Worm plots

Scientists sometimes spend hours conducting experiments only to find that the resulting data proves difficult to analyze with traditional visualization techniques. A typical laboratory experiment, for example, will setup several systems in each of two or more groups-a control group and various treatment groups. The investigator will then measure various parameters for each system over time (sometimes dozens to hundreds of parameters). The investigator tries to answer this question: What is different between the control and treatment groups? Field monitoring of polluted and unpolluted sites within a region result in the same kinds of data and the same difficulties in visualization. Plotting multiple lines on a single 2D plot quickly gets confusing. Plus, the dynamic interactions between parameters can be hard to see. 3D visualizations help researchers make qualitative insights about data more easily. We developed a 3D plotting technique, called “worm plots”, for visualizing these kinds of data. Our visualization tool examines how groups of points change over time. If we plot circles for each time slice, then these circles will change their relative sizes and positions as time goes by. To visualize these evolving dynamics, we connect these time slices with conic sections. This gives us spacetime worms that can be displayed graphically. In our experience, these simple circular cross sections work best when exploring data. They can be rendered quickly and give an easily intuited summary of each group. Further enhancements tend to make the image busy and difficult to interpret     

An alternative to ordinary q-q plots: Conditional q-q plots

An ordinary q-q plot has at least two faults: it has a wavy appearance and its degree of linearity is hard to quantify. We propose a remedy, called a conditional q-q plot that reduces the waviness by conditioning on functions of adjacent random variables. It provides an easy and useful plot for assessing the validity of distributional assumptions. Examples are given and discussed.     

Curvature combs and curvature plots

We compare curvature combs and curvature plots.     

Discontinuities in continuous scatter plots

The concept of continuous scatterplot (CSP) is a modern visualization technique. The idea is to define a scalar density value based on the map between an n-dimensional spatial domain and an m-dimensional data domain, which describe the CSP space. Usually the data domain is two-dimensional to visually convey the underlying, density coded, data. In this paper we investigate kinds of map-based discontinuities, especially for the practical cases n = m = 2 and n = 3 | m = 2, and we depict relations between them and attributes of the resulting CSP itself. Additionally, we show that discontinuities build critical line structures, and we introduce algorithms to detect them. Further, we introduce a discontinuity-based visualization approach—called contribution map (CM)—which establishes a relationship between the CSP's data domain and the number of connected components in the spatial domain. We show that CMs enhance the CSP-based linking & brushing interaction. Finally, we apply our approaches to a number of synthetic as well as real data sets.     

Faster plots by fan data compression

A fan data compression method is presented that tripled laser printer speed for Bode and simulation plots with many points. This reduced printer delays without the expense of a faster laser printer, and it saved computer time as well. The authors describe their problem, solution, and conclusions. They give the fan algorithm and present its performance for several applications. They include a pseudocode implementation     

Two axes re-ordering methods in parallel coordinates plots

Visualization and interaction of multidimensional data are challenges in visual data analytics, which requires optimized solutions to integrate the display, exploration and analytical reasoning of data into one visual pipeline for human-centered data analysis and interpretation. Even though it is considered to be one of the most popular techniques for visualization and analysis of multidimensional data, parallel coordinate visualization is also suffered from the visual clutter problem as well as the computational complexity problem, same as other visualization methods in which visual clutter occurs where the volume of data needs to be visualized to be increasing. One straightforward way to address these problems is to change the ordering of axis to reach the minimal number of visual clutters. However, the optimization of the ordering of axes is actually a NP-complete problem. In this paper, two axes re-ordering methods are proposed in parallel coordinates visualization: (1) a contribution-based method and (2) a similarity-based method.The contribution-based re-ordering method is mainly based on the singular value decomposition (SVD) algorithm. It can not only provide users with the mathmetical theory for the selection of the first remarkable axis, but also help with visualizing detailed structure of the data according to the contribution of each data dimension. This approach reduces the computational complexity greatly in comparison with other re-ordering methods. A similarity-based re-ordering method is based on the combination of nonlinear correlation coefficient (NCC) and SVD algorithms. By using this approach, axes are re-ordered in line with the degree of similarities among them. It is much more rational, exact and systemic than other re-ordering methods, including those based on Pearson’s correlation coefficient (PCC). Meanwhile, the paper also proposes a measurement of contribution rate of each dimension to reveal the property hidden in the dataset. At last, the rationale and effectiveness of these approaches are demonstrated through case studies. For example, the patterns of Smurf and Neptune attacks hidden in KDD 1999 dataset are visualized in parallel coordinates using contribution-based re-ordering method; NCC re-ordering method can enlarge the mean crossing angles and reduce the amount of polylines between the neighboring axes.     

