monte Carlo simulation for evaluation of financial risk of an information technology project selection decision is described. A major Thai bank considered the opportunity to expand credit card operations through information technology (IT). Alternatives considered were in-house development and outsourcing. There were many strategic reasons for the initiative. However, there were also many risks associated with the proposal. A Monte Carlo simulation spreadsheet model was used to model risk parameters, and to analyze key performance variables of financial performance. Key output variables were the number of cardholders expected, project net present value, net profit, and expected return on investment. The spreadsheet model made entry of model elements transparent, and Monte Carlo simulation provided clear visual display of the financial output variables. The bank used this information in its decision to outsource its credit card operations.     

Infovis and Statistical Graphics: Different Goals,Different Looks

The importance of graphical displays in statistical practice has been recognized sporadically in the statistical literature over the past century, with wider awareness following Tukey's Exploratory Data Analysis and Tufte's books in the succeeding decades. But statistical graphics still occupy an awkward in-between position: within statistics, exploratory and graphical methods represent a minor subfield and are not well integrated with larger themes of modeling and inference. Outside of statistics, infographics (also called information visualization or Infovis) are huge, but their purveyors and enthusiasts appear largely to be uninterested in statistical principles.

We present here a set of goals for graphical displays discussed primarily from the statistical point of view and discuss some inherent contradictions in these goals that may be impeding communication between the fields of statistics and Infovis. One of our constructive suggestions, to Infovis practitioners and statisticians alike, is to try not to cram into a single graph what can be better displayed in two or more. We recognize that we offer only one perspective and intend this article to be a starting point for a wide-ranging discussion among graphic designers, statisticians, and users of statistical methods. The purpose of this article is not to criticize but to explore the different goals that lead researchers in different fields to value different aspects of data visualization.     

Graphical Selection of Data Views

Abstract

Graphical selection of data views is a fundamental task in interactive statistical graphics. Linked plots provide a form of indirect selection, where direct manipulation of objects displayed in one plot indirectly selects objects in other plots. A pointing device or brush is typically used for direct manipulation, and so this indirect selection is commonly known as linked brushing. Most commonly, linked brushing is applied to two or more scatterplots showing various pairs of variables from a multivariable dataset. This article describes a generalization of linked brushing for the setting where plots display different, though related datasets. With this form of linking, we can graphically explore relationships between datasets. Our linking system is extensible and handles any kind of display of any kind of dataset, as well as arbitrary relationships between those datasets.     

Graphical Explanation in Belief Networks

Abstract

Belief networks provide an important bridge between statistical modeling and expert systems. This article presents methods for visualizing probabilistic “evidence flows” in belief networks, thereby enabling belief networks to explain their behavior. Building on earlier research on explanation in expert systems, we present a hierarchy of explanations, ranging from simple colorings to detailed displays. Our approach complements parallel work on textual explanations in belief networks. Graphical-Belief, Mathsoft Inc.'s belief network software, implements the methods.     

基于对故障规律统计分析的汽车备件需求预测

汽车备件的需求与汽车故障紧密相关,文章介绍了一种在对汽车故障进行统计分析并确定其分布规律的基础上预测备件需求的方法,预测中需要结合整车保有量的历史数据以及故障与备件的对应表。用统计的方法对某型客车的故障信息进行分析,认为故障的规律可用四种典型的分布进行描述。实例验证了这种方法的准确性高于传统方法,并且在计算机的辅助下可以方便操作。     

XGobi: Interactive Dynamic Data Visualization in the X Window System

Abstract

XGobi is a data visualization system with state-of-the-art interactive and dynamic methods for the manipulation of views of data. It implements 2-D displays of projections of points and lines in high-dimensional spaces, as well as parallel coordinate displays and textual views thereof. Projection tools include dotplots of single variables, plots of pairs of variables, 3-D data rotations, various grand tours, and interactive projection pursuit. Views of the data can be reshaped. Points can be labeled and brushed with glyphs and colors. Lines can be edited and colored. Several XGobi processes can be run simultaneously and linked for labeling, brushing, and sharing of projections. Missing data are accommodated and their patterns can be examined; multiple imputations can be given to XGobi for rapid visual diagnostics. XGobi includes an extensive online help facility. XGobi can be integrated in other software systems, as has been done for the data analysis language S, the geographic information system (GIS) Arc View?, and the interactive multidimensional scaling program XGvis. XGobi is implemented in the X Window System? for portability as well as the ability to run across a network.     

