Data Mining, Decision Trees and Earthquake Prediction Professor Sin-Min Lee.

Data Mining, Decision Trees Data Mining, Decision Trees and Earthquake Prediction and Earthquake Prediction

Professor Sin-Min Lee Professor Sin-Min Lee

What is Data Mining?What is Data Mining?

• Process of automatically finding the relationships and patterns, and extracting the meaning of enormous amount of data.

• Also called “knowledge discovery”

ObjectiveObjective

• Extracting the hidden, or not easily recognizable knowledge out of the large data… Know the past

• Predicting what is likely to happen if a particular type of event occurs … Predict the future

ApplicationApplication

• Marketing example– Sending direct mail to randomly chosen

people– Database of recipients’ attribute data (e.g.

gender, marital status, # of children, etc) is available

– How can this company increase the response rate of direct mail?

Application (Cont’d)Application (Cont’d)

• Figure out the pattern, relationship of attributes that those who responded has in common

• Helps making decision of what kind of group of people the company should target

• Data mining helps analyzing large amount of data, and making decision…but how exactly does it work?

• One method that is commonly used is decision tree

Decision TreeDecision Tree

• One of many methods to perform data mining - particularly classification

• Divides the dataset into multiple groups by evaluating attributes

• Decision tree can be explained a series of nested if-then-else statements.

• The Decision Tree is one of the most popular classification algorithms in current use in Data Mining

Decision Tree (Cont’d)Decision Tree (Cont’d)

• Each non-leaf node has a predicate associated, testing an attribute of data

• Leaf node represents a class, or category• To classify a data, start from root node and traverse down the

tree by testing predicates and taking branches

Example of Decision TreeExample of Decision Tree

What is a Decision Tree?What is a Decision Tree?

• 20-Questions Example– Progressive Yes-No Decisions Until an Answer

is Obtained

• 20-Questions Machine at Linens & Things

• Key to the Phylum – classification tool– Carl Linnaeus, Swedish Botanist, 1730’s– Classifies known species:

• Kingdoms, Phyla, Classes, Orders, Families, Genera, and Species

What is a Decision Tree?What is a Decision Tree?

Body Temperature

Root Node

Hibernates

Warm-Blooded

Non-Mammal

Cold-BloodedInternal Node

LeafNode

Yes No

Non-Mammal

Non-Mammal

Four-Legged

Yes No

Mammal

What are Decision Trees Used What are Decision Trees Used For?For?

How to Use a Decision TreeHow to Use a Decision Tree

Refund

MarSt

TaxInc

YESNO

NO

NO

Yes No

Married Single, Divorced

< 80K > 80K

Refund Marital Status

Taxable Income Cheat

No Married 80K ? 10

Start from the root of tree.

Refund

MarSt

TaxInc

YESNO

NO

NO

Yes No

Married Single, Divorced

< 80K >= 80K

Refund Marital Status


No Single 80K ? 10

Test Data

Deduction

How to Make a Decision TreeHow to Make a Decision Tree

Tid Refund MaritalStatus

TaxableIncome Cheat

1 Yes Single 125K No

2 No Married 100K No

3 No Single 70K No

4 Yes Married 120K No

5 No Divorced 95K Yes

6 No Married 60K No

7 Yes Divorced 220K No

8 No Single 85K Yes

9 No Married 75K No

10 No Single 90K Yes10

categoric

al

categoric

al

continuous

class

Training Data

Refund

MarSt

TaxInc

YESNO

NO

NO

Yes No

Single, Divorced

< 80K > 80K

Splitting Attributes

Model: Decision Tree

Induction

Hunt’s AlgorithmHunt’s Algorithm

• Let Dt be the set of training records that reach a node t

• General Procedure:– If Dt contains records that

belong the same class yt, then t is a leaf node labeled as yt

– If Dt is an empty set, then t is a leaf node labeled by the default class, yd

– If Dt contains records that belong to more than one class, use an attribute test to split the data into smaller subsets. Recursively apply the procedure to each subset.

Tid Refund Marital Status




3 No Single 70K No



6 No Married 60K No


8 No Single 85K Yes

9 No Married 75K No

10 No Single 90K Yes 10

Dt

?

