Knowledge Discovery and Data Mining from Big Data

Knowledge Discovery and Data Mining from Big Data Vipin Kumar Department of Computer Science University of Minnesota kumar@cs. umn. edu www. cs. umn. edu/~kumar

Introduction July 15, 2015 Mining Big Data 2

Mining Big Data: Motivation § Today’s digital society has seen enormous data growth in both commercial and scientific databases § Data Mining is becoming a commonly used tool to extract information from large and complex datasets § Homeland Security Examples: § Helps provide better customer service in business/commercial setting § Helps scientists in hypothesis formation Scientific Data Geo-spatial data Sensor Networks Business Data Computational Simulations

Data Mining for Life and Health Sciences § Recent technological advances are helping to generate large amounts of both medical and genomic data • • High-throughput experiments/techniques - Gene and protein sequences - Gene-expression data - Biological networks and phylogenetic profiles Electronic Medical Records - IBM-Mayo clinic partnership has created a DB of 5 million patients - Single Nucleotides Polymorphisms (SNPs) § Data mining offers potential solution for analysis of large-scale data • • • Automated analysis of patients history for customized treatment Prediction of the functions of anonymous genes Identification of putative binding sites in protein structures for drugs/chemicals discovery July 15, 2015 Mining Big Data Protein Interaction Network 4

Origins of Data Mining • Draws ideas from machine learning/AI, pattern recognition, statistics, and database systems • Traditional Techniques may be unsuitable due to Statistics/ Machine Learning/ AI – Enormity of data – High dimensionality of data – Heterogeneous, distributed nature of data July 15, 2015 Pattern Recognition Data Mining Database systems Mining Big Data 5

Data Mining as Part of the Knowledge Discovery Process July 15, 2015 Mining Big Data 6

Data Mining Tasks. . . Clu Data ste g rin lin e d g ion t cia so As s le Ru Milk iv ict d e Pr o M e An De oma tec ly tio n

Predictive Modeling: Classification July 15, 2015 Mining Big Data 8

General Approach for Building a Classification Model l o g te ca e iv t ita t n l a c i r o ca g te a c i r q ua ss a l c Test Set Training Set July 15, 2015 Mining Big Data Learn Classifier Model 9

Examples of Classification Task • Predicting tumor cells as benign or malignant • Classifying secondary structures of protein as alpha-helix, beta-sheet, or random coil • Predicting functions of proteins • Classifying credit card transactions as legitimate or fraudulent • Categorizing news stories as finance, weather, entertainment, sports, etc • Identifying intruders in the cyberspace July 15, 2015 Mining Big Data 10

Commonly Used Classification Models • Base Classifiers – – – Decision Tree based Methods Rule-based Methods Nearest-neighbor Neural Networks Naïve Bayes and Bayesian Belief Networks Support Vector Machines • Ensemble Classifiers – Boosting, Bagging, Random Forests July 15, 2015 Mining Big Data 11

Classification Model: Decision Tree Model for predicting credit worthiness Employed Class Yes No No Education Graduate Yes July 15, 2015 Mining Big Data { High school, Undergrad } Number of years > 7 yrs < 7 yrs Yes No 12

Constructing a Decision Tree Employed Yes Worthy: 4 Not Worthy: 3 No Education Worthy: 0 Not Worthy: 3 Graduate Worthy: 2 Not Worthy: 2 High School/ Undergrad Worthy: 2 Not Worthy: 4 Not Worthy Key Computation July 15, 2015 Employed = Yes 4 3 Employed = No 0 3 Mining Big Data 13

Constructing a Decision Tree Employed = Yes Employed = No July 15, 2015 Mining Big Data 14

Design Issues of Decision Tree Induction • How should training records be split? – Method for specifying test condition • depending on attribute types – Measure for evaluating the goodness of a test condition • How should the splitting procedure stop? – Stop splitting if all the records belong to the same class or have identical attribute values – Early termination July 15, 2015 Mining Big Data 15

How to determine the Best Split l Greedy approach: – Nodes with purer class distribution are preferred l Need a measure of node impurity: High degree of impurity July 15, 2015 Low degree of impurity Mining Big Data 16

Measure of Impurity: GINI • Gini Index for a given node t : (NOTE: p( j | t) is the relative frequency of class j at node t). – Maximum (1 - 1/nc) when records are equally distributed among all classes, implying least interesting information – Minimum (0. 0) when all records belong to one class, implying most interesting information July 15, 2015 Mining Big Data 17

