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

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!

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-1BOOK-2 NameNumberNameNumber Smith Smith Jones Smith Jones Jones

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 ~ B). National Virtual Observatory (aggregated astronomical data) (10 exabytes by 2010 ~ B?). Sensor networks (Micro and Nano -sensor networks) (10 zettabytes by 2015 ~ B?). WWW will continue to grow (and other text collections) (10 yottabytes by 2020 ~ B?). Micro-arrays, gene-chips and genome sequence data (10 gazillobytes by 20?0 ~ B?). Useful information must be teased out of these large volumes of data. That’s data mining. Correct Name?

EOS Data Mining example TIFF image Yield Map 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) 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.

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???

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 Gene2 Gene1Gene3 Gene8Gene6 Gene9 Gene5 Gene4Gene7

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??

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).

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 LearningData Mining Standard querying Searching and Aggregating Supervised Learning – Classificatior Regression Unsupervised Learning - Clustering Association Rule Mining Data Prospecting Fractals, … Walmart vs. KMart

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

Our Approach vertical data horizontally  Compressed, datamining-ready, data structure, Peano-tree (Ptree) 1 process vertical data horizontally horizontal data vertically 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

A table, R(A 1..A n ), is a horizontal structure (set of horizontal records) processed vertically (vertical scans) Vertical structure processed horizontally (ANDs) Ptrees vertical partition ; compress each vertical bit file into a basic Ptree; horizontally process these Ptrees using a multi-operand logical AND R( A 1 A 2 A 3 A 4 ) --> R[A 1 ] R[A 2 ] R[A 3 ] R[A 4 ] R 11 R 12 R 13 R 21 R 22 R 23 R 31 R 32 R 33 R 41 R 42 R Horizontal structure Processed vertically (scans) P 11 P 12 P 13 P 21 P 22 P 23 P 31 P 32 P 33 P 41 P 42 P Dimensional Ptrees are built by recording the truth of the predicate “pure 1” recursively on halves, until there is purity, P 11 : 1. Whole file is not pure1  st half is not pure1  nd half is not pure1  st half of 2 nd half not  nd half of 2 nd half is  st half of 1 st of 2 nd is  nd half of 1 st of 2 nd not  0

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.

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

A Count Ptree Counts are the ultimate goal, but P1trees are more compressed and produce the needed counts quite quickly.  Peano or Z-ordering  Pure (Pure-1/Pure-0) quadrant  Root Count  Level  Fan-out  QID (Quadrant ID) ( 7, 1 ) ( 111, 001 )

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

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.

Ptree dimension (1-D, 2-D, …)  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.

Ordering of Triangle Mesh 1,2 1,3 1,0 1,1 1 1,3,3 1,3,21,3,0 1,3,1

The Half Sphere up to 3 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.

Challenge 1: Many Records  Typical question How many records satisfy given conditions on the attributes?  Typical answer In record-oriented database systems  Database scan: O(N) Sorting / indexes?  Unsuitable for many problems  P-Trees Compressed, vertical, bit-column storage Bit-wise AND replaces database scan

1-D Ptrees: Compression Aspect

P-Trees: Ordering Aspect  Compression relies on long sequences of 0 or 1  Images Neighboring pixels are more likely to be similar using Peano-ordering (space filling curve)  Other data? Peano-ordering can be generalized Peano-order sorting of attributes to maximize compression.

Peano-Order Sorting

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

So Far  Answer to challenge 1: Many records P-Tree concept allows scaling better than O(N) for AND (equivalent to database scan) Introduced effective generalization to non-spatial data (thesis)  Challenge 2: Many attributes Focus: Classification Curse of dimensionality Some algorithms suffer more than others

Curse of Dimensionality  Many standard classification algorithms E.g., decision trees, rule-based classification For each attribute 2 halves: relevant  irrelevant How often can we divide by 2 before small size of “relevant” part makes results insignificant?  Inverse of Double number of rice grains for each square of the chess board  Many domains have hundreds of attributes Occurrence of terms in text mining Properties of genes

Possible Solution  Additive models Each attribute contributes to a sum Techniques exist (statistics)  Computationally intensive  Simplest: Naïve Bayes x (k) is value of k th attribute Considered additive model  Logarithm of probability additive

Semi-Naïve Bayes Classifier  Correlated attributes are joined Has been done for categorical data  Kononenko ’91, Pazzani ’96  Previously: Continuous data discretized  New (thesis) Kernel-based evaluation of correlation

Results  Error decrease in units of standard deviation for different parameter sets  Improvement for wide range of correlation thresholds: 0.05 (white) to 1 (blue)

So Far  Answer to challenge 1: More records Generalized P-tree structure  Answer to challenge 2: More attributes Additive algorithms Example: Kernel-based semi-naïve Bayes  Challenge 3: New subject domains Data on a graph Outlook: Data with time dependence

Standard Approach to Data Mining  Conversion to a relation (table) Domain knowledge goes into table creation Standard table can be mined with standard tools  Does that solve the problem? To some degree, yes But we can do better

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

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

Data on a Graph: Old Hat?  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

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

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

AHR 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 essential AHR essential AHR not essential

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)

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

KDD-Cup 02: Honorable Mention NDSU Team

e0e0 e1e1 e2e2 e3e o1o1 o2o2 o3o3 o0o0 Gene- Experiment- Organism Cube 3-D gene expression cube Organism Dimension Table 30001Mus musculus mouse Saccharomyces cerevisiae yeast 1850Drosophila melanogaster fly 30001Homo sapienshuman Genome Size (million bp) Vert Species Organism Gene Dimension Table 0011PolyA-Tail.9.1 StopCodonDensity apopmitomeioapop Function Ribo Nucl RiboMyta SubCell-Location Experiment Dimension Table (MIAME) 1asa42 1aca42 0hsb22 1hca23 NMHSADAD EDED STZSTZ CTYCTY STRSTR UNVUNV PIPI LABLAB g0g0 g1g1 g2g2 g3g3 e0e0 e1e1 e2e2 e3e3 17, 78 12, 60 Mi, 40 1, 48 10, , , , , 45 Pl, 43 Gene-Org Dim Table chromosome,length

g0g0 g1g1 g2g2 g3g3 g0g0 g1g1 g2g2 g3g3 g0g0 g1g1 g2g2 g3g3 Protien Interaction Pyramid (2-hop interactions) Gene Dimension Table 0011PolyA-Tail.9.1 StopCodonDensity apo p mit o mei o apo p Function Rib o NuclRib o Myt a SubCell- Location g4g g3g g2g g1g GENEGENE P ol y- A SCD1SCD1 MitoMito MeioMeio apopapop NuclNucl RiboRibo MytaMyta SCD2SCD2 SCD3SCD3 SCD4SCD4 Gene Dimension Table (Binary)