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Geog 463: GIS Workshop

Geog 463: GIS Workshop. May 17, 2006 Exploratory Spatial Data Analysis. Outlines. I. Fundamentals of ESDA What is Exploratory Spatial Data Analysis (ESDA)? ESDA basics II. Techniques of ESDA with focus on area-class data ESDA for describing non-spatial properties of attribute

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Geog 463: GIS Workshop

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  1. Geog 463: GIS Workshop May 17, 2006 Exploratory Spatial Data Analysis

  2. Outlines I. Fundamentals of ESDA • What is Exploratory Spatial Data Analysis (ESDA)? • ESDA basics II. Techniques of ESDA with focus on area-class data • ESDA for describing non-spatial properties of attribute • ESDA for describing spatial properties of attribute III. Applications of ESDA • Gallery of implemented ESDA systems

  3. I. Fundamentals of ESDA

  4. 1. What is ESDA? • Exploratory Spatial Data Analysis (ESDA) • Exploratory Data Analysis (EDA) • EDA and statistics • EDA and visualization • EDA and cartographic visualization

  5. Exploratory Spatial Data Analysis • Extension of exploratory data analysis (EDA) to detect spatial properties of data • EDA • consists of a collection of descriptive and graphical statistical tools • intended to discover patterns in data and suggest hypotheses • by imposing as little prior structure as possible • ESDA links numerical and graphical procedures with the map

  6. Exploratory Data Analysis • Aimed at (1) pattern detection (2) hypothesis formulation (3) model assessment • Use of graphical and visual methods (e.g. Box plot); Use of numerical techniques that are statistically robust (e.g. P-value) • Emphasis on descriptive methods rather than formal hypothesis testing • Exploratory in that it cannot explain the patterns it reveals

  7. EDA and Statistics • Evolutions of statistics: return of original goals of statistics in data-rich and high computing environment; stay close to the original data Image source: Adrienko’s website

  8. EDA and Visualization • By its very nature the main role of EDA is to open-mindedly explore, and graphics gives the analysts unparalleled power to do so • The greatest value of a picture is when it forces us to notice what we never expected to see – John W. Tukey

  9. EDA and Cartographic Visualization • Emphasis on the role of highly interactive maps in individual and small group efforts at hypothesis generation, data analysis, and decision-support • Contrast with static paper maps

  10. Early examples of ESDA death locations Dr. John Snow: Investigation of deaths from cholera London, September 1854 spatial cluster infected water pump? A good data representation is the key to solving the problem

  11. 2. ESDA Basics • Visual tools for non-spatial analyses • Univariate • Multivariate • Visual tools for spatial analyses • First-order properties • Second-order properties • Brushing & Linking

  12. Visual tool for non-spatial analyses • Univariate • Histogram • Box plot • Multivariate • Scatter plot • Parallel coordinates plot

  13. Histogram, box plot Dispersion graph Dot plot Distribution of attribute values within a range Box plot Histogram Distribution of attribute values at y-axis given categorical variables at x-axis

  14. Scatter plot Scatter plot: shows how two attributes are related Scatter plotmatrix: shows how a set of two attributes are related

  15. Parallel coordinates plot Parallel coordinates plot: object characteristics profiles; relationships between attributes (look at line slopes)

  16. Visual tools for spatial analyses • First order properties • Tools for exploring general trends • Spatially lagged boxplot • Kernel estimation • Second order properties • Tools for exploring spatial autocorrelation • Moran plot

  17. Spatially lagged boxplot • Boxplot in which the categorical variable is spatial lag order(as defined by spatial weight matrix) • After the user has selected an origin zone, a sequence of box plots (one for each lag order) is generated at increasing distancefrom the origin zone up to a user specified maximum

  18. Wise et al 1998

  19. Kernel Estimation • This method is used to smooth a given point pattern such as crime locations so that we can easily detect hot spot.

