V. Megalooikonomou, Temple University Clustering and Partitioning for Spatial and Temporal Data Mining Vasilis Megalooikonomou Data Engineering Laboratory (DEnLab) Dept. of Computer and Information Sciences Temple University Philadelphia, PA

V. Megalooikonomou, Temple University Outline Introduction –Motivation – Problems: Spatial domain Time domain –Challenges Spatial data –Partitioning and Clustering –Detection of discriminative patterns –Results Temporal data –Partitioning –Vector Quantization –Results Conclusions - Discussion

V. Megalooikonomou, Temple University Introduction Large spatial and temporal databases Meta-analysis of data pooled from multiple studies Goal: To understand patterns and discover associations, regularities and anomalies in spatial and temporal data

V. Megalooikonomou, Temple University Problem Spatial Data Mining: Given a large collection of spatial data, e.g., 2D or 3D images, and other data, find interesting things, i.e.: associations among image data or among image and non-image data discriminative areas among groups of images rules/patterns similar images to a query image (queries by content)

V. Megalooikonomou, Temple University Challenges How to apply data mining techniques to images? Learning from images directly Heterogeneity and variability of image data Preprocessing (segmentation, spatial normalization, etc) Exploration of high correlation between neighboring objects Large dimensionality Complexity of associations Efficient management of topological/distance information Spatial knowledge representation / Spatial Access Methods (SAMs)

V. Megalooikonomou, Temple University Example: Association Mining – Spatial Data Discover associations among spatial and non-spatial data: Images {i 1, i 2,…, i L } Spatial regions {s 1, s 2,…, s K } Non-spatial variables {c 1, c 2,…, c M } c1c1 c2c2 c3c3 c1c1 c7c7 c2c2 c9c9 c6c6 i1i1 i2i2 i3i3 i4i4 i5i5 i6i6 i7i7

V. Megalooikonomou, Temple University Example: fMRI contrast maps Control Patient

V. Megalooikonomou, Temple University Applications Medical Imaging, Bioinformatics, Geography, Meteorology, etc..

V. Megalooikonomou, Temple University Voxel-based Analysis No model on the image data Each voxel’s changes analyzed independently - a map of statistical significance is built Discriminatory significance measured by statistical tests (t- test, ranksum test, F-test, etc) Statistical Parametric Mapping (SPM) Significance of associations measured by chi-squared test, Fisher’s exact test (a contingency table for each pair of vars) Cluster voxels by findings [V. Megalooikonomou, C. Davatzikos, E. Herskovits, SIGKDD 1999]

V. Megalooikonomou, Temple University Analysis by grouping of voxels Grouping of voxels (atlas-based) Prior knowledge increases sensitivity Data reduction: 10 7 voxels R regions (structures) Map a ROI onto at least one region As good as the atlas being used M non-spatial variables, R regions Analysis Categorical structural variables Continuous structural variables M x R contingency tables, Chi-square/Fisher exact test multiple comparison problem log-linear analysis, multivariate Bayesian Logistic regression, Mann-Whitney

V. Megalooikonomou, Temple University Dynamic Recursive Partitioning Adaptive partitioning of a 3D volume

V. Megalooikonomou, Temple University Dynamic Recursive Partitioning Adaptive partitioning of a 3D volume Partitioning criterion: discriminative power of feature(s) of hyper-rectangle and size of hyper-rectangle

V. Megalooikonomou, Temple University Dynamic Recursive Partitioning Adaptive partitioning of a 3D volume Partitioning criterion: discriminative power of feature(s) of hyper-rectangle and size of hyper-rectangle

V. Megalooikonomou, Temple University Dynamic Recursive Partitioning Adaptive partitioning of a 3D volume Partitioning criterion: discriminative power of feature(s) of hyper-rectangle and size of hyper-rectangle

V. Megalooikonomou, Temple University Dynamic Recursive Partitioning Adaptive partitioning of a 3D volume Partitioning criterion: discriminative power of feature(s) of hyper-rectangle and size of hyper-rectangle Extract features from discriminative regions Reduce multiple comparison problem (# tests = # partitions < # voxels) tests downward closed [V. Megalooikonomou, D. Pokrajac, A. Lazarevic, and Z. Obradovic, SPIE Conference on Visualization and Data Analysis, 2002]

V. Megalooikonomou, Temple University Other Methods for Spatial Data Classification Distributional Distances: - Mahalanobis distance - Kullback-Leibler divergence (parametric, non- parametric) Maximum Likelihood: - Estimate probability densities and compute likelihood EM (Expectation-Maximization) method to model spatial regions using some base function (Gaussian) Static partitioning: Reduction of the # of attributes as compared to voxel-wise analysis Space partitioned into 3D hyper-rectangles (variables: properties of voxels inside hyper-rectangles) - incrementally increase discretization Distinguishing among distributions: D. Pokrajac, V. Megalooikonomou, A. Lazarevic, D. Kontos, Z. Obradovic, Artificial Intelligence in Medicine, Vol. 33, No. 3, pp , Mar * * * * * * * * *