Measure of Impurity: GINI • Gini Index for a given node t : (NOTE: p( j | t) is the relative frequency of class j at node t). – For 2 -class problem (p, 1 – p): • GINI = 1 – p 2 – (1 – p)2 = 2 p (1 -p) July 15, 2015 Mining Big Data 18

Computing Gini Index of a Single Node P(C 1) = 0/6 = 0 P(C 2) = 6/6 = 1 Gini = 1 – P(C 1)2 – P(C 2)2 = 1 – 0 – 1 = 0 P(C 1) = 1/6 P(C 2) = 5/6 Gini = 1 – (1/6)2 – (5/6)2 = 0. 278 P(C 1) = 2/6 P(C 2) = 4/6 Gini = 1 – (2/6)2 – (4/6)2 = 0. 444 July 15, 2015 Mining Big Data 19

Computing Gini Index for a Collection of Nodes l When a node p is split into k partitions (children) where, ni = number of records at child i, n = number of records at parent node p. l Choose the attribute that minimizes weighted average Gini index of the children l Gini index is used in decision tree algorithms such as CART, SLIQ, SPRINT July 15, 2015 Mining Big Data 20

Binary Attributes: Computing GINI Index l l Splits into two partitions Effect of Weighing partitions: – Larger and Purer Partitions are sought for. B? Yes Gini(N 1) = 1 – (5/6)2 – (1/6)2 = 0. 278 Node N 1 No Node N 2 Weighted Gini of N 1 N 2 = 6/12 * 0. 278 + 6/12 * 0. 444 = 0. 361 Gini(N 2) = 1 – (2/6)2 – (4/6)2 = 0. 444 July 15, 2015 Gain = 0. 486 – 0. 361 = 0. 125 Mining Big Data 21

Continuous Attributes: Computing Gini Index l Use Binary Decisions based on one value l Several Choices for the splitting value – Number of possible splitting values = Number of distinct values l Each splitting value has a count matrix associated with it – Class counts in each of the partitions, A < v and A v l Simple method to choose best v – For each v, scan the database to gather count matrix and compute its Gini index – Computationally Inefficient! Repetition of work. July 15, 2015 Mining Big Data ≤ 80 > 80 Yes 0 3 No 3 4 22

Decision Tree Based Classification l Advantages: – – Inexpensive to construct Extremely fast at classifying unknown records Easy to interpret for small-sized trees Robust to noise (especially when methods to avoid overfitting are employed) – Can easily handle redundant or irrelevant attributes (unless the attributes are interacting) l Disadvantages: – Space of possible decision trees is exponentially large. Greedy approaches are often unable to find the best tree. – Does not take into account interactions between attributes – Each decision boundary involves only a single attribute July 15, 2015 Mining Big Data 23

Handling interactions + : 1000 instances Entropy (X) : 0. 99 Entropy (Y) : 0. 99 o : 1000 instances Y X July 15, 2015 Mining Big Data 24

Handling interactions + : 1000 instances o : 1000 instances Entropy (X) : 0. 99 Entropy (Y) : 0. 99 Entropy (Z) : 0. 98 Y Adding Z as a noisy attribute generated from a uniform distribution Attribute Z will be chosen for splitting! X Z Z X July 15, 2015 Y Mining Big Data 25

Limitations of single attribute-based decision boundaries Both positive (+) and negative (o) classes generated from skewed Gaussians with centers at (8, 8) and (12, 12) respectively. July 15, 2015 Mining Big Data 26

Model Overfitting July 15, 2015 Mining Big Data 27

Classification Errors • Training errors (apparent errors) – Errors committed on the training set • Test errors – Errors committed on the test set • Generalization errors – Expected error of a model over random selection of records from same distribution July 15, 2015 Mining Big Data 28

Example Data Set Two class problem: + : 5200 instances • 5000 instances generated from a Gaussian centered at (10, 10) • 200 noisy instances added o : 5200 instances • Generated from a uniform distribution 10 % of the data used for training and 90% of the data used for testing July 15, 2015 Mining Big Data 29

Increasing number of nodes in Decision Trees July 15, 2015 Mining Big Data 30

Decision Tree with 4 nodes Decision Tree Decision boundaries on Training data July 15, 2015 Mining Big Data 31

Decision Tree with 50 nodes Decision Tree Decision boundaries on Training data July 15, 2015 Mining Big Data 32

Which tree is better? Decision Tree with 4 nodes Which tree is better ? Decision Tree with 50 nodes July 15, 2015 Mining Big Data 33