  20. Moran plot • A plot of attribute value on the vertical axis against the average of the attribute values in the adjacent areas using spatial weight matrix • A scatter of values sloping upward to the right is indicative of positive autocorrelation

  21. Brushing & linking • Brushing: a subset of data is selected and highlighted • Linking: map and graph are linked such that multiple views are displayed Image source: Symanzik’s website

  22. II. Techniques of ESDA

  23. 3. ESDA for describing non-spatial properties of attribute • Median • Measure of the center of the distribution of attribute values • ESDA queries: which are the areas with attribute values above (below) the median? • Quartile and inter-quartile spread • Measure of spread of values about the median • ESDA queries: which are the areas that lie in the upper (lower) quartile? • Box plots • Graphical summary of the distribution of attribute values • ESDA queries: where do cases that lie in specific parts of the boxplot occur on the map? Where are the outlier cases located on the map?

  24. 4. ESDA for describing spatial properties of attribute • Smoothing • Identifying trends and gradients on the map • Spatial autocorrelation • Detecting spatial outliers

  25. Smoothing • Smoothing may help to reveal the presence of general patterns that are unclear from the mosaic of values • ESDA techniques: spatial averaging – take the attribute value of an area and its neighbors and average them; repeat for each area

  26. Identifying trends and gradients on the map • Are there any general trends or gradients in the map distribution of values? • ESDA techniques include • Kernel estimation • Taking transects through the data and plotting with attribute value on vertical axis and spatial location on horizontal axis • Spatially lagged boxplot with lag order specified with respect to a particular area or zone

  27. Spatial autocorrelation • Propensity for attribute values in neighboring areas to be similar • ESDA techniques include • Moran plot

  28. Detecting spatial outliers • An individual attribute value is not necessarily extreme in the distributional sense but is extreme in terms of the attribute values in adjacent areas • ESDA technique: run a linear squares regression on the Moran plot, and select cases significantly deviated from the regression line

  29. III. Applications of ESDA

  30. 5. Gallery of ESDA systems • GeoDa • https://www.geoda.uiuc.edu/default.php • CommonGIS • http://www.commongis.com/

  31. Interactive map symbolization in CommonGIS By moving the slider, we see more patterns and gain more understanding of value distribution Porto Lisboa Clusters of low values around Porto and Lisboa Clusters of high values in central-east One more cluster of low values Coast-inland contrast West-to-east increase

  32. Link between information visualization techniques and maps Map and dot plot; each district shown on the map is also represented by a dot Map and scatter plot: the same technique Map Dot plot A district pointed on the map with the mouse is simultaneously highlighted on the map and the plot

  33. Using Cumulative Curves Some statistics about the result: In the most part of Portugal (coloured in blue) the proportion of people having high school education is below 4.67. However, on this large territory only one third of the country’s population lives. In these areas over 7.82% people have high school education. Here lives 33.1% of the total country’s population.

  34. Focusing & multiple views and here, An object pointed on the map with the mouse and here, but not here: this is an aggregated view that does not show individual objects is simultaneously highlighted here,

  35. Focusing and Visual Comparison on Other Map Types Outlier Maximum represented value Value to compare with Minimum value

  36. Spatial Distribution of Events The small circles represent the earthquakes that occurred in Western Turkey and the neighbourhood between 01.01.1976 and 30.12.1999 Here we see only the earthquakes that occurred during 30 days from 15.05.1977 to 13.06.1977 By applying the temporal filter, we can investigate the spatial distribution on any time interval

  37. Progress of Spatial Patterns over Time Map animation allows us to see how the spatial distribution of events and their characteristics evolve over time 25.05.1977 - 23.06.1977 04.06.1977 - 03.07.1977 15.05.1977 - 13.06.1977 14.06.1977 - 13.07.1977 04.07.1977 - 02.08.1977 24.06.1977 - 23.07.1977 Each animation frame in this example covers 30-days time interval. The step between the frames is 10 days. Hence, there is 20 days overlap between the adjacent frames.

  38. Exploration of Behaviors The value flow symbols show us the evolution of attribute values (behavior) at each location. Unfortunately, symbol overlapping creates significant inconveniences, and zooming does not always help

  39. Data Transformations for Behavior Exploration As with time maps, various data transformations can be applied to value flow maps. Here we have applied the comparison to the mean: the values for each moment are replaced by their differences to the country’s mean at the same moment. Yellow colour corresponds to positive differences, and blue – to negative. We have received a rather clear spatial pattern.

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