1. Pradnya Khutafale, Peter Lucas, Computer Science Department
Spatial Data Mining CS 697
Assignment 1
February 16, 2010
Pradnya Khutafale, Peter Lucas,
and Chris Maio
Advisor: Dr. Wei Ding
Computer Science Department
UMass Boston 1

2. Discovery of Climate Indices using Clustering
Principal Investigators
  Vipin Kumar (University of Minnesota)
  Michael Steinbach (University of Minnesota)
Collaborators
  Steven Klooster (Cal. State Univ, Monterey Bay)
  Christopher Potter (NASA Ames Research Center)
  Pang-Ning Tan (Michigan State University) 2

3. Discovery of Climate Indices using Clustering
Researchers
Department of Computer Science
and Engineering
Michael Steinbach
Pang-Ning Tan
Vipin Kumar
Leading educators in the field of spatial data mining
Investigating the use of data mining techniques to find interesting spatio-temporal patterns from Earth Science
Regarded as leaders in the field of climate indices identification and data mining research
Discovery of Climate Indices using Clustering

4. Discovery of Climate Indices using Clustering
Researchers
NASA & Ames Research Center team members:
Chris Potter
Steven Klooster
Both scientists work on modeling the environment and finding technical solutions to environmental problems.
Working on cutting edge computer science methods and technologies to be utilized for finding solutions to complex environmental problems.
Discovery of Climate Indices using Clustering

5. Discovery of Climate Indices using Clustering
Presentation Outline
Background: (Chris)
Climate Change
Earth System Linkages
Earth Science Data and Climate Indices (Chris)
Existing Eigenvalue Techniques and Limits (Pete)
New Clustering Based Methodology (Pete)
Results and Comparisons (Pradnya)
Conclusions and Future Research (Pradnya and Pete) 5
Discovery of Climate Indices using Clustering

6. Discovery of Climate Indices using Clustering
Presentation Outline
Background:
Climate Change
Earth System Linkages
Earth Science Data and Climate Indices
Existing Eigenvalue Techniques and Limitations
New Clustering Based Methodology
Results and Comparisons
Conclusions and Future Research 6
Discovery of Climate Indices using Clustering

7. Discovery of Climate Indices using Clustering
Climate Change
Background
Extinctions of plants and animals
Rise in global temperatures
Coastal systems and the enormous ecological and socioeconomic benefits they provide are under threat from a predicted rise in sea-level and increased occurrence and intensity of storm surges associated with current trends in global warming
The United Nations intergovernmental panel on climate change known as the IPCC a group of hundreds of international scientist have predicted a 1 meter rise in sea-level by This would cause Major changes to coastlines and inundation of low-lying areas
In a report by Kischen and other some of which are in our department, There would be an increase reoccurance and elevation of the hundred year flood in the Boston area. In this report it states that the hundred year flood may reoccur at intervals of as little as 8 years with an increase in elevation from the present 3 meters to 4.8 meters.
IPCC Predictions
Sea-level Rise 7
Discovery of Climate Indices using Clustering

8. Climate Change Impacts
Background
Climate Change Impacts
Climate Change leads to significant changes of rainfall and soil moisture (drought and flood)
Agricultural activities (crop growth cycle) and world food supplies are affected greatly by climatic factors (desertification)
Climate change increases the frequency, intensity, and distribution of natural hazards, such as hurricanes and other storms 8
Discovery of Climate Indices using Clustering

9. Discovery of Climate Indices using Clustering
Background
Earth System Linkages
Ocean, atmosphere, and land processes are highly coupled
Climate phenomena in one location can affect the climate at a far away location this is known as climate teleconnections
Understanding climate “teleconnections” key to knowing and predicting ecosystem response to climate change
Discovery of Climate Indices using Clustering

10. Discovery of Climate Indices using Clustering
Presentation Outline
Background:
Climate Change
Earth System Linkages
Earth Science Data and Climate Indices
Existing Eigenvalue Techniques and Limitations
New Clustering Based Methodology
Results and Comparisons
Conclusions and Future Research 10
Discovery of Climate Indices using Clustering

11. Time Series Data Sea Surface Temperature (SST)
Earth Science Data
Time Series Data
Sea Surface Temperature (SST)
Sea Level Pressure (SLP)

12. Discovery of Climate Indices using Clustering
Earth Science Data
Data Acquisition
There are thousands of floats, buoys, and other remote sensing devises throughout the oceans collecting enormous amount of oceanographic data periodically transmitted to shore via satellite (Naval Research Laboratory). 12
Discovery of Climate Indices using Clustering