V. Megalooikonomou, Temple University Experimental Results Areas discovered by DRP with t-test: significance threshold=0.05, maximum tree depth=3. Colorbar shows significance [D. Kontos, V. Megalooikonomou, D. Pokrajac, A. Lazarevic, Z. Obradovic, O. B. Boyko, J. Ford, F. Makedon, A. J. Saykin, MICCAI 2004] Number of tests Thresh. DepthDRPVoxel Wise Comparison of number of tests performed MethodClassification Accuracy (%) CriterionThresholdTree depthControlsPatientsTotal DRP correlation t-test ranksum Maximum Likelihood / EM Maximum Likelihood / k-means Kullback-Leibler / EM Kullback-Leibler / k-means776671

V. Megalooikonomou, Temple University Experimental Results Impact: Assist in interpretation of images (e.g., facilitating diagnosis) Enable researchers to integrate, manipulate and analyze large volumes of image data (a) (b) Discriminative sub-regions detected when applying (a) DRP and (b) voxel-wise analysis with ranksum test and significance threshold 0.05 to the real fMRI volume data

V. Megalooikonomou, Temple University Time Sequence Analysis Time series data abound in many applications … Challenges: –High dimensionality –Large number of sequences –Similarity metric definition Similarity analysis (e.g., find stocks similar to that of IBM) Goals: high accuracy, (high speed) in similarity searches among time series and in discovering interesting patterns Applications: clustering, classification, similarity searches, summarization Time Sequence: A sequence (ordered collection) of real values: X = x 1, x 2,…, x n

V. Megalooikonomou, Temple University Dimensionality Reduction Techniques DFT: Discrete Fourier Transform DWT: Discrete Wavelet Transform SVD: Singular Value Decomposition APCA: Adaptive Piecewise Constant Approximation PAA: Piecewise Aggregate Approximation SAX: Symbolic Aggregate approXimation …

V. Megalooikonomou, Temple University Similarity distances for time series A more intuitive idea: two series should be considered similar if they have enough non-overlapping time-ordered pairs of subsequences that are similar (Agrawal et al. VLDB, 1995) Euclidean Distance: most common, sensitive to shifts Envelope-based DTW: faster: O(n) Dynamic Time Warping: improving accuracy but slow: O(n 2 )

V. Megalooikonomou, Temple University Partitioning – Piecewise Constant Approximations Original time series (n points) Piecewise constant approximation (PCA) or Piecewise Aggregate Approximation (PAA), [Yi and Faloutsos ’00, Keogh et al, ’00] (n' segments) Adaptive Piecewise Constant Approximation (APCA), [Keogh et al., ’01] (n" segments)

V. Megalooikonomou, Temple University Multiresolution Vector Quantized approximation (MVQ) Partitions a sequence into equal-length segments and uses VQ to represent each sequence by appearance frequencies of key- subsequences 1) Uses a ‘vocabulary’ of subsequences (codebook) – training is involved 2) Takes multiple resolutions into account – keeps both local and global information 3) Unlike wavelets partially ignores the ordering of ‘codewords’ 3) Can exploit prior knowledge about the data 4) Employs a new distance metric [V. Megalooikonomou, Q. Wang, G. Li, C. Faloutsos, ICDE 2005]

V. Megalooikonomou, Temple University Methodology Codebook s=16 Generation Series Transformation Series Encoding …… c m d b c a i f a j b b m i n j j a ma I n j m h l d f k o p h c a k o o g c b l p o c c b l h l h n k k k p l c a c g k k g j h h g k g j l p …… s l

V. Megalooikonomou, Temple University Methodology Creating a ‘vocabulary’ Frequently appearing patterns in subsequences Output: A codebook with s codewords Q: How to create? A: Use Vector Quantization, in particular, the Generalized Lloyd Algorithm (GLA) Representing time series X = x 1, x 2,…, x n f = (f 1,f 2,…, f s ) is encoded with a new representation (f i is the frequency of the i th codeword in X)

V. Megalooikonomou, Temple University Methodology New distance metric: The histogram model is used to calculate similarity at each resolution level: wit h f i,t f i,q s

V. Megalooikonomou, Temple University Methodology Time series summarization: High level information (frequently appearing patterns) is more useful The new representation can provide this kind of information Both codeword (pattern) 3 & 5 show up 2 times

V. Megalooikonomou, Temple University Methodology Problems of frequency based encoding: It is hard to define an approximate resolution (codeword length) It may lose global information

V. Megalooikonomou, Temple University Methodology Solution: Use multiple resolutions: It is hard to define an approximate resolution (codeword length) It may lose global information