Model Overfitting Underfitting: when model is too simple, both training and test errors are large Overfitting: when model is too complex, training error is small but test error is large July 15, 2015 Mining Big Data 34

Model Overfitting Using twice the number of data instances • If training data is under-representative, testing errors increase and training errors decrease on increasing number of nodes • Increasing the size of training data reduces the difference between training and testing errors at a given number of nodes July 15, 2015 Mining Big Data 35

Reasons for Model Overfitting • Presence of Noise • Lack of Representative Samples • Multiple Comparison Procedure July 15, 2015 Mining Big Data 36

Effect of Multiple Comparison Procedure • Consider the task of predicting whether stock market will rise/fall in the next 10 trading days • Random guessing: P(correct) = 0. 5 • Make 10 random guesses in a row: Day 1 Up Day 2 Down Day 3 Down Day 4 Up Day 5 Down Day 6 Down Day 7 Up Day 8 Up Day 9 Up Day 10 Down July 15, 2015 Mining Big Data 37

Effect of Multiple Comparison Procedure • Approach: – Get 50 analysts – Each analyst makes 10 random guesses – Choose the analyst that makes the most number of correct predictions • Probability that at least one analyst makes at least 8 correct predictions July 15, 2015 Mining Big Data 38

Effect of Multiple Comparison Procedure • Many algorithms employ the following greedy strategy: – Initial model: M – Alternative model: M’ = M , where is a component to be added to the model (e. g. , a test condition of a decision tree) – Keep M’ if improvement, (M, M’) > • Often times, is chosen from a set of alternative components, = { 1, 2, …, k} • If many alternatives are available, one may inadvertently add irrelevant components to the model, resulting in model overfitting July 15, 2015 Mining Big Data 39

Effect of Multiple Comparison - Example Use additional 100 noisy variables generated from a uniform distribution along with X and Y as attributes. Use 30% of the data for training and 70% of the data for testing July 15, 2015 Using only X and Y as attributes Mining Big Data 40

Notes on Overfitting • Overfitting results in decision trees that are more complex than necessary • Training error does not provide a good estimate of how well the tree will perform on previously unseen records • Need ways for incorporating model complexity into model development July 15, 2015 Mining Big Data 41

Evaluating Performance of Classifier • Model Selection – Performed during model building – Purpose is to ensure that model is not overly complex (to avoid overfitting) • Model Evaluation – Performed after model has been constructed – Purpose is to estimate performance of classifier on previously unseen data (e. g. , test set) July 15, 2015 Mining Big Data 42

Methods for Classifier Evaluation • Holdout – Reserve k% for training and (100 -k)% for testing • Random subsampling – Repeated holdout • Cross validation – Partition data into k disjoint subsets – k-fold: train on k-1 partitions, test on the remaining one – Leave-one-out: k=n • Bootstrap – Sampling with replacement –. 632 bootstrap: July 15, 2015 Mining Big Data 43

Application on Biomedical Data July 15, 2015 Mining Big Data 44

Application : SNP Association Study • Given: A patient data set that has genetic variations (SNPs) and their associated Phenotype (Disease). • Objective: Finding a combination of genetic characteristics that best defines the phenotype under study. SNP 1 SNP 2 … SNPM Disease Patient 1 1 1 … 1 1 Patient 2 0 1 … 1 1 Patient 3 1 0 … 0 0 … … … Patient N 1 1 Genetic Variation in Patients (SNPs) as Binary Matrix and Survival/Disease (Yes/No) as Class Label. July 15, 2015 Mining Big Data 45

SNP (Single nucleotide polymorphism) • Definition of SNP (wikipedia) – A SNP is defined as a single base change in a DNA sequence that occurs in a significant proportion (more than 1 percent) of a large population Individual 1 Individual 2 Individual 3 Individual 4 Individual 5 AGCGTGA AGCGTGA TCGAGGCTA GCGAGGCTA TCGAGGCTA Each SNP has 3 values ( GG / GT / TT ) ( mm / Mm/ MM) SNP – How many SNPs in Human genome? – 10, 000 July 15, 2015 Mining Big Data 46

Why is SNPs interesting? • In human beings, 99. 9 percent bases are same. • Remaining 0. 1 percent makes a person unique. – Different attributes / characteristics / traits • how a person looks, • diseases a person develops. • These variations can be: – Harmless (change in phenotype) – Harmful (diabetes, cancer, heart disease, Huntington's disease, and hemophilia ) – Latent (variations found in coding and regulatory regions, are not harmful on their own, and the change in each gene only becomes apparent under certain conditions e. g. susceptibility to lung cancer) July 15, 2015 Mining Big Data 47

