1. William Perrizo Dept of Computer Science North Dakota State Univ.
Data Mining and Data Warehousing, many-to-many Relationships, applications
William Perrizo
Dept of Computer Science North Dakota State Univ.

2. Why Mining Data? Parkinson’s Law (for data)
Data expands to fill available
storage (and then some)
Disk-storage version of Moore’s law
Capacity  2 t / 9 months
Available storage doubles every 9 months!

3. Another More’s Law: More is Less
The more volume, the less information. (AKA: Shannon’s Canon)
A simple illustration: Which phone book is more helpful?
BOOK-1 BOOK-2
Name Number Name Number
Smith Smith
Jones Smith
Jones
Jones

4. Awash with data!
US EROS Data Center archives Earth Observing System (EOS) remotely sensed images (RSI), satellite and aerial photo data (10 petabytes by 2005 ~ 1016 B).
National Virtual Observatory (aggregated astronomical data) (10 exabytes by ~ 1019 B?).
Sensor networks (Micro and Nano -sensor networks) (10 zettabytes by 2015 ~ 1022 B?).
WWW will continue to grow (and other text collections) (10 yottabytes by 2020 ~ 1025 B?).
Micro-arrays, gene-chips and genome sequence data (10 gazillobytes by 20?0 ~ 1028 B?).
Useful information must be teased out of these large volumes of data That’s data mining.
Correct Name?

5. EOS Data Mining example
This dataset is a 320 row and 320 column (102,400 pixels) spatial file with 5 feature attributes (B,G,R,NIR,Y). The (B,G,R,NIR) features are in the TIFF image and the Y (crop yield) feature is color coded in the Yield Map (blue=low; red=high)
TIFF image
Yield Map
What is the relationship between the color intensities and yield? We can hypothsize:
hi_green and low_red  hi_yield which, while not a simply SQL query result, is not surprising. Data Mining is more than just confirming hypotheses
The stronger rule, hi_NIR and low_red  hi_yield is not an SQL result and is surprising. Data Mining includes suggesting new hypotheses.

6. Another Precision Agriculture Example Grasshopper Infestation Prediction
Grasshopper caused significant economic loss each year.
Early infestation prediction is key to damage control.
Association rule mining on remotely sensed imagery
holds significant promise to achieve early detection.
Can initial infestation be determined from RGB bands???

7. Gene Regulation Pathway Discovery
Results of clustering may indicate, for instance, that nine genes are involved in a pathway.
High confident rule mining on that cluster may discover the relationships among the genes in which the expression of one gene (e.g., Gene2) is regulated by others. Other genes (e.g., Gene4 and Gene7) may not be directly involved in regulating Gene2 and can therefore be excluded (more later).
Gene1
Gene2, Gene3
Gene4, Gene 5, Gene6
Gene7, Gene8
Gene9
Clustering
ARM
Gene4
Gene7
Gene1
Gene3
Gene8
Gene6
Gene9
Gene5
Gene2

8. Sensor Network Data Mining
Micro, even Nano sensor blocks are being developed
For sensing
Bio agents
Chemical agents
Movements
Coatings deterioration
etc.
There will be billions, even trillions of
individual sensors creating mountains of data.
The data must be mined for it’s meaning.
Other data requiring mining:
shopping market basket analysis (Walmart)
Keywords in text (e.g., WWW)
Properties of proteins
Stock market prediction
Astronomical data
UNIFIED BASES OF ALL THIS DATA??

9. Data Mining?
Querying asks specific questions and expect specific answers.
Data Mining goes into the MOUNTAIN of DATA,
and returns with information gems (rules?)
But also, some fool’s gold?
Relevance and interestingness analysis, serves as an
assay (help pick out the valuable information gems).

10. Data Mining versus Querying
There is a whole spectrum of techniques to get information from data:
On the Query Processing end, much work is yet to be done (D. DeWitt, ACM SIGMOD’02).
On the Data Mining end, the surface has barely been scratched.
But even those scratches had a great impact – becoming the biggest corporation in
the world and filing for bankruptcy
SQL
SELECT
FROM
WHERE
Complex queries
(nested, EXISTS..)
FUZZY query,
Search engines,
BLAST searches
OLAP (rollup, drilldown, slice/dice..
Machine Learning
Data Mining
Standard querying
Searching and Aggregating
Supervised Learning – Classificatior Regression
Unsupervised Learning - Clustering
Association Rule Mining
Data Prospecting
Fractals, …
Walmart vs. KMart

11. Data Mining
Knowledge
Data mining: the core of the knowledge discovery process.
Pattern Evaluation
Data Mining
OLAP
Classification
Clustering
ARM
Task-relevant Data
Data Warehouse: cleaned, integrated, read-only, periodic, historical raw database
Selection
Feature extraction, tuple selection
Data Cleaning/Integration:
missing data, outliers,
noise, errors
Raw Data

