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Spatiotemporal Stream Mining using TRACDS

Middle East Technical UniversityOctober 31, 2012

Margaret H Dunham, Michael Hahsler, Yu Su, Sudheer Chelluboina, and Hadil Shaiba

Computer Science and Engineering

This work is supported by NSFIIS-0948893

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IDA@SMUIntelligent Data Analysis Lab

Team led by Margaret H. Dunham Michael Hahsler

MissionAt IDA@SMU we create novel techniques inspired by knowledge discovery, data mining, machine learning, artificial intelligence and statistical analysis to work with data from various sources.

Current Focus Massive data stream modeling: TRACDSTM

Hurricane intensity prediction Effective metagenomic classification for the

Human Genome Project Recommender systems: R/Apache Mahout

http://www.lyle.smu.edu/IDA

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Outline

• Spatiotemporal Stream Data• TRACDS

• Hurricane Intensity Prediction

• PIIH

• PIIH online

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From Sensors to Streams

• Data captured and sent by a set of sensors is usually referred to as “stream data”.

• Real-time sequence of encoded signals which contain desired information. It is continuous, ordered (implicitly by arrival time or explicitly by timestamp or by geographic coordinates) sequence of items

• May be viewed as arriving in discrete time intervals.

• Stream data is infinite - the data keeps coming.

• Examples: Weather data, network data (VoIP), traffic data.

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Stream Data Format

• Events arriving in a stream

• At any time, t, we can view the state of the problem as represented by a vector of n numeric values: Vt = <S1t, S2t, ..., Snt>

V1 V2 … VqS1 S11 S12 … S1q

S2 S21 S22 … S2q

… … … … …Sn Sn1 Sn2 … Snq

Time

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Modeling Stream Data

– Summarization (Synopsis) of data

– Temporal and Spatial

– Dynamic

– Continuous (infinite stream)

– Concept Drift

• Learn

• Forget

– Sublinear growth rate - Clustering

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MM

A first order Markov Chain is a finite or countably infinite sequence of events {E1, E2, … } over discrete time points, where Pij = P(Ej | Ei), and at any time the future behavior of the process is based solely on the current state

A Markov Model (MM) is a graph with m vertices or states, S, and directed arcs, A, such that:

• S ={N1,N2, …, Nm}, and

• A = {Lij | i 1, 2, …, m, j 1, 2, …, m} and Each arc,

Lij = <Ni,Nj> is labeled with a transition probability

Pij = P(Nj | Ni).

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Problem with Markov Chains

• The required structure of the MC may not be certain at the model construction time.

• As the real world being modeled by the MC changes, so should the structure of the MC.

• Not scalable – grows linearly as number of events.

• Our solution:

– Extensible Markov Model (EMM)

– Cluster real world events

– Allow Markov chain to grow and shrink dynamically

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EMM (Extensible Markov Model)

• Time Varying Discrete First Order Markov Model• Continuously evolves• Nodes are clusters of real world states.• Learning continues during application phase.• Learning:

– Transition probabilities between nodes– Node labels (centroid of cluster)– Nodes are added and removed as data arrives

• Applications:– Anomaly/Rare Event Detection– Prediction– Classification

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EMM Definition

Extensible Markov Model (EMM): at any time t, EMM consists of an MC with designated current node and algorithms to modify it, where algorithms include:

• EMMCluster, which defines a technique for matching between input data at time t + 1 and existing states in the MC at time t.

• EMMIncrement algorithm, which updates MC at time t + 1 given the MC at time t and clustering measure result at time t + 1.

• EMMDecrement algorithm, which removes nodes from the EMM when needed.

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EMM Cluster

• Nearest Neighbor (or any clustering technique)

• If none “close” create new node

• Labeling of cluster is centroid of members in cluster or Clustering Feature

• O(n)

Here n is the number of states

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EMM Sublinear Growth

Servent Data

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Growth Rate Automobile Traffic

Minnesota Traffic Data

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EMM Learning

<18,10,3,3,1,0,0>

<17,10,2,3,1,0,0>

<16,9,2,3,1,0,0>

<14,8,2,3,1,0,0>

<14,8,2,3,0,0,0>

<18,10,3,3,1,1,0.>

1/3

N1

N2

2/3

N3

1/11/3

N1

N2

2/3

1/1

N3

1/1

1/2

1/3

N1

N2

2/3 1/2

1/2

N3

1/1

2/3

1/3

N1

N2

N1

2/21/1

N1

1

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N2

N1 N3

N5 N6

2/2

1/3

1/3

1/3

1/2

N1 N3

N5 N6

1/61/6

1/6

1/31/3

1/3

EMM Forgetting

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Outline

• Spatiotemporal Stream Data

• TRACDS• Hurricane Intensity Prediction

• PIIH

• PIIH online

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Traditional Stream Clustering

