Theories and Applications of Spatial-Temporal Data Mining and Knowledge Discovery

Theories and Applications of Spatial-Temporal Data Mining and Knowledge Discovery Yee Leung Email: [email_address] Department of Geography and Resource Management The Chinese University of Hong Kong

Daily rainfall data of two stations in Pearl River basin of China

The monthly sunspot time series.

The Portuguese Stock Index PSI-20 evolution from 1993 to 2002 (adopted from J.A.O. Matos et al. / Physica A 342 (2004) 665 – 676)

Outbreak of Avian Flu in different regions

What are the structures and processes hidden in spatial data? What are the Concepts hidden in the information system? Do the Concepts form a knowledge structure?

Typhoon Tracks Adapted from Wang and Chan

Typhoon/Hurricane Tracking Objective: Intensity, track (land falling, recurvature) Object: The space-time track of unusually low sea- surface air pressure in the x-y-z plane Data: potential temperature, horizontal velocity, vertical velocity, relative humidity, horizontal wind, etc Data: Hundreds and thousands of gigabytes within a specific time interval

Data Mining in Hyperspectral Images 1. Objective Classification, Pattern Recognition 2. Object Spectral Signatures of Objects 3. Data Spectral, Non-spectral Data 4. Data Volume e.g. ： AVIRIS ： from 0.4 to 2.45 micrometers, 224 bands HYDICE ： from 0.4 to 2.5 micrometers, 210 bands Hyperion ： from 0.4 to 2.5 micrometers, 220 bands, 30 meter resolution

The Objective of Knowledge Discovery and Data Mining Fayyad: The discovery of non-trivial, novel, potentially useful and interpretable knowledge/information from data Data Information Knowledge Decision

Characteristics of Spatial Data 1. 　 Voluminous 2. 　 Sparse 3. 　 Diversity 4. 　 Complex 5. 　 Dynamic 6. 　 Redundant 7. 　 Imperfect (random ， fuzzy ， granular ， incomplete ， noisy) 8. 　 Multi-scale

Main Tasks of Spatial Knowledge Discovery and Data Mining 1. Clustering 3. Association 2. Classification Spatial Relations Temporal Relations Spatial-temporal Relations * In particular ： the local-global issue 4. Processes

CLUSTERING The Scale-Space Filtering Approach The Regression-Classes Decomposition Approach

Scale Space Theory Given a primary image f (x) at a distance of σ from human eyes, the observed blur red image f (x, σ ) can be mathematically determined by the following partial differential equation : The solution of the above equation is explicitly expressed as where ‘∗’ denotes the convolution operation, g (x, σ ) is the Gaussian function

If the training samples are treated as an imaginary image with expression: Then the corresponding blurred image f (x, σ , D l ) at scale σ can be specified by

Essentials of Clustering by Scale-space Filtering 1. 　 Visual system simulation 2. 　 Cluster validity check 3. 　 Clustering validity check 4. 　 Relevant concepts (a) life time of a cluster (b) life time of a clustering (c) compactness (d) isolatedness

Ms-time plot of clustering results for earthquakes (Ms≥6): a) 3 clusters in the 59th~95th scale range; b) 17 clusters at the 6th scale step a) b)

Temporal segmentation of Strong Earthquakes (Ms≥6.0) of 1290A.D. - 2000A.D. Scale-space for earthquakes (Ms≥6)

Indices of clustering along the time scale for earthquakes (Ms≥6.0): a) number of clusters; b) Lifetime, Isolation and Compactness of the clustering a) b)

a) b) Ms-time plot of clustering results for earthquakes (Ms≥4.7): a) 2 clusters in the 74th~112th scale range; b) 18 clusters at the 10th scale step

Temporal Segmentation of Strong Earthquakes (Ms≥4.7) of 1484A.D. - 2000A.D. Indices of clustering along the time scale for earthquakes (Ms≥4.7): a) number of clusters ( The vertical axis just shows the part no larger than 150 ); b) Lifetime, Isolation and Compactness of the clustering a) b)

Table 1 Seismic active periods and episodes obtained by the clustering algorithm and the seismologists ( The number in parentheses is the number of earthquakes in the cluster )

Advantages of Scale-space Filtering Free from solving global optimization problem Independent of initialization Robust Outliers Detection Generalization of scale-related algorithms Consistent with visual system

5. Scale Space Clustering Scale-Space Filtering for Simulated Data

5. Scale Space Clustering Scale-Space Filtering for Remote-Sensing Data Clustering Tree Quasi-Light

Clustering by Regression-Classes Decomposition Method

Identification of line objects in remotely sensed data

Two ellipsoidal feature extraction

ANALYSIS OF SPATIAL RELATIONSHIP Global Description Moran’s I Geary’s c OLR Local Description Local Moran’s I Local Geary’s c G Statistic Geographically Weighted Regression Mixture Distribution

Geographically Weighted Regression Hypothesis testing 1. Ho: No difference between OLR and GWR 2. Ho: a 1k = a 2k = … = a nk

(Regression-Classes Decomposition Method)

CLASSIFICATION The Neural Network Approach The Classification and Regression Tree The Statistical Classifiers

Information Extraction and Classification Neural Networks for Classification--MLP-BP

Some Typical Feedforward Neural Networks Perception In late 1950s: layered feed forward networks named perceptron. Today: Perceptron : single-layer, feed-forward networks. See Fig. 8, each multi-output unit O is fed independently from the input units. Figure 8. Perceptrons

Mulitlayer Feedforward Neural Network Learning algorithms for multilayer networks are neither efficient nor guaranteed to converge to global optimum . Most popular learning method: back-propagation . Back-propagation learning The restaurant problem: use a 2-layer network, 10 attributes = 10 input units, 4 hidden units. See Fig. 13. Some Typical Feedforward Neural Networks (con ’ t) Fig. 13. A 2-layer feedforward network for the restaurant problem.