Hunt’s AlgorithmHunt’s AlgorithmTid Refund Marital

Status Taxable Income Cheat



3 No Single 70K No



6 No Married 60K No


8 No Single 85K Yes

9 No Married 75K No

10 No Single 90K Yes 10

Don’t Cheat

Refund

Don’t Cheat

Don’t Cheat

Yes No

Refund

Don’t Cheat

Yes No

MaritalStatus

Don’t Cheat

Cheat

Single,Divorced

Married

TaxableIncome

Don’t Cheat

< 80K >= 80K

Refund

Don’t Cheat

Yes No

MaritalStatus

Don’t Cheat

Cheat

Single,Divorced

Married

Measure of Purity: Measure of Purity: GiniGini• Gini Index for a given node t :

(NOTE: p( j | t) is the relative frequency of class j at node t).

– Maximum (1 - 1/nc) when records are equally distributed among all classes, implying least interesting information

– Minimum (0.0) when all records belong to one class, implying most interesting information

j

tjptGINI 2)]|([1)(

C1 0C2 6

Gini=0.000

C1 2C2 4

Gini=0.444

C1 3C2 3

Gini=0.500

C1 1C2 5

Gini=0.278

Advantage of Decision TreeAdvantage of Decision Tree• simple to understand and interpret

• require little data preparation

• able to handle nominal and categorical data.

• perform well with large data in a short time

• the explanation for the condition is easily explained by boolean logic.

Advantages of Decision TreeAdvantages of Decision Tree

• Easy to visualize the process of classification– Can easily tell why the data is classified in a

particular category - just trace the path to get to the leaf and it explains the reason

• Simple, fast processing– Once the tree is made, just traverse down the

tree to classify the data

Decision Tree is for…Decision Tree is for…

• Classifying the dataset which– The predicates return discrete values– Does not have an attributes that all data has

the same value

CMT catalog: Shallow earthquakes, 1976-2005

Gordon & Stein, 1992

INDIAN PLATE MOVES NORTHCOLLIDING WITH EURASIA

COMPLEX PLATE

BOUNDARY ZONE IN

SOUTHEAST ASIA

Northward motion of India deforms all of

the region

Many small plates (microplates) and

blocks

Molnar & Tapponier, 1977

India subducts India subducts beneath Burma beneath Burma

microplatemicroplateat about 50 at about 50

mm/yrmm/yr

Earthquakes Earthquakes occur at plate occur at plate

interface along interface along the Sumatra arc the Sumatra arc (Sunda trench)(Sunda trench)

These are These are spectacular & spectacular &

destructive destructive results of many results of many

years of years of accumulated accumulated

motionmotion

NOAA

IN DEEP OCEAN tsunami has long wavelength, travels fast, small amplitude - doesn’t affect ships

AS IT APPROACHES SHORE, it slows. Since energy is

conserved, amplitude builds up - very damaging

Because seismic waves travel much faster (km/s) than tsunamis, rapid analysis of seismograms can identify earthquakes likely to cause major tsunamis and predict when waves will arrive

TSUNAMI WARNING

Deep ocean buoys can measure wave heights, verify tsunami and reduce false alarms

HOWEVER, HARD TO PREDICT EARTHQUAKES recurrence is highly variable

M>7 mean 132 yr 105 yr Estimated probability in 30 yrs 7-51%

Sieh et al., 1989

Extend earthquake history with geologic records -paleoseismology

EARTHQUAKE RECURRENCE AT SUBDUCTION ZONES IS

COM PLICATED

In many subduction zones, thrust earthquakes have patterns in space and time. Large earthquakes occurred in the Nankai trough area of Japan approximately every 125 years since 1498 with similar fault areas

In some cases entire region seems to have slipped at once; in others slip was divided into several events over a few years.

Repeatability suggests that a segment that has not slipped for some time is a gap due for an earthquake, but it’s hard to use this concept well because of variability

GAP?

NOTHING YET Ando, 1975

1985 MEXICO EARTHQUAKE1985 MEXICO EARTHQUAKE1985 MEXICO EARTHQUAKE1985 MEXICO EARTHQUAKE

• SEPTEMBER 19, 1985

• M8.1

• A SUBDUCTION ZONE QUAKE

• SEPTEMBER 19, 1985

• M8.1

• A SUBDUCTION ZONE QUAKE

• ALTHOUGH LARGER THAN USUAL, THE EARTHQUAKE WAS NOT A “SURPRISE”

• A GOOD, MODERN BUILDING CODE HAD BEEN ADOPTED AND IMPLEMENTED

• ALTHOUGH LARGER THAN USUAL, THE EARTHQUAKE WAS NOT A “SURPRISE”