Standard Data Stream Clustering ignores temporal aspect of data

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Stream Clustering

• Clusters change over time – they move

• Some techniques use micro clusters/reclustering

• Reclustering is often off line (batch while stream data comes).

• STREAM

– Partitions stream data into segments

– Clusters each segment (k-medians)

– Iteratively reclusters the centers of these clustersS. Guha, A. Meyerson, N. Mishra, R. Motwani, and L. O'Callaghan. “Clustering data streams: Theory and practice.” IEEE Transactions on Knowledge and Data Engineering, 15(3):515-528, 2003.

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Temporal Relationship Among Clusters in Data Streams

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TRACDS NOTE• TRACDS is not:

– Another stream clustering algorithm

• TRACDS is:

– A new way of looking at clustering

– Built on top of an existing clustering algorithm

• TRACDS may be used with any stream clustering algorithm

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TRAC-DS Overview

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TRACDS Clustering Operations

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TRACDS Example

C

EMM

http://www.lyle.smu.edu/IDA/TRACDS

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Outline

• Spatiotemporal Stream Data

• TRACDS

• Hurricane Intensity Prediction• PIIH

• PIIH online

10/31/2012, METULower 9th Ward of New Orleans, Louisiana, Feb 27, 2006

Photographer: Mackenzie Schott

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The major issues in forecasting hurricanes are predicting their tracks of movement and their intensities. Compared with prediction of track movement, intensity prediction is still relatively inaccurate.

Hurricanes are tropical cyclones with sustained winds of at least 64 kt (119 km/h, 74 mph) .

Time step [0h, 12h, 24h, …, 120h]

Hurricanes

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Hurricane Intensity Prediction

Hurricane Intensity:

Maximum sustained surface wind.

Highest average wind speed within 1 minute and10m above surface.

Rapid Intensification

24-h increase in maximum wind speed >= 30knots.

“Maximum Sustained Wind”. Wikipedia. Wikimedia foundation, 27 August 2011. Web. 4 December 2011. Retrieved from http://en.wikipedia.org/wiki/Maximum_sustained_wind.

“Rapid Intensification,” accessed on 10/24/12, http://www.hurrnet.com/tutorial/forecasts/intensity/rapid.htm .

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Predicting Intensity

• Statistical models predict intensity based on measured stream data.

• Current state of storm

• History of this storm

• How similar storms behaved in past

• Regression models are the most popular.

• NOAA (branch of U.S. Government)

– collects stream data.

– Yearly updates it models based on data from previous year

– Makes predictions in a quasi-real time manner.

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Hurricane Intensity Prediction

Category 5 - 175 mph Damage: estimated $125 billion Fatalities: >1,800 “Hurricane Katrina – Most Destructive Hurricane Ever to Strike the U.S.”,

August 28, 2005, February 12, 2007, http://www.katrina.noaa.gov/ .

“Objective: Improve forecast skill to accuracy and confidence levels required for decision‐making and risk management”

NOAA’s National Weather Service Strategic Plan 2010-2020

Very difficult to predict Intensity(rapid intensification)

National Hurricane Center (NHC) uses

– Dynamical models: computational intensive and slow

– Statistical models: Statistical Hurricane Intensity Prediction Scheme (SHIPS)

• Current Storm – SANDYhttp://www.nhc.noaa.gov/archive/2012/SANDY_graphics.shtml

Path of Hurricane Katrina (2005)Color shows intensity

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Remote Sensing

Storm features are gathered from the earth's observations

using remote sensing. Real time data are gathered every few hours and stored in

large databases. Historical data of more than 20 years of the earth's

behavior is stored in the database. Methods:

Satellite Buoy Ship Aircraft

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Outline

• Spatiotemporal Stream Data

• TRACDS

• Hurricane Intensity Prediction

• PIIH• PIIH online

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Hurricane DataThe data contains 16 predictors. The dataset is formed by time ordered 12 hour interval records and contains the hurricane data from seasons 1982 to 2003. 1982

