DATA VISUALIZATION. Lecture 4--Information Visualization

Transcription

1 DATA VISUALIZATION Lecture 4--Information Visualization Simple Graphs and Charts Scatter Plots and Parallel Coordinates Glyphs and Other Methods Lin Lu

2 SIMPLE DATA PRESENTATION Graphs and Charts

3 Simple Data Presentation Simple data tables are often presented as line graphs, bar graphs, pie charts, dot graphs, histograms Which should we use and when?

4 Line Graph Fundamental technique of data presentation Used to compare two variables X-axis is often the control variable Y-axis is the response variable Good at: Showing specific values Trends Trends in groups (using multiple line graphs) Students participating in sporting activities Mobile Phone use Note: graph labelling is fundamental

5 宽高比

6 尺度 (scales) 哪一幅图比较好?

7 清晰标识尺度的中断 标识的不好 [Cleveland 85] 标识的非常好 [Cleveland 85]

8 尺度中断与 log 尺度 都提高了视觉分辨率 Log 尺度 容易比较所有数据尺度中断 很难跨越中断比较所有数据

9 线性尺度和 log 尺度

10 Simple Representations Bar Graph Bar graph Presents categorical variables Height of bar indicates value Double bar graph allows comparison Note spacing between bars Can be horizontal (when would you use this?) Number of police officers Internet use at a school

11 Simple Representations Bar Graph 每个国家消费了多少啤酒? 捷克爱尔兰德国澳大利亚英国美国 每人每周消耗的瓶数 加拿大南非墨西哥日本巴西中国

12 尺度

13 偏离设计 显示到主集合值的不同

14 使用零点为基准点

15 不必要的三维设计

16 堆叠柱状图 stacked bar chart

17 堆叠柱状图 stacked bar chart

18 对偶柱状图 dual bar chart

19 对偶柱状图 dual bar chart

20 Dot Graph Very simple but effective Horizontal to give more space for labelling

21 Pie Chart Pie chart summarises a set of categorical/nominal data But use with care too many segments are harder to compare than in a bar chart Should we have a long lecture? Favourite movie genres

22 Histograms Histograms summarise discrete or continuous data that are measured on an interval scale No gaps if variable is continuous Distribution of salaries in a company

23 Scatter Plot Used to present measurements of two variables Effective if a relationship exists between the two variables Car ownership by household income Example taken from NIST Handbook Evidence of strong positive correlation

24 Scatter Plots in Excel The scatter plot is a fundamental tool in Excel Chart type XY (Scatter) and subtype Unconnected Points

25 Regression Line Excel allows you to add a linear regression line (trend line) Remember: correlation does not imply causality ie a relationship exists but one is not necessarily causing the other there may be a third factor?

26 Tukey Sum-Difference Plot Better understanding of residuals

27 Box Plots In some situations we have, not a single data value at a point, but a number of data values, or even a probability distribution When might this occur? Tukey proposed the idea of a boxplot to visualize the distribution of values For explanation and some history, see: M median Q1 lower quartile Q3 upper quartile Whiskers 1.5 * interquartile range Dots - outliers Darwin s plant study WhiskerPlot.html

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29 用数据讲故事 Gapminder Video

30 MULTIVARIATE DATA EXPLORATION Scatter plots and parallel coordinates Glyphs and other methods

31 Data Tables Multivariate datasets can be expressed as a data table Each entry in table is an observation An observation consists of values of a set of variables, or variates variables A B C observations

32 Scatter Plot For two variates, we have already met the scatter plot technique It is useful for showing what happens to one variable as another changes

33 Scatter Plot Here is an example scatter plot, visualizing the speed of the (receding) galaxy NGC7531 relative to the earth, measurements of speed being taken at different points on galaxy Circles represent measurements at 133 o to horizon; pluses at 43 o What can you observe?

34 3D Scatter Plot Visicube has a tool specifically for 3D scatter plots Third variate expressed as a vertical axis and widget lets you take slices at different heights Here we have same dataset but X and Y are positions, and Z axis is velocity ie layered by velocity here 3 rd layer ( km/sec) Observations less than 1500 km/sec highlighted in yellow (almost allowing 4D) Conclusion?

35 3D Scatter Plots XRT/3d Here is an alternative approach, using 3D plotting does this work?