• A GOOD, MODERN BUILDING CODE HAD BEEN ADOPTED AND IMPLEMENTED

1985 MEXICO EARTHQUAKE1985 MEXICO EARTHQUAKE1985 MEXICO EARTHQUAKE1985 MEXICO EARTHQUAKE

• EPICENTER LOCATED 240 KM FROM MEXICO CITY

• EPICENTER LOCATED 240 KM FROM MEXICO CITY

• 400 BUILDINGS COLLAPSED IN OLD LAKE BED ZONE OF MEXICO CITY

• SOIL-STRUCTURE RESONANCE IN OLD LAKE BED ZONE WAS A MAJOR FACTOR

• 400 BUILDINGS COLLAPSED IN OLD LAKE BED ZONE OF MEXICO CITY

• SOIL-STRUCTURE RESONANCE IN OLD LAKE BED ZONE WAS A MAJOR FACTOR

1985 MEXICO EARTHQUAKE: 1985 MEXICO EARTHQUAKE: ESSENTIAL STRUCTURES--ESSENTIAL STRUCTURES--

SCHOOLSSCHOOLS

1985 MEXICO EARTHQUAKE: 1985 MEXICO EARTHQUAKE: ESSENTIAL STRUCTURES--ESSENTIAL STRUCTURES--

SCHOOLSSCHOOLS

1985 MEXICO EARTHQUAKE: 1985 MEXICO EARTHQUAKE: STEEL FRAME BUILDINGSTEEL FRAME BUILDING

1985 MEXICO EARTHQUAKE: 1985 MEXICO EARTHQUAKE: STEEL FRAME BUILDINGSTEEL FRAME BUILDING

1985 MEXICO EARTHQUAKE: 1985 MEXICO EARTHQUAKE: POUNDINGPOUNDING

1985 MEXICO EARTHQUAKE: 1985 MEXICO EARTHQUAKE: POUNDINGPOUNDING

1985 MEXICO EARTHQUAKE: 1985 MEXICO EARTHQUAKE: NUEVA LEON APARTMENT NUEVA LEON APARTMENT

BUILDINGS BUILDINGS

1985 MEXICO EARTHQUAKE: 1985 MEXICO EARTHQUAKE: NUEVA LEON APARTMENT NUEVA LEON APARTMENT

BUILDINGS BUILDINGS

1985 MEXICO EARTHQUAKE: 1985 MEXICO EARTHQUAKE: SEARCH AND RESCUESEARCH AND RESCUE

1985 MEXICO EARTHQUAKE: 1985 MEXICO EARTHQUAKE: SEARCH AND RESCUESEARCH AND RESCUE

• Definition

• Characteristics

• Project:California Earthquake Prediction)

Characteristics (cont.)Characteristics (cont.)


• 2. Locality: information transferred by a neuron is limited by its nearby neurons.

• CAEP: short term earthquake prediction is highly influenced by it’s geologic figure locally.


• 3. Weighted sum and activation function with nonlinearity: input signal is weighted at the synoptic connection by a connection weight.

• CAEP: nearby location will be weighted with each activation function.

Characteristics (cont.)Characteristics (cont.)• 4. Plasticity: connection weights

change according to the information fed to the neuron and the internal state. This plasticity of the connection weights leads to learning and self-organization. The plasticity realizes the adaptability against the continuously varying environment.

• CAEP: calculate the stress of focused point according to the seismic wave history in the around area

Characteristics (cont.)Characteristics (cont.)• 5. Generalization: A neural

network constructs its own view of the world by inferring an optimal action on the basis of previously learned events by interpolation, and extrapolation.

• CAEP: get a view of one area from past experience by pattern representation Prediction.

Basic Function of CSEPBasic Function of CSEP

• Neuron: list of locations along San Andreas Fault, and two of the associated faults—Hayward and Calaveras.

Basic Function of CSEP (cont.)Basic Function of CSEP (cont.)

• Neuron’s parameters: magnitude, date, latitude, longitude, depth, location, ground water, observation, etc.