2003

Hurricane D

ata

hurricane 1 0h, 12h, 24h, …

0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,025,0,1,-5.83,668,0,140,14.9,-53.5,13.25,40.5,23,6.6,27,372.5,1960025,0,1,-5.83,708,0,140,12.7,-53.45,13.65,37.5,17.5,5.69,4,317.5,1960030,5,1,-3.58,682,150,135,12.75,-53.35,13.25,34,1.5,5.79,15,382.5,1822535,5,1,-4.9,674,175,130,14.2,-53.35,13.4,33,-12,6.66,-13,497,1690050,15,1,0.44,681,750,113.52,17.1,-53.15,13.2,35,-20,8.32,-7,855,12885.790,0,0,0,0,0,0,0,0,0,0,0,0,0,0,030,0,0.99,-7.02,656,0,124.55,19.05,-52.55,14.75,51,0.5,6.68,45,571.5,15512.4930,0,0.98,-7.02,675,0,123.75,17.3,-52.6,14.15,54,5,6.63,22,519,15314.2835,5,0.98,-4.16,722,175,119.55,17.9,-52.6,14.65,58,10,7.43,34,626.5,1429265,30,0.97,4.09,635,1950,88.77,19.15,-52.1,14.7,54.5,27.5,8.63,33,1244.75,7879.2675,10,0.97,6.25,724,750,70.08,17.8,-52.15,12.55,54,48.5,8.61,45,1335,4910.9295,20,0.96,9.17,641,1900,37.59,14.85,-52.9,11.1,56.5,55,7.87,15,1410.75,1413.1395,0,0.96,7.2,691,0,33.33,15.6,-53.45,9.25,51.5,44.5,8.97,32,1482,1110.9895,0,0.95,0.82,713,0,35.62,17.9,-53.25,7.85,47,38,10.72,31,1700.5,1268.4395,0,0.95,2.4,813,0,28.12,20.85,-52.65,7.25,45,45,12.84,63,1980.75,790.65115,20,0.93,10.65,635,2300,-11.1,24.45,-52.7,4.55,41.5,57.5,15.81,24,2811.75,123.2110,-5,0.93,14.51,622,-550,-26.24,30.7,-53.55,1.15,40.5,50.5,21.2,28,3377,688.7190,-20,0.91,18.15,613,-1800,-17.97,37.05,-53.95,0,46,29.5,27.08,42,3334.5,322.9970,-20,0.91,21.86,668,-1400,1.01,40.3,-53.7,0,52.5,20,30.72,41,2821,1.0270,0,0.89,26.22,688,0,2.35,45.05,-52.7,0.25,50.5,37.5,35.18,31,3153.5,5.50,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0……

0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

hurricane 2 0h, 12h, 24h, …

…hurricane 274 0h, 12h, 24h,

……

16 predictors

Intensity

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Construct EMM

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Use EMM for Prediction

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EMM, TRACDS and Hurricane Data

• Approach: Using TRACDS algorithms, construct multiple EMMs. One will be built for each time point into the future for which predictions are to be made: 12 hours, …, 120 hours.

• NOAA provides 16 different features or predictors (attribute values).

• Clustering is performed based on a distance calculation from input feature vector to centroid of clusters in EMMs.

• However the importance of these to intensity prediction is not uniform.

• How can we determine weight for each feature? Used during clustering.

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Weighted Feature Learning -Extensible Markov Model (WFL-EMM)

WFL-EMM assumes that the different predictors contribute differently during the prediction.

V1 = <20 50 100 30 25 4 10>V2 = <20 80 50 20 10 10 10>……

f1 f2 f3 f4 f5 f6 f7

1

0

Weights for predictors

In WFL-EMM, a weight vector u = <u1, …, un > to indicate the weights for different predictors, where ui [0, 1] . ∈ ui =1 means the ith predictor is important and ui =0 implies that the ith predictor is ignored.

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Weighted Feature Learning -Extensible Markov Model (WFL-EMM)

The question is how to locate a fitness weight vector u = <u1, …, un > for hurricane intensity predictions.

Genetic algorithm (GA) is introduced in WFL-EMM to find the best fitness weight vector, which gives the smallest error of the prediction.