Issues in SNP Association Study • In disease association studies number of SNPs varies from a small number (targeted study) to a million (GWA Studies) • Number of samples is usually small • Data sets may have noise or missing values. • Phenotype definition is not trivial (ex. definition of survival) • Environmental exposure, food habits etc adds more variability even among individuals defined under the same phenotype • Genetic heterogeneity among individuals for the same phenotype July 15, 2015 Mining Big Data 48

Existing Analysis Methods • Univariate Analysis: single SNP tested against the phenotype for correlaton and ranked. – Feasible but doesn’t capture the existing true combinations. • Multivariate Analysis: groups of SNPs of size two or more are tested for possible association with the phenotype. – Infeasible but captures any true combinations. • These two approaches are used to identify biomarkers. • Some approaches employ classification methods like SVMs to classify cases and controls. July 15, 2015 Mining Big Data 49

Discovering SNP Biomarkers • Given a SNP data set of Myeloma patients, find a combination of 3404 SNPs that best predicts survival. • • • cases 3404 SNPs selected from various regions of the chromosome 70 cases (Patients survived shorter than 1 year) 73 Controls (Patients survived longer than 3 years) Controls Complexity of the Problem: • Large number of SNPs (over a million in GWA studies) and small sample size • Complex interaction among genes may be responsible for the phenotype • Genetic heterogeneity among individuals sharing the same phenotype (due to environmental exposure, food habits, etc) adds more variability • Complex phenotype definition (eg. survival) July 15, 2015 Mining Big Data 50

Discovering SNP Biomarkers • Given a SNP data set of Myeloma patients, find a combination of 3404 SNPs that best predicts survival. • • • cases 3404 SNPs selected from various regions of the chromosome 70 cases (Patients survived shorter than 1 year) 73 Controls (Patients survived longer than 3 years) Controls Odds ratio Measures whether two groups have the same odds of an event. OR = 1 Odds of event is equal in both groups OR > 1 Odds of event is higher in cases OR < 1 Odds of event is higher in controls Biomarker (SNPs) Has Marker CLASS Lacks Marker CASE a b Control c d Odds ratio is invariant to row and column scaling July 15, 2015 Mining Big Data 51

P-value • P-value – Statistical terminology for a probability value – Is the probability that the we get an odds ratio as extreme as the one we got by random chance – Computed by using the chi-square statistic or Fisher’s exact test • Chi-square statistic is not valid if the number of entries in a cell of the contingency table is small • p-value = 1 – hygecdf( a – 1, a+b+c+d, a+c, a+b ) if we are testing value is higher than expected by random chance using Fisher’s exact test • A statistical test to determine if there are nonrandom associations between two categorical variables. – P-values are often expressed in terms of the negative log of p-value, e. g. , -log 10(0. 005) = 2. 3 July 15, 2015 Mining Big Data 53 53

Example: High pvalue, moderate odds ratio Biomarker (SNPs) Has Marker CASE CLASS Control Lacks Marker (a) 40 (b) 30 (c) 19 (d) 54 Highest p-value, moderate odds ratio Odds ratio = (a*d)/(b*c) = (40 * 54) / (30 * 19) = 3. 64 P-value = 1 – hygecdf( a – 1, a+b+c+d, a+c, a+b ) = 1 – hygecdf( 39, 143, 59, 70 ) log 10(0. 0243) = 3. 85 July 15, 2015 Mining Big Data 55 55

Example … Biomarker (SNPs) Has Marker CASE CLASS Control Lacks Marker (a) 7 (b) 63 (c) 1 (d) 72 Odds ratio = (a*d)/(b*c) = (7 * 72) / (63* 1) = 8 Highest odds ratio, moderate p value P-value = 1 – hygecdf( a – 1, a+b+c+d, a+c, a+b ) = 1 – hygecdf( 6, 143, 8, 70) log 10(pvalue) = 1. 56 July 15, 2015 Mining Big Data 56 56

Example … Biomarker (SNPs) Has Marker CLASS Lacks Marker CASE (a) 70 (b) 630 Control (c) 10 (d) 720 x 10 Odds ratio = (a*d)/(b*c) = (70 * 720) / (630* 10) = 8 P-value = 1 – hygecdf( a – 1, a+b+c+d, a+c, a+b ) = 1 – hygecdf( 60, 1430, 80, 700) log 10(pvalue) = 6. 56 July 15, 2015 Mining Big Data 57