Visualizing Loglinear Models

Abstract

We consider visual methods based on mosaic plots for interpreting and modeling categorical data. Categorical data are most often modeled using loglinear models. For certain loglinear models, mosaic plots have unique shapes that do not depend on the actual data being modeled. These shapes reflect the structure of a model, defined by the presence and absence of particular model coefficients. Displaying the expected values of a loglinear model allows one to incorporate the residuals of the model graphically and to visually judge the adequacy of the loglinear fit. This procedure leads to stepwise interactive graphical modeling of loglinear models. We show that it often results in a deeper understanding of the structure of the data. Linking mosaic plots to other interactive displays offers additional power that allows the investigation of more complex dependence models than provided by static displays.     

A novel combined cryptographic and hash algorithm based on chaotic control character

A novel combined cryptographic and hash algorithm based on chaotic control character is proposed in this paper. The control character is generated by chaotic iteration. The plaintext is pre-processed in terms of control character, and then encrypted by the look-up index table. At the same time, the chaotic trajectory is changed continuously according to the control character, which can avoid the dynamical degradation of chaos. Besides, the look-up index table is updated by utilizing the control character continuously, and the index item of the final look-up index table can be considered as the hash value of the whole paragraph of plaintext. Therefore, the proposed algorithm can perform both encryption/decryption and hash in a combined manner. Compared with Wong’s and our former algorithms, the proposed one has decreased the ratio of ciphertext/plaintext to 1, and improved the efficiency greatly. Theoretical analysis and computer simulation verify the validity of the proposed algorithm.     

How visual representations participate in algebra classes’ mathematical activity

Our aim is to discuss how a visual display introduced in a classroom activity to represent a specific algebraic procedure is transformed, taking a central role and modifying the ongoing activity. To discuss how visualization comes about in this activity, we describe an illustrative example selected from observations carried out in a 9th grade classroom and analyze the class interaction from a cultural-historical perspective. Our analysis illuminates the tensions that emerge from a difference between the teacher’s way of signifying the algebraic procedure and the students’ overuse of a visual display they associate with it, and how these tensions impel changes in the activity. We further discuss some pros and cons of using visual displays in algebra classes, and we argue that it is very important for the teacher to be aware of them in order to realize the benefits of using such displays.     

On the Cost of Data Analysis

Abstract

A regression analysis usually consists of several stages, such as variable selection, transformation and residual diagnosis. Inference is often made from the selected model without regard to the model selection methods that preceeded it. This can result in overoptimistic and biased inferences. We first characterize data-analytic actions as functions acting on regression models. We investigate the extent of the problem and test bootstrap, jackknife, and sample-splitting methods for ameliorating it. We also demonstrate an interactive LISP-STAT system for assessing the cost of the data analysis while it is taking place.     

A two-step method for forecasting spare parts demand using information on component repairs

Forecasting spare parts demand is notoriously difficult, as demand is typically intermittent and lumpy. Specialized methods such as that by Croston are available, but these are not based on the repair operations that cause the intermittency and lumpiness of demand. In this paper, we do propose a method that, in addition to the demand for spare parts, considers the type of component repaired. This two-step forecasting method separately updates the average number of parts needed per repair and the number of repairs for each type of component. The method is tested in an empirical, comparative study for a service provider in the aviation industry. Our results show that the two-step method is one of the most accurate methods, and that it performs considerably better than Croston’s method. Moreover, contrary to other methods, the two-step method can use information on planned maintenance and repair operations to reduce forecasts errors by up to 20%. We derive further analytical and simulation results that help explain the empirical findings.     