12. Our Approach
Compressed, datamining-ready, data structure, Peano-tree (Ptree)1 process vertical data horizontally
Whereas, standard DBMSs process horizontal data vertically
Facilitate data mining
Address curses of scalability and dimensionality.
Compressed, OLAP-ready data warehouse structure, Peano Data Cube (PDcube)1
Facilitates OLAP operations and query processing.
Fast logical operations on Ptrees are used.
1 Technology is patent pending
by North Dakota State University

13. --> R[A1] R[A2] R[A3] R[A4]
A table, R(A1..An), is a horizontal
structure (set of horizontal records)
Ptrees vertical partition; compress each vertical bit file into a basic Ptree;
horizontally process these Ptrees using one multi-operand logical AND operation.
processed vertically (vertical scans)
R( A1 A2 A3 A4)
--> R[A1] R[A2] R[A3] R[A4]
R11 R12 R13 R21 R22 R23 R31 R32 R33 R41 R42 R43
Horizontal structure
Processed vertically
(scans) 1
1-Dimensional Ptrees are built by recording the truth of the predicate “pure 1” recursively on halves, until there is purity, P11:
1. Whole file is not pure1 0
2. 1st half is not pure1  0
3. 2nd half is not pure1  0
0 0
P11 P12 P13 P21 P22 P23 P31 P32 P33 P41 P42 P43
0 0
0 1 10
1 0 01
1 0
0 1
7. 2nd half of 1st of 2nd not 0
0 0
0 1 10
4. 1st half of 2nd half not  0
0 0
6. 1st half of 1st of 2nd is  1
0 0
0 1 1
5. 2nd half of 2nd half is  1
0 0
0 1
Eg, to count, s, use “pure ”: level
P11^P12^P13^P’21^P’22^P’23^P’31^P’32^P33^P41^P’42^P’43 = level =2
level

14. Ptrees
Ptrees are fixed-size-run-length-compressed, lossless, vertical, structures representing the data, that facilitate fast logical operations on vertical data.
The most useful form of a Ptree is the predicate-Ptree e.g. (from previous slide) Pure1-tree or P1tree (1-bit at a node iff the corresponding half is pure1 or NonPure0-tree or NP0tree (1 iff half is not pure0).
So far, Ptrees have all been 1-dimensional (recursively halving the bit file),
Ptrees for spatial data are usually 2-dimensional (recursively quartering, in Peano order),
Ptrees can be 3, 4, etc. –dimensional.

15. A 2-Dimensional Pure1tree
A 2-D P1tree node is 1 iff that quadrant is purely 1-bits, e.g.,
A bit-file (from, e.g., a 2-D image)
The corresponding raster ordered spatial matrix 1 1 1 1 1 1 1 1 1 1 1

16. A Count Ptree Counts are the ultimate goal, but P1trees are more compressed and produce the needed counts quite quickly.
001
level 16 8 15
level 3 4 1
level
level 1 2 3 2 3
111
Peano or Z-ordering
Pure (Pure-1/Pure-0) quadrant
Root Count
Levels: or just 3, 2, 1, 0
Fan-out = 4
QID (Quadrant ID)
( 7, 1 )
( 111, 001 )

17. NP0tree
NP0tree: Node=1 iff that sub-quadrant is not purely 0s NP0 and P1 are examples of <predicate>trees: node=1 iff sub-quadrant satisfies <predicate> 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

18. Logical Operations on P-trees
Operations are level by level
Consecutive 0’s holes can be filtered out
E.g., We only need to load quadrant with Qid 2 for ANDing NP0-tree1 and NP0-tree2.

19. Ptree dimension
The dimension of the Ptree structure is a user chosen parameter
It can be chosen to fit the data
Relations in general are 1-D (fanout=2 trees)
images are 2-D (fanout=4 trees)
solids are 3-D (fanout=8 trees)
Or it can be chosen to optimize compression or increase processing speed.

20. P-Trees: Ordering Aspect
Compression relies on long runs of 0s or 1s
Images
Neighboring pixels are more likely to be similar using Peano-ordering (space filling curve which preserves “closeness”)
Other data?
Peano-ordering can be generalized
Peano-order sorting of attributes to maximize compression.

21. Peano-Order Sorting

22. Impact of Peano-Order Sorting
KNN Speed improvement especially for large data sets
Less than O(N) scaling for all algorithms

23. Content Hierarchical Triangle Mesh (HTM)
Peano Triangle Mesh Tree (PTM-tree)
SDSS

24. Subdivisions of the sphere
Sphere is divided into triangles
Triangle sides are always great circle segments.

25. Comparison of HTM and PTM-trees
1,2
1,3
1,0
1,1 1
1,3,3
1,3,2
1,3,0
1,3,1
1,2
1,1
1,0
1,3 1
1,1,2
1,1,0
1,1,1
1.1.3
Ordering of PTM-tree
Ordering of HTM

26. PTM-tree up to 2 Levels
Traverse the south hemisphere in the revere direction (just the identical pattern pushed down instead of pulled up, arriving at the Southern neighbor of the start point.