Competitive Pattern Recognition by Recurrent NN

Trees by Classification and Regression Tree (CART) MSW 6/12/18: Maximum Sustained Wind of TC 6/12/18 hours before recurvature. 0: Recurve,1: Straight

1. If MSW of a TC is smaller than or equal to 34 m/s and MSW of that TC is smaller than 2 m/s 6 hours later, then the TC will recurve in 12 hours with 96% accuracy. 2. If MSW of a TC is smaller than or equal to 34 m/s and MSW of that TC is larger than 2 m/s 6 hours later, the TC will move straight in 12 hours with 86.8% accuracy. 3. If MSW of a TC is larger than 34 m/s, it will recurve in 18 hours with 94.1% accuracy. Rules by CART

DISCOVERY OF TEMPORAL PROCESSES The Multifractal Approach Conventional Time Series Analyses

Mining of Scaling Behavior by Multifractal Analysis

Multiplicative Cascade An approach to the study of scaling behavior with multiple scales (granules). Multiplicative Binomial Cascade

Schematic representation of cascade (adopted from Puente and Lopez, 1995, Physical Letters A)

TEMPORAL ANALYSIS Linear Time Invariant System  Self Similarity  Multiscaling  Infinitely Divisible Cascade Stationary Process Non-stationary Process Random Walk Fractional Brownian Motion, fmb Multifractal Analysis of Stochastic Trends

The Multifractal Approach Establish a data model for stochastic time series Discovery of relevant models in stochastic time series

MF-DFA Detrended fluctuation analysis (DFA) is a method for detecting the long-range correlation and fractal property in the both stationary and non-stationary time series. MF-DFA , which is based on DFA, can give full description of more complicated scaling behavior of time series

MF-DFA Given a time series with length N. Step1: i=1,2,…,N; Step2: Divide Y(i) into non-overlapping segments of equal lengths s. In order not to disregard this part of the series, the same procedure is repeated starting from the opposite end. Thereby, 2 Ns segments are obtained altogether.

MF-DFA Step 3 . Calculate the local trend for each of the 2 N s segments by a least squares fit of the series. Then determine the variance for each segment ν , ν = 1 , . . .,N s , and for ν = N s + 1 , . . . , 2 N s . Here, is the fitting polynomial in segment ν, whose order m can be 1, 2, 3 … . Step 4 . Average over all segments to obtain the q th-order fluctuation function, defined Where , s ≥ m + 2.

MF-DFA Step5: Determine the scaling behavior of the fluctuation function by analyzing log-log plots of Fq(s) versus s for each value of q . If we have , for large values of s, we get the exponent h(q), which may depend on q generally. H=h(q=2), for stationary time series; H=h(q=2)-1, for non-stationary time series.

MF-DFA For MF-DFA, if h(q) is constant for all q , the corresponding time series is mono-fractal. However, if h(q) varies with q, that means multifractal.

( adopted from Peng et. al., 1994 )

Log-log plots of F q (s) versus s for the daily rainfall time series of station 56691 in Pearl River basin (left) and Station Chuantang in East River basin (right) with q =2.

The h ( q ) curves of daily rainfall time series of stations in the Pearl River basin (left) and stations in the East River basin (right).

The curves of daily rainfall time series of stations in the Pearl River basin (left) and stations in the East River basin (right).

The curves of daily rainfall time series of stations in the Pearl River basin (left) and stations in the East River basin (right)

The curves of daily rainfall time series of 5 stations in the Pearl River basin

The curves of daily rainfall time series of stations in the Pearl River basin (left) and stations in the East River basin (right). The real lines are their cascade model fitting.

The correlation relationship between the altitude of the rainfall stations in the East River basin and the D (2) value of the rainfall time series.

Elevation of rainfall stations in the East River basin with the D2 values of their rainfall data. Elevation (m above MSL)

DISCOVERY OF KNOWLEDGE STRUCTURES The Concept Lattice Approach

Discovery of Hierarchical Knowledge from Relational Spatial Data

Spatial Concept/Class and Data Encapsulation

Generalization and Specialization

Summary (1)Concept lattice as a mathematical foundation for object-oriented spatial information system (2)Concpet lattice can be employed as method to unravel hierarchical structure from spatial information system (3)A bridge between relational spatial information system (vector-based, raster-based) and object-oriented spatial information system.

Yee Leung. Knowledge Discovery in Spatial Data. Berlin: Springer-Verlag, 2010. [email_address] IGU-Commission on Modeling Geographical Systems http://www.science.mcmaster.ca/~igu~cmgs/

Theories and Applications of Spatial-Temporal Data Mining and Knowledge Discovery

More Related Content

What's hot (20)

Viewers also liked (17)

Similar to Theories and Applications of Spatial-Temporal Data Mining and Knowledge Discovery (20)

More from Beniamino Murgante (20)

Recently uploaded (20)

Theories and Applications of Spatial-Temporal Data Mining and Knowledge Discovery