V. Megalooikonomou, Temple University Methodology Proposed distance metric: Weighted sum of similarities, at all resolution levels level i where c is the number of resolution levels lacking any prior knowledge equal weights to all resolution levels works well most of the time

V. Megalooikonomou, Temple University MVQ: Example of Codebooks Codebook for the first level Codebook for the second level (more codewords since there are more details)

V. Megalooikonomou, Temple University Experiments Datasets SYNDATA (control chart data): synthetic CAMMOUSE: 3 *5 sequences obtained using the Camera Mouse Program RTT: RTT measurements from UCR to CMU with sending rate of 50 msec for a day

V. Megalooikonomou, Temple University Experiments Best Match Searching: Matching accuracy: % of knn’s (found by different approaches) that are in same class

V. Megalooikonomou, Temple University Experiments Best Match Searching MethodWeight Vector Accuracy Single level VQ [ ]0.55 [ ]0.70 [ ]0.65 [ ]0.48 [ ]0.46 MVQ[ ]0.83 Euclidean0.51 SYNDATACAMMOUSE MethodWeight VectorAccuracy Single level VQ [ ]0.56 [ ]0.60 [ ]0.44 [ ]0.56 [ ]0.60 MVQ[ ]0.83 Euclidean0.58

V. Megalooikonomou, Temple University Experiments Best Match Searching (a) (b) Precision-recall for different methods (a) on SYNDATA dataset (b) on CAMMOUSE dataset MVQ

V. Megalooikonomou, Temple University Experiments Clustering experiments Given two clusterings, G=G 1, G 2, …, G K (the true clusters), and A = A 1, A 2, …, A k (clustering result by a certain method), the clustering accuracy is evaluated with the cluster similarity defined as: with [Gavrilov, M., Anguelov, D., Indyk, P. and Motwani, R., KDD 2000]

V. Megalooikonomou, Temple University Experiments Clustering experiments. MethodWeight Vector Accuracy Single level VQ [ ]0.69 [ ]0.71 [ ]0.63 [ ]0.51 [ ]0.49 MVQ[ ]0.82 DFT0.67 SAX0.65 DTW0.80 Euclidean0.55 SYNDATARTT MethodWeight Vector Accuracy Single level VQ [ ]0.55 [ ]0.52 [ ]0.57 [ ]0.80 [ ]0.79 MVQ[ ]0.81 DFT0.54 SAX0.54 DTW0.62 Euclidean0.50

V. Megalooikonomou, Temple University Experiments Summarization (SYNDATA) Typical series:

V. Megalooikonomou, Temple University Experiments First LevelSecond Level

V. Megalooikonomou, Temple University Given two time series t1 and t2 as follows: In the first level, they are encoded with the same codeword (3), so they are not distinguishable In the second level, more details are recorded. These two series have different encoded form: the first series is encoded with codeword 1 and 4, the second one is encoded with codewords 9 and 12. MVQ: Example: Two Time Series

V. Megalooikonomou, Temple University Hilbert Space Filling Curve Binning Statistical tests of significance on groups of points Identification of discriminative areas by back-projection (a) linear mapping of a 3D fMRI scan, (b) effect of binning by representing each bin with its V mean measurement, (c) the discriminative voxels after applying the t-test with θ=0.05 (a)(b)(c) Analysis of images by projection to 1D [D. Kontos, V. Megalooikonomou, N. Ghubade, and C. Faloutsos. IEEE Engineering in Medicine and Biology Society (EMBS), 2003]

V. Megalooikonomou, Temple University Areas discovered: (a) θ=0.05, (b) θ=0.01. The colorbar shows significance. (a) (b) Variation: Concatenate the values of statistically significant areas  spatial sequences Pattern analysis using the similarity between spatial sequences and time sequences SVD, DFT, DWT, PCA (clustering accuracy: %) Applying time series techniques Results: 87%-98% classification accuracy (t-test, CATX) [Q. Wang, D. Kontos, G. Li and V. Megalooikonomou, ICASSP 2004]

V. Megalooikonomou, Temple University Conclusions ‘Find patterns/interesting things’ efficiently and robustly in spatial and temporal data Use of partitioning and clustering Analysis at multiple resolutions Reduction of the number of tests performed Intelligent exploration of the space to find discriminative areas Reduction of dimensionality Symbolic representation Nice summarization

V. Megalooikonomou, Temple University Collaborators Faculty: Zoran Obradovic Orest Boyko James Gee Andrew Saykin Christos Faloutsos Christos Davatzikos Edward Herskovits Fillia Makedon Dragoljub Pokrajac Students: Despina Kontos Qiang Wang Guo Li Others: James Ford Alexandar Lazarevic

V. Megalooikonomou, Temple University Thank you! Acknowledgements This research has been funded by: –National Science Foundation CAREER award –National Science Foundation Grant –National Institutes of Health Grant R01 MH68066 funded by NIMH, NINDS, and NIA