Exploratory Statistical Techniques

Many graphical methods for displaying multivariate data consist of arrangements of multiple displays of one or two variables; scatterplot matrices and parallel coordinates plots are two such methods. In principle these methods generalize to arbitrary numbers of variables but become difficult to interpret for even moderate numbers of variables. This article demonstrates that the impact of high dimensions is much less severe when the component displays are clustered together according to some index of merit. Effectively, this clustering reduces the dimensionality and makes interpretation easier. For scatterplot matrices and parallel coordinates plots clustering of component displays is achieved by finding suitable permutations of the variables. I discuss algorithms based on cluster analysis for finding permutations, and present examples using various indices of merit.

This paper describes an R package which produces tours of multivariate data. The package includes functions for creating different types of tours, including grand, guided, and little tours, which project multivariate data (p-D) down to 1, 2, 3, or, more generally, d (≤ p) dimensions. The projected data can be rendered as densities or histograms, scatterplots, anaglyphs, glyphs, scatterplot matrices, parallel coordinate plots, time series or images, and viewed using an R graphics device, passed to GGobi, or saved to disk. A tour path can be stored for visualisation or replay. With this package it is possible to quickly experiment with different, and new, approaches to tours of data. This paper contains animations that can be viewed using the Adobe Acrobat PDF viewer.

Multivariate data visualization is a classic topic, for which many solutions have been proposed, each with its own strengths and weaknesses. In standard solutions the structure of the visualization is fixed, we explore how to give the user more freedom to define visualizations. Our new approach is based on the usage of Flexible Linked Axes: The user is enabled to define a visualization by drawing and linking axes on a canvas. Each axis has an associated attribute and range, which can be adapted. Links between pairs of axes are used to show data in either scatter plot- or Parallel Coordinates Plot-style. Flexible Linked Axes enable users to define a wide variety of different visualizations. These include standard methods, such as scatter plot matrices, radar charts, and PCPs [11]; less well known approaches, such as Hyperboxes [1], TimeWheels [17], and many-to-many relational parallel coordinate displays [14]; and also custom visualizations, consisting of combinations of scatter plots and PCPs. Furthermore, our method allows users to define composite visualizations that automatically support brushing and linking. We have discussed our approach with ten prospective users, who found the concept easy to understand and highly promising.

Traditional multidimensional visualization techniques, such as glyphs, parallel coordinates and scatterplot matrices, suffer from clutter at the display level and difficult user navigation among dimensions when visualizing high dimensional datasets. In this paper, we propose a new multidimensional visualization technique named a value and relation (VaR) display, together with a rich set of navigation and selection tools, for interactive exploration of datasets with up to hundreds of dimensions. By explicitly conveying the relationships among the dimensions of a high dimensional dataset, the VaR display helps users grasp the associations among dimensions. By using pixel-oriented techniques to present values of the data items in a condensed manner, the VaR display reveals data patterns in the dataset using as little screen space as possible. The navigation and selection tools enable users to interactively reduce clutter, navigate within the dimension space, and examine data value details within context effectively and efficiently. The VaR display scales well to datasets with large numbers of data items by employing sampling and texture mapping. A case study on a real dataset, as well as the VaR displays of multiple real datasets throughout the paper, reveals how our proposed approach helps users interactively explore high dimensional datasets with large numbers of data items

We explore how to rigorously evaluate multidimensional visualizations for their ability to support decision making. We first define multi-attribute choice tasks, a type of decision task commonly performed with such visualizations. We then identify which of the existing multidimensional visualizations are compatible with such tasks, and set out to evaluate three elementary visualizations: parallel coordinates, scatterplot matrices and tabular visualizations. Our method consists in first giving participants low-level analytic tasks, in order to ensure that they properly understood the visualizations and their interactions. Participants are then given multi-attribute choice tasks consisting of choosing holiday packages. We assess decision support through multiple objective and subjective metrics, including a decision accuracy metric based on the consistency between the choice made and self-reported preferences for attributes. We found the three visualizations to be comparable on most metrics, with a slight advantage for tabular visualizations. In particular, tabular visualizations allow participants to reach decisions faster. Thus, although decision time is typically not central in assessing decision support, it can be used as a tie-breaker when visualizations achieve similar decision accuracy. Our results also suggest that indirect methods for assessing choice confidence may allow to better distinguish between visualizations than direct ones. We finally discuss the limitations of our methods and directions for future work, such as the need for more sensitive metrics of decision support.

Multidimensional projections are an increasingly popular technique for visualizing large datasets containing observations having tens or even hundreds of dimensions. Compared to other techniques such as parallel coordinates, tables, and scatterplot matrices, they support tasks such as finding groups of related observations and outliers in simpler, more effective, ways. The authors discuss here the advantages of multidimensional projections, how to compute them, and recent advances that enhance them by visual explanatory techniques, so as to make them efficient and effective instruments that should be part of the toolkit of any scientist interested in high-dimensional data exploration.