Example … Biomarker (SNPs) Has Marker CLASS Lacks Marker CASE (a) 140 (b) 1260 Control (c) 20 (d) 1440 x 20 Odds ratio = (a*d)/(b*c) = (140 * 1440) / (1260* 20) = 8 P-value = 1 – hygecdf( a – 1, a+b+c+d, a+c, a+b ) = 1 – hygecdf( 139, 2860, 1400) log 10(pvalue) = 11. 9 July 15, 2015 Mining Big Data 58

Issues with Traditional Methods Top ranked SNP: • Each SNP is tested and ranked individually -log 10 P-value = 3. 8; Odds Ratio = 3. 7 • Individual SNP associations with true phenotype are not distinguishable from random permutation of phenotype Van Ness et al 2009 However, most reported associations are not robust: of the 166 putative associations which have been studied three or more times, only 6 have been consistently replicated. July 15, 2015 Mining Big Data 59

Evaluating the Utility of Univariate Rankings for Myeloma Data Feature Selection Leave-one-out Cross validation With SVM Biased Evaluation July 15, 2015 Mining Big Data 60

Evaluating the Utility of Univariate Rankings for Myeloma Data Feature Selection Leave-one-out Cross validation with SVM Leave-one-out Cross validation With SVM Feature Selection Biased Evaluation July 15, 2015 Clean Evaluation Mining Big Data 61

Random Permutation test • • 10, 000 random permutations of real phenotype generated. • For each one, Leave-one-out cross validation using SVM. Accuracy larger than 65% are highly significant. (p-value is < 10 -4) July 15, 2015 Mining Big Data 62

Nearest Neighbor Classifier July 15, 2015 Mining Big Data 63

Nearest Neighbor Classifiers • Basic idea: – If it walks like a duck, quacks like a duck, then it’s probably a duck Compute Distance Training Records July 15, 2015 Test Record Choose k of the “nearest” records Mining Big Data 64

Nearest-Neighbor Classifiers l Requires three things – The set of stored records – Distance metric to compute distance between records – The value of k, the number of nearest neighbors to retrieve l To classify an unknown record: – Compute distance to other training records – Identify k nearest neighbors – Use class labels of nearest neighbors to determine the class label of unknown record (e. g. , by taking majority vote) July 15, 2015 Mining Big Data 65

Nearest Neighbor Classification… • Choosing the value of k: – If k is too small, sensitive to noise points – If k is too large, neighborhood may include points from other classes July 15, 2015 Mining Big Data 66

Clustering July 15, 2015 Mining Big Data 67

Clustering • Finding groups of objects such that the objects in a group will be similar (or related) to one another and different from (or unrelated to) the objects in other groups Inter-cluster distances are maximized Intra-cluster distances are minimized July 15, 2015 Mining Big Data 68

Applications of Clustering • Applications: – Gene expression clustering – Clustering of patients based on phenotypic and genotypic factors for efficient disease diagnosis – Market Segmentation – Document Clustering – Finding groups of driver behaviors based upon patterns of automobile motions (normal, drunken, sleepy, rush hour driving, etc) Courtesy: Michael Eisen July 15, 2015 Mining Big Data 69

Notion of a Cluster can be Ambiguous How many clusters? Six Clusters Two Clusters Four Clusters July 15, 2015 Mining Big Data 70

Similarity and Dissimilarity Measures • Similarity measure – Numerical measure of how alike two data objects are. – Is higher when objects are more alike. – Often falls in the range [0, 1] • Dissimilarity measure – Numerical measure of how different are two data objects – Lower when objects are more alike – Minimum dissimilarity is often 0 – Upper limit varies • Proximity refers to a similarity or dissimilarity July 15, 2015 Mining Big Data 71

Euclidean Distance • Euclidean Distance Where n is the number of dimensions (attributes) and xk and yk are, respectively, the kth attributes (components) or data objects x and y. • Correlation July 15, 2015 Mining Big Data 72

Types of Clusterings • A clustering is a set of clusters • Important distinction between hierarchical and partitional sets of clusters • Partitional Clustering – A division data objects into non-overlapping subsets (clusters) such that each data object is in exactly one subset • Hierarchical clustering – A set of nested clusters organized as a hierarchical tree July 15, 2015 Mining Big Data 73

