Mr. Idrissa Y. H. Assistant Lecturer, Geography & Environment Department of Social Sciences School of Natural & Social Sciences State University of Zanzibar LECTURE 8a_ SPATIAL STATISCAL ANALYSIS

 Introduction to spatial analysis  Judging spatial association visually  The concept of Clustering and Cluster analysis  Spatial Cross-Correlation  Pearson, Spearman  Multivariate spatial association measures

 That Spatial Statistics, extends traditional statistics on two fronts. First, it seeks to map the variation in a data set and Secondly, it can uncover “numerical spatial relationships” within and among mapped data layers.  Tobler’s Law  “Everything is related to everything else, but near things are more related than distant things”  3 major benefits of spatial analysis  Pattern Analysis  Feature count Analysis

February 24, 2016Data Mining: Concepts and Techniques4 1. What is Cluster Analysis? 2. Types of Data in Cluster Analysis 3. A Categorization of Major Clustering Methods 4. Partitioning Methods 5. Hierarchical Methods 6. Density-Based Methods 7. Grid-Based Methods 8. Model-Based Methods 9. Clustering High-Dimensional Data 10. Constraint-Based Clustering 11. Outlier Analysis 12. Summary

February 24, 2016Data Mining: Concepts and Techniques5  Cluster: a collection of data objects  Similar to one another within the same cluster  Dissimilar to the objects in other clusters  Cluster analysis  Finding similarities between data according to the characteristics found in the data and grouping similar data objects into clusters  Unsupervised learning: no predefined classes  Typical applications  As a stand-alone tool to get insight into data distribution  As a preprocessing step for other algorithms

February 24, 2016Data Mining: Concepts and Techniques6  Pattern Recognition  Spatial Data Analysis  Create thematic maps in GIS by clustering feature spaces  Detect spatial clusters or for other spatial mining tasks  Image Processing  Economic Science (especially market research)  WWW  Document classification  Cluster Weblog data to discover groups of similar access patterns

February 24, 2016Data Mining: Concepts and Techniques7  Marketing: Help marketers discover distinct groups in their customer bases, and then use this knowledge to develop targeted marketing programs  Land use: Identification of areas of similar land use in an earth observation database  Insurance: Identifying groups of motor insurance policy holders with a high average claim cost  City-planning: Identifying groups of houses according to their house type, value, and geographical location  Earth-quake studies: Observed earth quake epicenters should be clustered along continent faults

February 24, 2016Data Mining: Concepts and Techniques8  A good clustering method will produce high quality clusters with  high intra-class similarity  low inter-class similarity  The quality of a clustering result depends on both the similarity measure used by the method and its implementation  The quality of a clustering method is also measured by its ability to discover some or all of the hidden patterns

February 24, 2016Data Mining: Concepts and Techniques9  Dissimilarity/Similarity metric: Similarity is expressed in terms of a distance function, typically metric: d(i, j)  There is a separate “quality” function that measures the “goodness” of a cluster.  The definitions of distance functions are usually very different for interval-scaled, boolean, categorical, ordinal ratio, and vector variables.  Weights should be associated with different variables based on applications and data semantics.  It is hard to define “similar enough” or “good enough”  the answer is typically highly subjective.

February 24, 2016Data Mining: Concepts and Techniques10  Partitioning approach:  Construct various partitions and then evaluate them by some criterion, e.g., minimizing the sum of square errors  Typical methods: k-means, k-medoids, CLARANS  Hierarchical approach:  Create a hierarchical decomposition of the set of data (or objects) using some criterion  Typical methods: Diana, Agnes, BIRCH, ROCK, CAMELEON  Density-based approach:  Based on connectivity and density functions  Typical methods: DBSACN, OPTICS, DenClue

February 24, 2016Data Mining: Concepts and Techniques11  Grid-based approach:  based on a multiple-level granularity structure  Typical methods: STING, WaveCluster, CLIQUE  Model-based:  A model is hypothesized for each of the clusters and tries to find the best fit of that model to each other  Typical methods: EM, SOM, COBWEB  Frequent pattern-based:  Based on the analysis of frequent patterns  Typical methods: pCluster  User-guided or constraint-based:  Clustering by considering user-specified or application-specific constraints  Typical methods: COD (obstacles), constrained clustering

February 24, 2016Data Mining: Concepts and Techniques12  Given k, the k-means algorithm is implemented in four steps:  Partition objects into k nonempty subsets  Compute seed points as the centroids of the clusters of the current partition (the centroid is the center, i.e., mean point, of the cluster)  Assign each object to the cluster with the nearest seed point  Go back to Step 2, stop when no more new assignment

February 24, 2016Data Mining: Concepts and Techniques13  Example K=2 Arbitrarily choose K object as initial cluster center Assign each objects to most similar center Update the cluster means reassign

February 24, 2016Data Mining: Concepts and Techniques14  Strength: Relatively efficient: O(tkn), where n is # objects, k is # clusters, and t is # iterations. Normally, k, t << n. ▪ Comparing: PAM: O(k(n-k) 2 ), CLARA: O(ks 2 + k(n-k))  Comment: Often terminates at a local optimum. The global optimum may be found using techniques such as: deterministic annealing and genetic algorithms  Weakness  Applicable only when mean is defined, then what about categorical data?  Need to specify k, the number of clusters, in advance  Unable to handle noisy data and outliers  Not suitable to discover clusters with non-convex shapes

February 24, 2016Data Mining: Concepts and Techniques15  Cluster analysis groups objects based on their similarity and has wide applications  Measure of similarity can be computed for various types of data  Clustering algorithms can be categorized into partitioning methods, hierarchical methods, density-based methods, grid- based methods, and model-based methods  Outlier detection and analysis are very useful for fraud detection, etc. and can be performed by statistical, distance- based or deviation-based approaches  There are still lots of research issues on cluster analysis