Flow-shop scheduling with setup and assembly operations

A scheduling model for a production system including machining, setup and assembly operations is considered. Production of a number of single-item products is ordered. Each product is made by assembling a set of several different parts. First, the parts are manufactured in a flow-shop consisting of multiple machines. Then, they are assembled into products on a single assembly stage. Setup operation and setup time are needed when a machine starts processing the parts or it changes items. The operations are partitioned into several blocks. Each block consists of the machining operations, the setup operations, and the assembly operation(s) for one or several products. The parts of the same item in a block are processed successively. The objective function is the mean completion time for all products. We consider a problem to partition the operations into blocks and sequence the parts in each block so as to minimize the objective function. Solution procedures using pseudo-dynamic programming and a branch-and-bound method are proposed. Computational experiments are carried out to evaluate the performance of the solution procedures. It has been found that a good near-optimal schedule is obtained efficiently by the proposed solution procedures.     

A note on table look-up

A more realistic bound for the average number of comparisons needed to match an incoming identifier by table look-up, when the table is still growing, is derived.Work carried out under a National Research Council of Canada Grant No. A-7700.     

Weighted Statistical Relative Invariant Mean in Modular Function Spaces with Related approximation Results

Abstract

The idea of statistical relative convergence on modular spaces has been introduced by Orhan and Demirci. The notion of σ-statistical convergence was introduced by Mursaleen and Edely and further extended based on a fractional order difference operator by Kadak. The concern of this paper is to define two new summability methods for double sequences by combining the concepts of statistical relative convergence and σ-statistical convergence in modular spaces. Furthermore, we give some inclusion relations involving the newly proposed methods and present an illustrative example to show that our methods are nontrivial generalizations of the existing results in the literature. We also prove a Korovkin-type approximation theorem and estimate the rate of convergence by means of the modulus of continuity. Finally, using the bivariate type of Stancu-Schurer-Kantorovich operators, we display an example such that our approximation results are more powerful than the classical, statistical, and relative modular cases of Korovkin-type approximation theorems.     

The Visual Separability of Plotting Symbols in Scatterplots

Abstract

Which symbols should be used to represent different groups of data in the same scatterplot? Hypotheses are derived to predict which symbol pairs should lead to good separability, based on the contrast of the symbols' visual properties or “features.” In two experiments, experimental scatterplots were shown to subjects on a computer screen; the dependent variable was the decision time to judge which of the two presented symbols was the more frequent one. Analyses of the within-subject effects yielded the following results: (1) Important feature contrasts are brightness, number of line endings, and curvature. (2) Symbols that differ simultaneously in two feature dimensions may be more separable than symbols that differ only in either one. (3) The contrasts between circular symbols and radial line symbols like the plus sign or the asterisk are excellent. Practical applications of these findings are discussed, as well as their contribution to the theory of visual perception.     

A vision architecture for unconstrained and incremental learning of multiple categories

We present an integrated vision architecture capable of incrementally learning several visual categories based on natural hand-held objects. Additionally we focus on interactive learning, which requires real-time image processing methods and a fast learning algorithm. The overall system is composed of a figure-ground segregation part, several feature extraction methods and a life-long learning approach combining incremental learning with category-specific feature selection. In contrast to most visual categorization approaches, where typically each view is assigned to a single category, we allow labeling with an arbitrary number of shape and color categories. We also impose no restrictions on the viewing angle of presented objects, relaxing the common constraint on canonical views.     

Improvement in peak stress estimates through post-processing

Three alternatives for calculating the peak stress in the vicinity of a stress raiser have been proposed in previous research: an iterative method, a stiffness derivative method, and a table look-up method. The goal of each is to improve the estimate of the peak stress through post-processing rather than multiple analyses utilizing mesh refinement. In the present paper, the relative effectiveness of the methods is studied by means of test cases. An improved stiffness derivative method is suggested for use in fracture mechanics applications.     

Multiple taxicab correspondence analysis

We compare the statistical analysis of multidimensional contingency tables by multiple correspondence analysis (MCA) and multiple taxicab correspondence analysis (MTCA). We will show in this paper: First, MTCA and MCA can produce different results. Second, taxicab correspondence analysis of a Burt table is equivalent to centroid correspondence analysis of the indicator matrix. Third, along the first principal axis, the projected response patterns in MTCA will be clustered and the number of cluster points is less than or equal to 1+ the number of variables. Fourth, visual maps produced by MTCA seem to be clearer and more readable in the presence of rarely occurring categories of the variables than the graphical displays produced by MCA. Two well known data sets are analyzed.