27. PTM-tree up to 3 Levels
LRLR LRLR LRLR LRLR

28. PTM-tree up to 4 Levels
LRLR RLRL LRLR RLRL LRLR RLRL LRLR RLRL

29. A simpler alternative scheme: SDSS
Unlike PTM-tree which partitions the sphere into the 8 faces of an octahedron, SDSS partitions the sphere into a cylinder.
SDSS is stored in Galactic coordinates. Ra is from o. Dec is -90o – 90o.
SDSS keeps the Galactic coordinates. The cylinder has the perimeter of 360o and height of 180o (-90o – 90o).

30. SDSS: Sphere  Cylinder  Plane
90o 0o
-90o
North Plane
South Plane
0o o

31. Structure of SDSS
SDSS is bitwise and quadrant index data structure. Like P-trees, it is built from a bit sequential file (bSQ).
SDSS recursive subdivides the half plain into four squares.
The squares of the same level are in Peano order except the first levels

32. Peano Order bSQ File Subdivision up to 4 Levels
Z Z
Z Z
Z Z
Z Z
Z Z
Z Z
Z Z
Z Z
Z Z
Z Z
Z Z
Z Z
Z Z
Z Z
Z Z
Z Z

33. “Everything should be made as simple as possible, but not simpler”
Albert Einstein

34. Claim: Representation as single relation is not rich enough for graph data
Example: Contribution of a graph structure to standard mining problems
Genomics
Protein-protein interactions
WWW
Link structure
Scientific publications
Citations
Scientific American 05/03

35. Data on a Graph: Old Hat? Google Biological Networks Chemistry
Common Topics
Analyze edge structure
Google
Biological Networks
Sub-graph matching
Chemistry
Visualization
Focus on graph structure
Our work
Focus on mining node data
Graph structure provides connectivity

36. Protein-Protein Interactions
Protein data
From Munich Information Center for Protein Sequences (also KDD-cup 02)
Hierarchical attributes
Function
Localization
Pathways
Gene-related
properties
Interactions
From experiments
Undirected graph

37. *AHR: Aryl Hydrocarbon Receptor Signaling Pathway
Questions
Prediction of a property
(KDD-cup 02: AHR*)
Which properties in neighbors are relevant?
How should we integrate neighbor knowledge?
What are interesting patterns?
Which properties say more about neighboring nodes than about the node itself?
But not:
*AHR: Aryl Hydrocarbon Receptor Signaling Pathway

38. Possible Representations
OR-based
At least one neighbor has property
Example: Neighbor essential true
AND-based
All neighbors have property
Example: Neighbor essential false
Path-based
(depends on maximum hops)
One record for each path
Classification: weighting?
Association Rule Mining:
Record base changes
AHR
essential
AHR
essential
AHR
not essential

39. Association Rule Mining
OR-based representation
Conditions
Association rule involves AHR
Support across a link greater than within a node
Conditions on minimum confidence and support
Top 3 with respect to support:
(Results by Christopher Besemann, project CSci 366)
AHR  essential
AHR  nucleus (localization)
AHR  transcription (function)

40. Classification Results
Problem
(especially path-based representation)
Varying amount of information per record
Many algorithms unsuitable in principle
E.g., algorithms that divide domain space
KDD-cup 02
Very simple additive model
Based on visually identifying relationship
Number of interacting essential genes adds to probability of predicting protein as AHR

41. KDD-Cup 02: Honorable Mention
NDSU Team

42. Gene-Org Dim Table chromosome,length
Gene Dimension Table 1
PolyA-Tail .9 .1
StopCodonDensity
apop
mito
meio
Function
Ribo
Nucl
Myta
SubCell-Location
Organism Dimension Table
3000 1
Mus
musculus
mouse
12.1
Saccharomyces
cerevisiae
yeast
185
Drosophila
melanogaster
fly
Homo sapiens
human
Genome Size (million bp)
Vert
Species
Organism
Gene-Org Dim Table chromosome,length g0 g1 g2 g3 o1 o2 o3 o0
17, , Mi, , 48
10, , 40 ,
16, , Pl, 43 1 e0 e1 e2 e3
Experiment Dimension Table (MIAME) 1 a s 4 2 c h b 3 N M H S AD ED
STZ
CTY
STR
UNV PI
LAB e0 e1 e2 e3
Gene-Experiment-Organism Cube 3-D gene expression cube

43. Protien Interaction Pyramid (2-hop interactions)
SubCell-Location
Myta
Ribo
Nucl
Ribo
Function
apop
meio
mito
apop
StopCodonDensity .1 .1 .1 .9
Gene Dimension Table
PolyA-Tail 1 1
Myta
Ribo
Nuc l
apop Me i o Mi to
SCD 1
SCD 2
SCD 3
SCD 4
Poly-A G E N g0 g1 g2 g3 g0 g1 g2 g3 g0 g1 g2 g3 1 1 1 1 1 1 g1 1 1 1 1 1 1 g2 1 1 1 g3 1 1 1 1 g4
Gene Dimension Table (Binary)