13. Preprocessing Required
Earth Science Data
Preprocessing Required
Spatial and temporal nature of data poses a number of challenges
Noisy
Cycles of varying lengths and regularity
Strong seasonal component
Displays long term trends
Displays temporal and spatial Autocorrelation
Interested in patterns represent deviations from normal seasonal variation (El Nino and Global Warming) Cycles
Monthly Z score effective at removing seasonal component 13
Discovery of Climate Indices using Clustering

14. Discovery of Climate Indices using Clustering
Climate Indices = Data time series that summarize physical behavior of different regions of ocean and atmosphere
Distill climate variability at regional or global scale into a single and manageable time series
Usually based on sea level pressure and sea surface temperature
Past methods of indication painstakingly slow and tedious 14
Discovery of Climate Indices using Clustering

15. Discovery of Climate Indices using Clustering
Climate Index: Nino 1+2 15
Discovery of Climate Indices using Clustering

16. Discovery of Climate Indices using Clustering16
Discovery of Climate Indices using Clustering

17. Climate Indices
El Nino Correlations
SST of El Nino correlated indices

18. Detection of Climate Indices
Earth Scientists have devoted a significant amount of time discovering climate indices
Traditional approaches include direct observation of climate phenomena (El Nino)
Use of linear algebra techniques including eigenvalue analysis
Discovery of Climate Indices using Clustering

19. Discovery of Climate Indices using Clustering
Eigenvalue Analysis
Driven by massive amount of data obtained from satellites and remote sensing devises
Provides a way to quickly and automatically detect patterns in large amounts of data
Jason-2 IR satellite image
Discovery of Climate Indices using Clustering

20. Discovery of Climate Indices using Clustering
Eigenvalue Analysis
Eigenvalue techniques include:
Principle Components Analysis (PCA)
Single Value Decomposition (SVD)
Limitations of Eigenvalue Analysis
Weaker signals may be masked by stronger signals
All Discovered signals must be orthogonal to each other making it difficult to attach a physical interpretation to them
Discovery of Climate Indices using Clustering

21. Alternative Clustering Methodology
Climate Indices
Utilization of data mining techniques and enormous amount of remote sensing data to find climate indices
Analysis yields clusters that represent ocean regions with relatively homogeneous behavior
Centroids of these areas summarize behavior particular region
Finding “meaningful” clusters will enable Earth Scientists to better predict changes in climate system
Discovery of Climate Indices using Clustering

22. Benefits of Clustering
Climate Indices
Benefits of Clustering
Discovered signals do not need to be orthogonal or statistically independent of one another
Signals are more easily interpreted
Weaker signals are more readily detected
It provides an efficient way to determine the influence of large set of points (all ocean point) on another large set of points (all land points)
Discovery of Climate Indices using Clustering

23. Results of Clustering Methodology
Climate Indices
Results of Clustering Methodology
Candidate Indices highly correlated to known indices representing rediscovery of well known indices and validation of methods
Variants to well-known indices which may be better predictors of land behavior for some regions of land
Cluster centroids that have medium or low correlation with known indices may represent new Earth science phenomena
Discovery of Climate Indices using Clustering

24. Discovery of Climate Indices using Clustering
Presentation Outline
Background:
Climate Change
Earth System Linkages
Earth Science Data and Climate Indices
Existing Eigenvalue Techniques and Limitations
New Clustering Based Methodology
Results and Comparisons
Conclusions and Future Research 24
Discovery of Climate Indices using Clustering

25. Finding Spatial or Temporal Patterns using SVD Analysis
Eigenvalue Techniques
Finding Spatial or Temporal Patterns using SVD Analysis
SVD: Singular Value Decomposition
Earth Scientists typically used SVD analysis to identify climate indices
Goal : To find a new set of attributes that better describe variability in the data, through dimensionality reduction
Its operation can be thought of as revealing the internal structure of the data in a way which best explains the variance in the data
Karl Pearson, Statistician
1857 – 1936
Discovery of Climate Indices using Clustering

26. Overview of SVD Analysis
Eigenvalue Techniques
Overview of SVD Analysis
These techniques applied to a data set in the form of a data matrix (m by n)
m rows (objects)
n columns (attributes)
Data Matrix: a variation of
record data in that it consists
of all numeric attributes
Example of a data matrix
Discovery of Climate Indices using Clustering

27. Overview of SVD Analysis
Eigenvalue Techniques
Overview of SVD Analysis
Assume the data objects in a matrix all have the same fixed set of attributes
Each data object can be thought of as a point, or Vector in multidimensional space
Each spatial dimension
represents a distinct attribute describing the object
Discovery of Climate Indices using Clustering