LearningLearning

• Learning is essential for unknown environments,– i.e., when designer lacks omniscience

• Learning is useful as a system construction method,– i.e., expose the agent to reality rather than trying to

write it down

• Learning modifies the agent's decision mechanisms to improve performance

Learning agentsLearning agents

Learning elementLearning element

• Design of a learning element is affected by– Which components of the performance element are to

be learned– What feedback is available to learn these components– What representation is used for the components

• Type of feedback:– Supervised learning: correct answers for each

example– Unsupervised learning: correct answers not given– Reinforcement learning: occasional rewards

Inductive learningInductive learning

• Simplest form: learn a function from examples

f is the target function

An example is a pair (x, f(x))

Problem: find a hypothesis hsuch that h ≈ fgiven a training set of examples

(This is a highly simplified model of real learning:– Ignores prior knowledge– Assumes examples are given)

–

•

•

Learning decision treesLearning decision trees

Problem: decide whether to wait for a table at a restaurant, based on the following attributes:1. Alternate: is there an alternative restaurant nearby?2. Bar: is there a comfortable bar area to wait in?3. Fri/Sat: is today Friday or Saturday?4. Hungry: are we hungry?5. Patrons: number of people in the restaurant (None, Some, Full)6. Price: price range ($, $$, $$$)7. Raining: is it raining outside?8. Reservation: have we made a reservation?9. Type: kind of restaurant (French, Italian, Thai, Burger)10. WaitEstimate: estimated waiting time (0-10, 10-30, 30-60, >60)

Attribute-based representationsAttribute-based representations

• Examples described by attribute values (Boolean, discrete, continuous)

• E.g., situations where I will/won't wait for a table:

• Classification of examples is positive (T) or negative (F)

•

Decision treesDecision trees

• One possible representation for hypotheses• E.g., here is the “true” tree for deciding whether to wait:

ExpressivenessExpressiveness

• Decision trees can express any function of the input attributes.• E.g., for Boolean functions, truth table row → path to leaf:

• Trivially, there is a consistent decision tree for any training set with one path to leaf for each example (unless f nondeterministic in x) but it probably won't generalize to new examples

• Prefer to find more compact decision trees

Hypothesis spacesHypothesis spaces

How many distinct decision trees with n Boolean attributes?

= number of Boolean functions

= number of distinct truth tables with 2n rows = 22n

• E.g., with 6 Boolean attributes, there are 18,446,744,073,709,551,616 trees

Hypothesis spacesHypothesis spaces

How many distinct decision trees with n Boolean attributes?= number of Boolean functions= number of distinct truth tables with 2n rows = 22n

• E.g., with 6 Boolean attributes, there are 18,446,744,073,709,551,616 trees

How many purely conjunctive hypotheses (e.g., Hungry Rain)?• Each attribute can be in (positive), in (negative), or out

3n distinct conjunctive hypotheses• More expressive hypothesis space

– increases chance that target function can be expressed– increases number of hypotheses consistent with training set

may get worse predictions

Decision tree learningDecision tree learning

• Aim: find a small tree consistent with the training examples• Idea: (recursively) choose "most significant" attribute as root of

(sub)tree

Choosing an attributeChoosing an attribute

• Idea: a good attribute splits the examples into subsets that are (ideally) "all positive" or "all negative"

• Patrons? is a better choice

•

Using information theoryUsing information theory

• To implement Choose-Attribute in the DTL algorithm

• Information Content (Entropy):

I(P(v1), … , P(vn)) = Σi=1 -P(vi) log2 P(vi)

• For a training set containing p positive examples and n negative examples:

np

n

np

n

np

p

np

p

np

n

np

pI

22 loglog),(

Information gainInformation gain

• A chosen attribute A divides the training set E into subsets E1, … , Ev according to their values for A, where A has v distinct values.

• Information Gain (IG) or reduction in entropy from the attribute test:

• Choose the attribute with the largest IG

v

i ii

i

ii

iii

np

n

np

pI

np

npAremainder

1

),()(

)(),()( Aremaindernp

n

np

pIAIG

Information gainInformation gain

For the training set, p = n = 6, I(6/12, 6/12) = 1 bit

Consider the attributes Patrons and Type (and others too):

Patrons has the highest IG of all attributes and so is chosen by the DTL algorithm as the root

bits 0)]4

2,

4

2(

12

4)

4

2,

4

2(

12

4)

2

1,

2

1(

12

2)

2

1,

2

1(

12

2[1)(

bits 0541.)]6

4,

6

2(

12

6)0,1(

12

4)1,0(

12

2[1)(

IIIITypeIG

IIIPatronsIG

Example contd.Example contd.• Decision tree learned from the 12 examples:

• Substantially simpler than “true” tree---a more complex hypothesis isn’t justified by small amount of data

Data Mining, Decision Trees and Earthquake Prediction Professor Sin-Min Lee.

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