Enabling automatic clutter reduction in parallel coordinate plots

We have previously shown that random sampling is an effective clutter reduction technique and that a sampling lens can facilitate focus+context viewing of particular regions. This demands an efficient method of estimating the overlap or occlusion of large numbers of intersecting lines in order to automatically adjust the sampling rate within the lens. This paper proposes several ways for measuring occlusion in parallel coordinate plots. An empirical study into the accuracy and efficiency of the occlusion measures show that a probabilistic approach combined with a 'binning' technique is very fast and yet approaches the accuracy of the more expensive 'true' complete measurement     

基于实时方差时间图法的DDoS攻击检测

分布式拒绝服务攻击(DDoS)是目前最难解决的网络安全问题之一。基于自相似理论求解Hurst参数值存在的问题,在改进的方差时间图算法(OTVTP)的基础上,文章提出了基于自相似参数方差检测DDoS攻击的方法,并设计了采用该方法检测DDoS攻击的模型。实验结果表明,提出的方法能实时、准确检测和区分由DDoS攻击引起的Hurst参数变化,且检测率比传统方法要高。     

Visualization of multivariate data with radial plots using SAS

Data visualization tools can provide very powerful information and insight when performing data analysis. In many situations, a set of data can be adequately analyzed through data visualization methods alone. In other situations, data visualization can be used for preliminary data analysis. In this paper, radial plots are developed as a SAS-based data visualization tool that can improve one's ability to monitor, analyze and control a process. Using the program developed in this research, we present two examples of data analysis using radial plots; the first example is based on data from a particle board manufacturing process and the second example is a business process for monitoring the time-varying level of stock return data.     

Exploratory data analysis and model criticism with posterior plots

The use of techniques of exploratory data analysis and model criticism represent important stages in many statistical investigations. One of the attractive features of a Bayesian analysis is that it can lend itself well to graphical summary. To produce this graphical summary it is generally necessary to restrict attention to a small number of key parameters. The graphical approach described can be adopted whenever an appropriate likelihood function can be specified. Solutions to some of the principal computational problems associated with implementing a graphical Bayesian analysis based on posterior plots are presented. Nuisance parameters are handled in two ways: by incorporating them directly into the computation of exact posterior distributions; and by integrating them out of a conditional analysis at an early stage when the former approach is infeasible. The latter proposal facilitates the handling of higher dimensional nuisance parameter vectors. Examples taken from the areas of time series and microeconomics are presented to illustrate the efficacy of the approach.     

Informative PLS score-loading plots for process understanding and monitoring

Principal component regression (PCR) based on principal component analysis (PCA) and partial least squares regression (PLSR) are well known projection methods for analysis of multivariate data. They result in scores and loadings that may be visualized in a score-loading plot (biplot) and used for process monitoring. The difficulty with this is that often more than two principal or PLS components have to be used, resulting in a need to monitor more than one such plot. However, it has recently been shown that for a scalar response variable all PLSR/PCR models can be compressed into equivalent PLSR models with two components only. After a summary of the underlying theory, the present paper shows how such two-component PLS (2PLS) models can be utilized in informative score-loading biplots for process understanding and monitoring. The possible utilization of known projection model monitoring statistics and variable contribution plots is also discussed, and a new method for visualization of contributions directly in the biplot is presented. An industrial data example is included.     

Absolute stability results for non-linear systems using logarithmic plots

Absolute stability of non-linear systems is examined using the conventional techniques, and a representation of Popov line in the logarithmic gain and phase versus frequency plane. A grapho-analytical procedure is advanced for the Popov line transference to the Bode plane. The technique may be used either as an analytical tool for investigating absolute stability of systems with specified non-linearity sector, or as a synthesis technique for compensator design. The application of the proposed method for substantiating compensator design results is illustrated by two examples.     

Generation and sensitivity of input/output DC plots

A computer program operating in an interactive mode enables input/output DC plots of nonlinear systems to be generated and sensitivity properties to be studied. The computational method is based on the piecewise-linear approach. The technique is applied to simulate transistor curve tracers and to carry out worst-case analysis of transfer characteristics in digital circuits.     

产品设计中的产品识别

产品识别(PI)是产品获得归属感和家族感,企业文化获得认同感的有效设计手段之一。本文对PI概念及其组成要素进行归纳,具体从市场及竞争认知与分析、企业意象、产品意象、产品造型基因四个方面提出PI的构建模式。从产品设计的角度出发,初步探讨产品识别(PI)设计的理论框架。