28. Simple Example of SVD Analysis
Just using web, it’s hard to find intuitive explanation of SVD
Again, SVD is a way to expose underlying details of matrix
Simple Example using Golf : 3 golfers play 9 holes, par every hole
How to predict score for a player on a given hole?
Assume two vectors, Player Ability and Hole Difficulty
Predicted score = Player Ability * Hole Difficulty
Hole difficulty is Left Singular Vector
Player Ability is Right Singular Vector
Discovery of Climate Indices using Clustering

29. Finding Spatial or Temporal Patterns using SVD Analysis
Eigenvalue Techniques
Finding Spatial or Temporal Patterns using SVD Analysis
Given a data matrix, whose rows consist of time series from various points on the globe, the objective is to discover the strong temporal or spatial patterns in the data
SVD decomposes a matrix into two sets of patterns, which, that correspond to a set of spatial patterns (left singular vectors) and a set of temporal patterns (right singular vectors).
We can plot the temporal patterns regular line plot and the spatial patterns on a spatial grid and visualize these patterns.
Discovery of Climate Indices using Clustering

30. Example : Plotting SST (Sea Surface Temp)
Eigenvalue Techniques
Example : Plotting SST (Sea Surface Temp)
Temporal pattern of SST (blue)
plotted against the NINO4 index (green)
Strongest spatial pattern of SST
Discovery of Climate Indices using Clustering

31. Limitations of SVD Analysis
Eigenvalue Techniques
Limitations of SVD Analysis
Only useful for finding a few of the strongest signals
Smaller patterns in data may be obscured
Signals must be orthogonal to each other (statistically independent)
May not identify all patterns in data
Efficiency can be a concern
Discovery of Climate Indices using Clustering

32. Discovery of Climate Indices using Clustering
Presentation Outline
Background:
Climate Change
Earth System Linkages
Earth Science Data and Climate Indices
Existing Eigenvalue Techniques and Limitations
New Clustering Based Methodology
Results and Comparisons
Conclusions and Future Research 32
Discovery of Climate Indices using Clustering

33. Clustering Based Methodology for the Discovery of Climate Indices
Clustering Methods
Clustering Based Methodology for the Discovery of Climate Indices
Two key steps for finding climate indices
Find candidate indices using clustering
Evaluate these candidate indices for Earth Science significance
Clustering Method used for this study:
SNN Clustering Algorithm Method
“Searching Nearest Neighbors”
Discovery of Climate Indices using Clustering

34. Finding Candidate Indices Using Clustering
Clustering Methods
Finding Candidate Indices Using Clustering
SNN Clustering Algorithm
First finds the nearest neighbors of each data point
Next, redefines the similarity between pairs in terms of how many nearest neighbors the two points share
Using this definition of similarity the algorithm identifies core points
These Core Points are used to build clusters
SNN algorithms have time complexity O(n*log(n))
Graph of functions n(log n) and n
Discovery of Climate Indices using Clustering

35. Evaluation of Candidate Indices
Clustering Methods
Evaluation of Candidate Indices
Indices must be evaluated in terms of Earth Science significance
(meaning the strength of the association between the behavior of a candidate index and land climate)
Goal is to find a numerical measure of the strength and association between the behavior of an index and land climate
To evaluate influence of climate indices on land, the researchers use Area-Weighted Correlation
Definition : The weighted average of the correlation of the candidate index with all land points, where weight is based on the area of the land grid point
Discovery of Climate Indices using Clustering

36. Calculating Area-weighted Correlation
Clustering Methods
Step 1 : Compute the correlation of the time series of the candidate index with the same time series associated with each land point
Step 2 : Compute the weighted average of the correlations, where the weight associated with each land point is its area
The resulting area-weighted correlation
can be at most 1, min is 0
General Formula for W.A.
Wc = weight of each value M
Mc = some value to average
General Correlation Index. 1 being strongest
Discovery of Climate Indices using Clustering

37. Comparison of Area-Weighted Correlations
Clustering Methods
Comparison of Area-Weighted Correlations
Development of Baseline to compare the values of area weighted correlations of candidate indices
Histogram of area weighted correlation of 1000 random time series
No time series has a WAC >.1 This will be the baseline, and indicates whether a good candidate index
Discovery of Climate Indices using Clustering

38. Validation of Comparison Baseline
Clustering Methods
Validation of Comparison Baseline
Below shown are weighted area correlations of 11 known indices
Note that 10/11 indices have a weighted area correlation of >.1
If candidate index shows weighted area correlation >.1, investigate
Graph of Weighted Area Correlation of
Well know Climate Indices
Discovery of Climate Indices using Clustering