Other Distinctions Between Sets of Clusters • Exclusive versus non-exclusive – In non-exclusive clusterings, points may belong to multiple clusters. – Can represent multiple classes or ‘border’ points • Fuzzy versus non-fuzzy – In fuzzy clustering, a point belongs to every cluster with some weight between 0 and 1 – Weights must sum to 1 – Probabilistic clustering has similar characteristics • Partial versus complete – In some cases, we only want to cluster some of the data • Heterogeneous versus homogeneous – Clusters of widely different sizes, shapes, and densities July 15, 2015 Mining Big Data 74

Clustering Algorithms • K-means and its variants • Hierarchical clustering • Other types of clustering July 15, 2015 Mining Big Data 75

K-means Clustering • • • July 15, 2015 Partitional clustering approach Number of clusters, K, must be specified Each cluster is associated with a centroid (center point) Each point is assigned to the cluster with the closest centroid The basic algorithm is very simple Mining Big Data 76

Example of K-means Clustering

K-means Clustering – Details • The centroid is (typically) the mean of the points in the cluster • Initial centroids are often chosen randomly – Clusters produced vary from one run to another • ‘Closeness’ is measured by Euclidean distance, cosine similarity, correlation, etc • Complexity is O( n * K * I * d ) – July 15, 2015 n = number of points, K = number of clusters, I = number of iterations, d = number of attributes Mining Big Data 78

Evaluating K-means Clusters • Most common measure is Sum of Squared Error (SSE) – For each point, the error is the distance to the nearest cluster – To get SSE, we square these errors and sum them • x is a data point in cluster Ci and mi is the representative point for cluster Ci – Given two sets of clusters, we prefer the one with the smallest error – One easy way to reduce SSE is to increase K, the number of clusters July 15, 2015 Mining Big Data 79

Two different K-means Clusterings Original Points Optimal Clustering July 15, 2015 Sub-optimal Clustering Mining Big Data 80

Limitations of K-means • K-means has problems when clusters are of differing – Sizes – Densities – Non-globular shapes • K-means has problems when the data contains outliers. July 15, 2015 Mining Big Data 81

Limitations of K-means: Differing Sizes K-means (3 Clusters) Original Points July 15, 2015 Mining Big Data 82

Limitations of K-means: Differing Density K-means (3 Clusters) Original Points July 15, 2015 Mining Big Data 83

Limitations of K-means: Non-globular Shapes Original Points July 15, 2015 K-means (2 Clusters) Mining Big Data 84

Hierarchical Clustering • Produces a set of nested clusters organized as a hierarchical tree • Can be visualized as a dendrogram – A tree like diagram that records the sequences of merges or splits 3 5 2 1 2 3 4 July 15, 2015 Mining Big Data 1 5 6 4 85

Strengths of Hierarchical Clustering • Do not have to assume any particular number of clusters – Any desired number of clusters can be obtained by ‘cutting’ the dendrogram at the proper level • They may correspond to meaningful taxonomies – Example in biological sciences (e. g. , animal kingdom, phylogeny reconstruction, …) July 15, 2015 Mining Big Data 86

Hierarchical Clustering • Two main types of hierarchical clustering – Agglomerative: • Start with the points as individual clusters • At each step, merge the closest pair of clusters until only one cluster (or k clusters) left – Divisive: • Start with one, all-inclusive cluster • At each step, split a cluster until each cluster contains a point (or there are k clusters) • Traditional hierarchical algorithms use a similarity or distance matrix – Merge or split one cluster at a time July 15, 2015 Mining Big Data 87

Agglomerative Clustering Algorithm • More popular hierarchical clustering technique • Basic algorithm is straightforward 1. 2. 3. 4. 5. 6. • Compute the proximity matrix Let each data point be a cluster Repeat Merge the two closest clusters Update the proximity matrix Until only a single cluster remains Key operation is the computation of the proximity of two clusters – July 15, 2015 Different approaches to defining the distance between clusters distinguish the different algorithms Mining Big Data 88

Starting Situation • Start with clusters of individual points and p 1 p 2 p 3 p 4 p 5. . . a proximity matrix p 1 p 2 p 3 p 4 p 5. . . July 15, 2015 Mining Big Data Proximity Matrix 89

Intermediate Situation • After some merging steps, we have some clusters C 1 C 2 C 3 C 4 C 5 C 1 Proximity Matrix C 2 July 15, 2015 C 5 Mining Big Data 90