Discovering and extracting linear trends and correlations in datasets is very important for analysts to understand multivariate phenomena. However, current widely used multivariate visualization techniques, such as parallel coordinates and scatterplot matrices, fail to reveal and illustrate such linear relationships intuitively, especially when more than 3 variables are involved or multiple trends coexist in the dataset. We present a novel multivariate model parameter space visualization system that helps analysts discover single and multiple linear patterns and extract subsets of data that fit a model well. Using this system, analysts are able to explore and navigate in model parameter space, interactively select and tune patterns, and refine the model for accuracy using computational techniques. We build connections between model space and data space visually, allowing analysts to employ their domain knowledge during exploration to better interpret the patterns they discover and their validity. Case studies with real datasets are used to investigate the effectiveness of the visualizations.

Advanced composites such as fiber reinforced polymers are promising candidate materials for future components as they allow integrating the continuously rising demands of industry regarding cost-effectiveness, function-orientation, integration and weight. The most important structures of fiber reinforced polymers are the individual fibers, as their characteristics (stiffness, strength, ductility, durability, etc.) to a large extent determine the properties of the final component. The main contribution of this paper is the introduction of a new system for interactive exploration and visual analysis of fiber properties in X-ray computed tomography data of fiber reinforced polymers. The presented tool uses parallel coordinates to define and configure initial fiber classes. Using a scatter plot matrix linked to the parallel coordinates the initial classification may be refined. This allows to analyze hidden relationships between individual fiber properties. 2D and 3D views depict the resulting fiber classifications. By using polar plots an intuitive rendering of the fiber orientation distribution is provided. In addition, two modules of higher abstraction are proposed: The Blob visualization creates a hull around fibers with similar characteristics. The fiber metadata visualization allows to calculate overlays for 2D and 3D views containing regional information of particular material characteristics. The proposed system has been evaluated by two groups of domain experts. Applying the presented concepts the user feedback shows that the domain experts are now able to efficiently perform tasks as classification of fibers, visualization of fiber lengths and orientations, and visualization of fiber regions. The insights gained can be forwarded to the design office as well as to material development and simulation, in order to speed up the development of novel composite components.

This study aimed at ascertaining what role agricultural extension plays in mitigating the effects of climate change and variability using farmers’ perceptions in Gqumashe village, Raymond Mhlaba Local Municipality, Eastern Cape, South Africa. The survey research design was adopted for the study, and data for the study were collected from 50 respondents using a convenience sampling method in the study area. Data was analysed using SPSS and descriptive statistics (means, percentages and graphs) were produced. Farmers in the study area were aware of and perceived climate change and variability as detrimental to agricultural production as they reported various problems associated with changes and variability in climate to their extension workers and other available agricultural officials. The paper concludes by making three recommendations: a) Extension agents as the disseminators of information to farmers need to conduct targeted training for farmers in order to raise more awareness about climate change and variability as a subject; b)Extension agents need to visit farmers regularly and also provide information on current issues related to farming, new technology development for agriculture and farming, climate change and variability issues, as well as training about new agricultural techniques to counteract climate change and variability effects; and c) Extension agents need to proactively meet the expressed need for market information and storage facilities. Keywords: Perceptions, capacity development, climate smart agriculture, agricultural extension

Descriptive Analysis of Employment In Azerbaijan: Possibilities of the Dutch Disease

To reduce the waste of vegetables and guarantee revenues for supermarkets, this paper explores the construction of a comprehensive optimization model to help the supermarket select the specific suitable replenishment scheme and pricing strategy. This sets the bedrock for it to both gain the maximum revenue and timely supply various categories of vegetables that the market demands. The expectation for further relevant research to better complete the model is also mentioned. First, the attached data were preprocessed, and no missing values and outliers were detected. Consequently, the data of multiple forms was merged, and data related to categories of vegetables was counted. In response to Question 1, descriptive statistics were conducted on different individual items and categories of vegetables. Sales volumes of categories of vegetables were visualized through sales volume statistical graphs, profit line graphs, and quarterly sales change graphs. Following, the sales volumes were verified to have satisfied the conditions for calculating the Pearson Correlation Coefficient, and heat maps were drawn for correlation analysis. For individual items, hierarchical clustering was carried out with indicators, such as sales volume, unit price, number of purchases, and wastage rate. The basis of categorization of each category of vegetable was also explored. For Question 2, average pricing was used to replace cost-plus pricing first. Then, BP Neural Net Fitting was leveraged to analyze the relation between total sales volume and average pricing of different vegetable categories. The average wholesale price of the next seven days of each vegetable category was predicted with ARIMA Model, in order to gain the profit of different categories. Finally, a nonlinear objective planning model to achieve maximum benefit for the supermarket was constructed. Corresponding constraints were given to propose a reasonable total replenishment and pricing strategy for each vegetable category. In solving Question 3, constraints were added based on the nonlinear objective planning model in Question 2, and the prediction model was optimized. In the case of meeting market demand, the replenishment volume and pricing strategy for individual items on July 1, 2023, were proposed based on a combination of factors, as a way to maximize the benefits for the supermarket.