GA Learning Process

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Weighted Feature Learning -Extensible Markov Model (WFL-EMM)

Given a weights vector u = <u1, …, un >. Two steps of data transformation Normalization: normalize all the predictor within the range of [0, 1]

First standardize the predictor values by

Transformation: Assume a normalized record d = <d1,…, dn>. Then the record is transformed as d’ = < u1 d1,…, un dn>.

where and sd(x) are the mean and standard deviation of the ith predictor.Then a non-linear normalization maps zi to interval [0, 1],

where is damping coefficient.

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Weighted Feature Learning -Extensible Markov Model (WFL-EMM)

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Weighted Feature Learning -Extensible Markov Model (WFL-EMM)

• The question is how to locate a fitness weight vector u = <u1, …, un > for hurricane intensity predictions.

• These weights are used during the clustering and applied to the distance/similarity measure used for clustering

• Genetic algorithm (GA) is introduced in WFL-EMM to find the best fitness weight vector, which gives the smallest error of the prediction

.

GA Learning Process

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GAs try to locate a fitness solution from the a solution space.

Solution space

Fitness solution

Weight vector u = <u1, …, un > spans a vector space [0, 1]n since each ui is a real value ranged in [0, 1].

Weighted Feature Learning -Extensible Markov Model (WFL-EMM)

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Weighted Feature Learning -Extensible Markov Model (WFL-EMM)

Genetic algorithm evolution

Each time, two chromosomes are selected randomly from the ith population with a probability proportional to their fitness, where a chromosome is a Gray code string of a weight vector u.

Chromosome 1

Chromosome 2

GA Learning Process

Population i

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Weighted Feature Learning -Extensible Markov Model (WFL-EMM)

Genetic algorithm evolution

GA Learning Process

Chromosome 1

Chromosome 2

Calculate the fitness of the obtained chromosome and place itinto the population i+1

New chromosome

crossover mutation

Randomly alter one or more bits in the offspring based on a given probability.

inversion

Randomly select a break point in a chromosome and then exchange the position of the two pieces.

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Weighted Feature Learning -Extensible Markov Model (WFL-EMM) GA Learning Process

Fitness of the chromosome

A chromosome is first decoded into a weight vector u. Apply this obtained u to generate a GEMM by using the training data. Then the fitness is calculated by either mean absolute deviation (MAD) or root mean square error (RMSE) based on the testing data. The best fitness weight vector u is located during the evolution of a GA.

Fitness

where

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Results

- Experiment 2: Evaluating WFL-EMM by using k-fold cross validation technique over the dataset from 1982 to 2003 (set MAD as fitness).

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Results

It is interesting to look at the weights of the features because these weights reveals information about what the main drivers of intensity change might be.

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Learn feature weights using Genetic Algorithm.

Weights for features over time.

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PIIH – Prediction Intensity Interval Model for Hurricanes

Historic hurricane data

Features Current wind speed Various temperatures Time of the year Direction of movement GOES Satellite Data (IR)

Currently 23 features from the Statistical Hurricane Intensity Prediction Scheme (SHIPS)

TRACDSTM

Data stream clustering + temporal

order model

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Prediction using PIIH – Irene (2011)

Current features of hurricane

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Prediction using PIIH – Irene (2011)

Current features of hurricane

Aggregate possible future scenarios into a prediction

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PIIH Output for Irene (2011)

MAD MSEPIIH 14.28 310.79

SHIFOR 5* 12.64 229.49

LGEM 15.06 411.73SHIPS 14.80 319.64

D-SHIPS 17.11 500.36

MAD … Mean average deviationMSE … Mean squared error* Baseline model

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PIIH Advantages• Real Time

• Dynamic

• Machine Learning

• Confidence Bands

• By analyzing the 2011 storms through Nate, we observed the following:– 96.33% of observations fell within the 95% confidence band– 92.8% of observations fell within the 90% confidence band– 74.27% of observations fell within the 68% confidence band

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Outline

• Spatiotemporal Stream Data

• TRACDS

• Hurricane Intensity Prediction

• PIIH

• PIIH online

10/31/2012, METU http://IDA.lyle.smu.edu/PIIH/

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Future Work

1. Deploy model with NOAA Add decay model over land Evaluate additional features Predict rapid intensification Interface with NOAA’s systems

2. Improve the TRACDSTM model Data stream clustering Higher-order effects Improve model selection and outlier handling

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PIIH Bibliography

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Thank you!

http://www.lyle.smu.edu/IDA