Chuck Cartledge, PhD. 23 September 2017
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1 Introduction Definitions Numerical data Hands-on Q&A Conclusion References Files Big Data: Data Analysis Boot Camp Agglomerative Clustering Chuck Cartledge, PhD 23 September /30
2 Table of contents (1 of 1) 1 Introduction 2 Definitions 3 Numerical data 4 Hands-on 6 Conclusion 7 References 8 Files 5 Q & A 2/30
3 What are we going to cover? We re going to talk about: Different types of clustering approaches, How different measurement techniques affect clustering, and How clusters can interact. 3/30
4 Basic ideas Constructive (agglomerative) or deconstructive (divisive) approach? Basic approaches:[2] Agglomerative each observation starts in its own cluster, and pairs of clusters are merged as one moves up the hierarchy Divisive all observations start in one cluster, and splits are performed recursively as one moves down the hierarchy Image from [1]. 4/30
5 Basic ideas Same image. Image from [1]. 5/30
6 Basic ideas Agglomerative and divisive are SLOW Big O complexity of both approaches:[2] Agglomerative O(n 2 log(n)) Divisive O(2 n ) Blind clustering is too slow for large datasets. Special cases may have complexity of O(n 2 ). 6/30
7 Basic ideas Types of clusterings[3]: Hierarchical versus partitional: clusters are nested or not Exclusive vs. overlapping vs. fuzzy: clusters can overlap or not, or membership is not a binary value Complete versus partial: all members are assigned to a cluster or not 7/30
8 Basic ideas Types of clusters[3]: Well-separated: each member is closer to the centroid than any other member not in the cluster Prototype-based: members are closer to the cluster prototype (or medoid) vice any other prototype Graph based: members have a connection (edge or arc) to other members in the cluster Density-based: a cluster is an area of high density surrounded by areas of low density Shared-property: members share some common attribute 8/30
9 Basic ideas Data characteristics that will affect clustering[3]: High dimensionality: in high dimensioned space, Euclidean distance becomes less useful Size: many clustering algorithms do not scale well Sparseness: members with many attributes, may have zero values that might be important Noise and outliers: may cause members to be incorrectly added to a cluster Types of attributes and data set: categorical, quantitative, binary, discrete, continuous Scale: units of attribute measures may affect cluster assignment Mathematical properties of the data space: ideas of mean, Euclidean distance, density may be applicable to the data space and therefore will affect clustering 9/30
10 Basic ideas Considerations when choosing a clustering algorithm[3]: Type of clustering Type of cluster Characteristics of a cluster Characteristics of the dataset and attributes Each consideration will affect the outcome. Noise and outliers Number of data objects Number of attributes Cluster description Algorithmic considerations 10/30
11 Our clustering explorations We will be exploring agglomerative hierarchical clusters using hclust(). Because: Our data support this approach, It is easy to understand, It is the text. 11/30
12 Life expectancy in different forms Life expectancy from text 1 Load the attached file chapter-05-life-expectancy.r into the editor 2 Execute the entire file (highlight and press the run button) 3 Execute: main(false) in the console Attached file. 12/30
13 Life expectancy in different forms Same image. Attached file. 13/30
14 Life expectancy in different forms What is happening? 1 Rows (countries) that are close to each other are clustered (agglomerated) 2 How far the centroid is from each row is the height value (height can be thought of as distance ) 3 Clusters that are close to each other are clustered (hence hierarchy) At any time, a horizontal line will give clusters and membership. 14/30
15 Swiss voting data Exploring Swiss voting results Analyzing a common datafile with different clustering approaches. complete: produces compact clusters single: more inclusive clusters average: clusters between compact and inclusive Program in attached file (chapter-05-swiss-voting.r). Attached file. 15/30
16 Swiss voting data Same image. Attached file. 16/30
17 Swiss voting data Swiss voting data in different forms 1 Load the attached file chapter-05-swiss-voting.r into the editor 2 Execute the entire file (highlight and press the run button) 3 Execute: main(false) in the console Attached file. 17/30
18 Swiss voting data Same image. Attached file. 18/30
19 Swiss voting data Interesting things about clusters Some interesting things: Data was cut based on complete clustering and k = 4 Colors match the cluster each cannon is assigned to There are two well separated clusters There are two over-lapping clusters Based on the clusterings, more investigation into why there are similarities and differences is warranted. Attached file. 19/30
20 Swiss voting data Same image. Attached file. 20/30
21 Binary data Looking at British truck accident data Some notes: Data was collected in Britain before and after new safety regulations Raw data is mostly categorical (two values) Categorical data converted to binary Distance is still valid measurement Attached file. 21/30
22 Binary data Same image. Attached file. 22/30
23 Binary data Loading the truck accident software 1 Load the attached file chapter-05-trucks.r into the editor 2 Execute the entire file (highlight and press the run button) 3 Execute: main(false) in the console 23/30
24 Binary data More detailed investigation Index period collision parked Only 6 of possible 8 combinations. 24/30
25 Binary data A final look 1 Load the attached file chapter-05-trucks-help.r into the editor 2 Execute the entire file From *help[r](trucks)* 25/30
26 Some simple exercises to get familiar with data clustering 1 What are the height values for the life expectancy plots (requires looking at code)? 2 Change the life expectancy plots to display raw values. 3 Change the Swiss voting example to use Manhattan distance. Which distance measurement is better/best? Why? 26/30
27 Q & A time. Q: How did you get into artificial intelligence? A: Seemed logical I didn t have any real intelligence. 27/30
28 What have we covered? Looked at different types of clustering approaches Looked at different types of clusters and data characteristics Looked at clustering considerations Looked at how distance computations can affect clustering Looked at how clusters can interrelate looked at continuous and binary data clustering Next: LPAR Chapter 9, linear regression 28/30
29 References (1 of 1) [1] Erin Shellman, BI Tech CP303 - Data Mining, http: //erinshellman.github.io/data-mining-starter-kit/, [2] Wikipedia Staff, Hierarchical clustering, https: //en.wikipedia.org/wiki/hierarchical_clustering, [3] Pang-Ning Tan, Michael Steinbach, and Vipin Kumar, Introduction to Data Mining, Pearson Education India, /30
30 Files of interest 1 Revised life-expectancy clustering (chapter-05-lifeexpectancy.r) 2 Revised Swiss voting 3 Revised truck accidents 4 Truck accidents (a final look) clustering 5 R library script file 30/30
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