39. Discovery of Climate Indices using Clustering
Presentation Outline
Background:
Climate Change
Earth System Linkages
Earth Science Data and Climate Indices
Existing Eigenvalue Techniques and Limitations
New Clustering Based Methodology
Results and Comparisons
Conclusions and Future Research 39
Discovery of Climate Indices using Clustering

40. SST Based Candidate Indices
Results
SST Based Candidate Indices
Used SST data over time period from 1958 and 1998 and applied SNN clustering
Obtained 107 clusters
Cluster centroids were used to categorize clusters into G0,G1,G2 and G3 groups depending on their correlation to known indices
Discovery of Climate Indices using Clustering

41. 107 Sea Surface Temperature (SST) Clusters
Results
107 Sea Surface Temperature (SST) Clusters
Find Correlation with known index like SOI, NINO1+2 etc
Find Area Weighted correlation with land
Discovery of Climate Indices using Clustering

42. SST Cluster Correlation
Results
SST Cluster Correlation
Correlation between known indices with SST cluster centroids and SVD Components
Discovery of Climate Indices using Clustering

43. G0: Clusters with correlation to known indices >= 0.8
Results
G0: Clusters with correlation to known indices >= 0.8
NINO 1+2
NINO 3
NINO 3.4
NINO 4
Very highly correlated
Rediscovered well-known indices
Serve to validate the approach
Discovery of Climate Indices using Clustering

44. G0: SST Cluster Correlation
Results
G0: SST Cluster Correlation
Correlation between known indices with SST cluster centroids and SVD Components
Discovery of Climate Indices using Clustering

45. G1: Clusters with correlation to known indices from 0.4 to 0.8
Results
G1: Clusters with correlation to known indices from 0.4 to 0.8
Discovery of Climate Indices using Clustering

46. G1: Cluster 29 vs. El Nino Indices
Results
G1: Cluster 29 vs. El Nino Indices
Cluster 29
Discovery of Climate Indices using Clustering

47. G2: Clusters with correlation to known indices from 0.25 to 0.4
Results
G2: Clusters with correlation to known indices from 0.25 to 0.4
Less correlated
May represent new earth science
phenomena
May be new index
Discovery of Climate Indices using Clustering

48. Cluster 62 vs. El Nino Indices
Results
Cluster 62 vs. El Nino Indices
Cluster 62
Discovery of Climate Indices using Clustering

49. G3: Clusters with correlation to known indices <= 0.25
Results
G3: Clusters with correlation to known indices <= 0.25
Less correlated
May represent new earth science
phenomena or weaker version of
known phenomena
New index
Discovery of Climate Indices using Clustering

50. SLP­based Candidate Indices
Results
SLP­based Candidate Indices
SLP data over time period from
1958 to 1998
Correlation measured as difference
of all pairs of cluster centriods
Negative correlation are interesting
candidates
25 Clusters found
25 Sea Level Pressure Based Clusters
Discovery of Climate Indices using Clustering

51. SLP Clusters Pairwise Correlation
Results
SLP Clusters Pairwise Correlation
Note :Only negative correlation values shown
Discovery of Climate Indices using Clustering

52. Comparison with SVD based Indices
Comparisons
Comparison with SVD based Indices
Correlation of Cluster Centroids with land temperature
Correlation of first 30 SVD components with land temperature
Discovery of Climate Indices using Clustering

53. SST Clusters : Performance Comparison
Comparisons
SST Clusters : Performance Comparison
Correlation for known indices with SST cluster centroids and SVD components
Discovery of Climate Indices using Clustering

54. SLP Clusters : Performance Comparison
Comparisons
SLP Clusters : Performance Comparison
Discovery of Climate Indices using Clustering

55. SLP clusters Performance Comparison
Comparisons
SLP clusters Performance Comparison
Area-weighted correlation for known indices with SLP cluster centroids and SVD components
Discovery of Climate Indices using Clustering

56. Discovery of Climate Indices using Clustering
Conclusions
Demonstrated that clustering is a viable alternative to eigenvalue based approach for the discovery of climate indices
Can replicate many well-known climate indices
Have also discovered variants of known indices that may be “better” for some regions
Some indices may represent new Earth Science phenomena
No need for discovered indices to be orthogonal
No need to pre-select the area to analyze
Discovery of Climate Indices using Clustering

57. Discovery of Climate Indices using Clustering
Future Work
Investigation of candidate indices by Earth Scientists
Investigate whether there are climate indices that cannot be represented by clusters
Noise elimination and other preprocessing improvements
Aggregation
Discovery of Climate Indices using Clustering

58. QUESTIONS ???