Intermediate Situation • We want to merge the two closest clusters (C 2 and C 5) and update the proximity matrix. C 1 C 2 C 3 C 4 C 5 Proximity Matrix C 1 C 2 July 15, 2015 C 5 Mining Big Data 91

After Merging • The question is “How do we update the proximity C 2 matrix? ” U C 1 C 2 U C 5 C 3 C 4 ? ? ? C 3 ? C 4 ? Proximity Matrix C 1 C 2 U C 5 July 15, 2015 Mining Big Data 92

How to Define Inter-Cluster Distance p 1 p 2 p 3 p 4 p 5 . . . p 1 Similarity? p 2 p 3 • • • p 4 MIN p 5 MAX. Group Average. Proximity Matrix Distance Between Centroids. Other methods driven by an objective function – Ward’s Method uses squared error July 15, 2015 Mining Big Data 93

How to Define Inter-Cluster Similarity p 1 p 2 p 3 p 4 p 5 . . . p 1 p 2 p 3 • • • p 4 MIN p 5 MAX. Group Average. Distance Between Centroids. Proximity Matrix Other methods driven by an objective function – Ward’s Method uses squared error July 15, 2015 Mining Big Data 94

How to Define Inter-Cluster Similarity p 1 p 2 p 3 p 4 p 5 . . . p 1 p 2 p 3 p 4 • • • MIN p 5 MAX. . Group Average. Distance Between Centroids Proximity Matrix Other methods driven by an objective function – Ward’s Method uses squared error July 15, 2015 Mining Big Data 95

Other Types of Cluster Algorithms • Hundreds of clustering algorithms • Some clustering algorithms – K-means – Hierarchical – Statistically based clustering algorithms • Mixture model based clustering – Fuzzy clustering – Self-organizing Maps (SOM) – Density-based (DBSCAN) • Proper choice of algorithms depends on the type of clusters to be found, the type of data, and the objective July 15, 2015 Mining Big Data 98

Cluster Validity • For supervised classification we have a variety of measures to evaluate how good our model is – Accuracy, precision, recall • For cluster analysis, the analogous question is how to evaluate the “goodness” of the resulting clusters? • But “clusters are in the eye of the beholder”! • Then why do we want to evaluate them? – – July 15, 2015 To avoid finding patterns in noise To compare clustering algorithms To compare two sets of clusters To compare two clusters Mining Big Data 99

Clusters found in Random Data Random Points DBSCAN K-means July 15, 2015 Complete Link Mining Big Data 100

Different Aspects of Cluster Validation • Distinguishing whether non-random structure actually exists in the data • Comparing the results of a cluster analysis to externally known results, e. g. , to externally given class labels • Evaluating how well the results of a cluster analysis fit the data without reference to external information • Comparing the results of two different sets of cluster analyses to determine which is better • Determining the ‘correct’ number of clusters July 15, 2015 Mining Big Data 101

Using Similarity Matrix for Cluster Validation • Order the similarity matrix with respect to cluster labels and inspect visually. July 15, 2015 Mining Big Data 102

Using Similarity Matrix for Cluster Validation • Clusters in random data are not so crisp DBSCAN July 15, 2015 Mining Big Data 103

Using Similarity Matrix for Cluster Validation • Clusters in random data are not so crisp K-means July 15, 2015 Mining Big Data 104

Using Similarity Matrix for Cluster Validation • Clusters in random data are not so crisp Complete Link July 15, 2015 Mining Big Data 105

Measures of Cluster Validity • Numerical measures that are applied to judge various aspects of cluster validity, are classified into the following three types of indices. – External Index: Used to measure the extent to which cluster labels match externally supplied class labels. • Entropy – Internal Index: Used to measure the goodness of a clustering structure without respect to external information. • Sum of Squared Error (SSE) – Relative Index: Used to compare two different clusterings or clusters. • Often an external or internal index is used for this function, e. g. , SSE or entropy • For futher details please see “Introduction to Data Mining”, Chapter 8. – http: //www-users. cs. umn. edu/~kumar/dmbook/ch 8. pdf July 15, 2015 Mining Big Data 106

Clustering Microarray Data July 15, 2015 Mining Big Data 107

Clustering Microarray Data • Microarray analysis allows the monitoring of the activities of many genes over many different conditions • Data: Expression profiles of approximately 3606 genes of E Coli are recorded for 30 experimental conditions • SAM (Significance Analysis of Microarrays) package from Stanford University is used for the analysis of the data and to identify the genes that are substantially differentially upregulated in the dataset – 17 such genes are identified for study purposes C 1 C 2 C 3 C 4 C 5 C 6 C 7 Gene 1 Gene 2 Gene 3 Gene 4 Gene 5 Gene 6 Gene 7 …. • Hierarchical clustering is performed and plotted using Tree. View July 15, 2015 Mining Big Data 108