36 Extending to Higher Numbers of Variables Additional variables can be visualized by colour and shape coding IRIS Explorer ( a scientific visualization system!) used to visualize data from BMW Five variables displayed using spatial arrangement for three, colour and object type for others Notice the clusters But there are clearly limits to how much this will scale Kraus & Ertl, U Stuttgart

37 Multivariate Visualization Techniques Software: Techniques designed for any number of variables Scatter plot matrices Parallel co-ordinates Glyph techniques Xmdvtool Matthew Ward Acknowledgement: Many of images in following slides taken from Ward s work

38 What are these?

39 Multivariate Visualization Example of iris data set 150 observations of 4 variables (length, width of petal and sepal) Check wikipedia for explanations of petals & sepals Techniques aim to display relationships between variables the analytical task Challenge in visualization is to design the visualization to match the analytical task

40 Multivariate Visualization

41 Scatter Plot Matrices

42 Scatter Plot Matrices For table data of M variables, we can look at pairs in 2D scatter plots The pairs can be juxtaposed: C B A With luck, you may spot correlations between pairs as linear structures or you may observe clusters A B C

43 Scatter Plot Matrix Iris Data Set

44 Scatter Plot Matrix Car Data Set Data represents 7 aspects of cars: what relationships can we notice? For example, what correlates with high MPG?

45 Parallel Coordinates

46 Parallel Coordinates A B C D E F create M equidistant vertical axes, each corresponding to a variable each axis scaled to [min, max] range of the variable each observation corresponds to a line drawn through point on each axis corresponding to value of the variable

47 Parallel Coordinates A B C D E F correlations may start to appear as the observations are plotted on the chart here there appears to be negative correlation between values of A and B for example this has been used for applications with thousands of data items

48 Parallel Coordinates Iris Data

49 Parallel Coordinates Example Detroit homicide data 7 variables 13 observations

50 Parallel Coordinates Concept due to Alfred Inselberg Conceived the idea as a research student in 1959 idea gradually refined over next 40 years

51 Parallel Coordinates Parallel coordinates is a clever mechanism for transforming geometry from one space to another To get a handle on the idea, consider two variables X,Y In parallel coordinates, a point (X,Y) becomes what? A line becomes what? Use this space to sketch the answers Why is the ordering of the axes important?

52 The Screen Space Problem All techniques, sooner or later, run out of screen space Parallel co-ordinates Usable for up to 150 variates Unworkable greater than 250 variates Remote sensing: 5 variates, 16,384 observations)

53 Brushing as a Solution Brushing selects a restricted range of one or more variables Selection then highlighted

54 Scatter Plot Use of a brushing tool can highlight subsets of data..now we can see what correlates with high MPG

55 Parallel Coordinates Brushing picks out the high MPG data Can you observe the same relations as with scatter plots? More or less easy?

56 Parallel Coordinates Here we highlight high MPG and not 4 cylinders

57 REDUCING COMPLEXITY IN MULTIVARIATE DATA EXPLORATION

58 Clustering as a Solution Success has been achieved through clustering of observations Hierarchical parallel coordinates Cluster by similarity Display using translucency and proximity-based colour

59 Comparison One of 3 clusters

60 Hierarchical Parallel Co-ordinates

61 Reduction of Dimensionality of Variable Space Reduce number of variables, preserve information Principal Component Analysis Transform to new co-ordinate system Hard to interpret Hierarchical reduction of variable space Cluster variables where distance between observations is typically small Choose representative for each cluster Subgroup has then been identified showing what? 42 dimensions, 200 observations

62 Glyph Techniques

63 Glyph Techniques Map data values to geometric and colour attributes of a glyph or marker symbol Very many types of glyph have been suggested: Star glyphs Faces Arrows Sticks Shape coding

64 Glyph Layouts How do we place the glyphs on a chart? Sometimes there will be a natural location for example? If not two of the variates can be allocated to spatial position, and the remainder to the attrributes of the glyph

65 Glyph Techniques Star Plots Each observation represented as a star Each spike represents a variable Length of spike indicates the value

66 Glyph Techniques Star Plots Each observation represented as a star Each spike represents a variable Length of spike indicates the value Crime in Detroit

67 Star Glyphs Iris Data Set

68 Chernoff Faces Chernoff suggested use of faces to encode a variety of variables - can map to size, shape, colour of facial features - human brain rapidly recognises faces

69 Chernoff Faces Here are some of the facial features you can use

70 Chernoff Faces Demonstration applet at:

71 Chernoff s Face.. And here is Chernoff s face

72 Stick Figures Glyph is a matchstick figure, with variables mapped to angle and length of limbs - different angles that may be varied are shown As with Chernoff faces, two variables are mapped to display axes Stick figures useful for very large data sets Texture patterns emerge Idea due to RM Pickett & G Grinstein

73 Stick Figures 5D image data from Great Lakes region

74 Shape Coding Suitable where a variable has a Boolean value, ie on/off A data item is represented as an array of elements, each element corresponding to a variable shade in box if value of corresponding variable is on Arrays laid out in a line, or plane, as with other icon-based methods

75 Shape Coding Time series of NASA earth observation data

76 Daisy Charts Dry * variables and their values placed around circle Leeds Wet Showery * lines connect the values for one observation Sahara Saturday Amazon Sunday This item is { wet, Saturday, Amazon }

77 Daisy Charts - Underground Problems

78 Daisy Charts News Analysis Four variates: day, source, search terms, keywords