1. 한국방송통신대학교 2013/01/19
통계적 시각화
Statistical Visualization: Small Ideas and Significant Differences
허 명 회 (고려대학교) stat420@korea.ac.kr
⇒
1

2. Background...
§ 통계 그래프 statistical graph → 데이터 시각화 data visualization
§ 文盲 illiteracy, 數盲 innumeracy, 圖盲 graph blind
§ 데이터 기술 data technology (DT)
§ 멋, 재미 artistic and fun!
2013/01/19 myung.hoe.huh
2

3. Divertmento...
- Two Monocycles
play 1 play 2
2013/01/19 myung.hoe.huh
3

4. Outlines...
- Moving Conditioning Plot
- Rotating Data Clouds
- Regression Biplot
- Exploring Many Variables
- Visualizing A Function of Multiple Variables
2013/01/19 myung.hoe.huh
4

5. Moving Conditioning Plot
- Scatterplot can show only two variables (x,y) at a time.
- How to show the third variable z?
- Example: lattice library quakes data (longitude, latitude, depth, magnitude)
2013/01/19 myung.hoe.huh
5

6. Moving Conditioning Plot
- Dynamic Version: Plot (x,y) only for observations with z in      ,
where      ↑ as  (time) passes.
Demo 1, 2
time
    ∣ 
2013/01/19 myung.hoe.huh
6

7. Rotating Data Clouds
- The Case of  ≧   Variables (x,y,z)
- Plot of z vs.  cos   x +  sin   y, for  from 0 to   .
For    , the graph shows the pattern of z vs. x.

For    , the graph shows the pattern of z vs. y.

⋮
z
y
x
2013/01/19 myung.hoe.huh
7

8. Rotating Data Clouds
- Example: mclust library diabetes data (insulin, sspg, glucose)
Demo
the weights given to
x and y.
2013/01/19 myung.hoe.huh
8

9. Regression Biplot
- Linear Regression:  equals     ⋯     ,
  
  

where   ⋯    are  ×  standardized explanatory vectors.
 
 

1. The predicted is directed along the  ×  weight vector   ⋮ .

 

2. For the    ⋯    th case, the predicted equals    ,
 
where   is  ×  explanatory vector observed at the  th case.

3. To explore the explanatory space, we walk on the principal route (vector)
   ×   which is orthogonal to    ×  .
 




2013/01/19 myung.hoe.huh
9

10. Regression Biplot
- Examples: L. Stack Loss data (y = stack.loss, x1,x2,x3)
R. Aerobic Fitness data (y = oxygen uptake, x1,x2,x3,x4,x5,x6)
* Filled circles represent fitted values and open circles represent the observed values.
2013/01/19 myung.hoe.huh
10

11. Exploring Many Variables
- Tour on the Globe:
  
 ×  standardized variables   ⋯   such that ∥  ∥      .

  
*
* *
*
*
*

- Shortest path touring  locations,   ⋯    on the globe (of radius  ):
 
1) Traveling Salesman’s Problem, 2) Hurley’s endlink.
2013/01/19 myung.hoe.huh
11

12. Exploring Many Variables
- Combining Local Views (rather than A Single Global Picture):
- Example: gclus library body parts data,    .
V1 V2 V3 V4 V5 V6 V7 V8 V9
V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V14
V9 V10 V11 V12 V13 V14 V15 V16 V17 V18 V19
V14 V15 V16 V17 V18 V19 V20 V21
Demo
2013/01/19 myung.hoe.huh
12

13. More Topics
- Visualizing A Function of Multiple Variables ...
- Moving Data Pictures ...
2013/01/19 myung.hoe.huh
13

14. http://blog.naver.com/huh4200
2013/01/19 myung.hoe.huh
14