Clustering Microarray Data… July 15, 2015 Mining Big Data 109

CLUTO for Clustering for Microarray Data • CLUTO (Clustering Toolkit) George Karypis (Uof. M) http: //glaros. dtc. umn. edu/gkhome/views/cluto/ • CLUTO can also be used for clustering microarray data July 15, 2015 Mining Big Data 110

Issues in Clustering Expression Data • Similarity uses all the conditions – We are typically interested in sets of genes that are similar for a relatively small set of conditions • Most clustering approaches assume that an object can only be in one cluster – A gene may belong to more than one functional group – Thus, overlapping groups are needed • Can either use clustering that takes these factors into account or use other techniques – For example, association analysis July 15, 2015 Mining Big Data 111

Clustering Packages • Mathematical and Statistical Packages – – MATLAB SAS SPSS R • CLUTO (Clustering Toolkit) George Karypis (UM) http: //glaros. dtc. umn. edu/gkhome/views/cluto/ • Cluster Michael Eisen (LBNL/UCB) (microarray) • http: //rana. lbl. gov/Eisen. Software. htm http: //genome-www 5. stanford. edu/resources/restech. shtml (more microarray clustering algorithms) Many others – KDNuggets http: //www. kdnuggets. com/software/clustering. html July 15, 2015 Mining Big Data 112

Association Analysis July 15, 2015 Mining Big Data 113

Association Analysis • Given a set of records, find dependency rules which will predict occurrence of an item based on occurrences of other items in the record Rules Discovered: {Milk} --> {Coke} (s=0. 6, c=0. 75) {Diaper, Milk} --> {Beer} (s=0. 4, c=0. 67) • Applications – Marketing and Sales Promotion – Supermarket shelf management – Traffic pattern analysis (e. g. , rules such as "high congestion on Intersection 58 implies high accident rates for left turning traffic") July 15, 2015 Mining Big Data 114

Association Rule Mining Task • Given a set of transactions T, the goal of association rule mining is to find all rules having – support ≥ minsup threshold – confidence ≥ minconf threshold • Brute-force approach: Two Steps – Frequent Itemset Generation • Generate all itemsets whose support minsup – Rule Generation • Generate high confidence rules from each frequent itemset, where each rule is a binary partitioning of a frequent itemset • Frequent itemset generation is computationally expensive July 15, 2015 Mining Big Data 115

Efficient Pruning Strategy (Ref: Agrawal & Srikant 1994) If an itemset is infrequent, then all of its supersets must also be infrequent Found to be Infrequent Pruned supersets July 15, 2015 Mining Big Data 116

Illustrating Apriori Principle Items (1 -itemsets) Pairs (2 -itemsets) (No need to generate candidates involving Coke or Eggs) Minimum Support = 3 Triplets (3 -itemsets) If every subset is considered, 6 C + 6 C = 41 1 2 3 With support-based pruning, 6 + 1 = 13 July 15, 2015 Mining Big Data 117

Association Measures • Association measures evaluate the strength of an association pattern – Support and confidence are the most commonly used – The support, (X), of an itemset X is the number of transactions that contain all the items of the itemset • Frequent itemsets have support > specified threshold • Different types of itemset patterns are distinguished by a measure and a threshold – The confidence of an association rule is given by conf(X Y) = (X Y) / (X) • Estimate of the conditional probability of Y given X • Other measures can be more useful – H-confidence – Interest July 15, 2015 Mining Big Data 118

Application on Biomedical Data July 15, 2015 Mining Big Data 119

Mining Differential Coexpression (DC) • Differential expression Differential coexpression • Differential Expression (DE) – Traditional analysis targets the changes of expression level cases Expression level controls Expression over samples in controls and cases [Golub et al. , 1999], [Pan 2002], [Cui and Churchill, 2003] etc. July 15, 2015 Mining Big Data 120

Differential Coexpression (DC) • Differential Coexpression (DC) – Targets changes of the coherence of expression controls genes controls cases interesting, Question: Is this gene i. e. associated w/ the phenotype? cases Answer: No, in term of differential expression (DE). However, what if there another two genes ……? Matrix of expression values Yes!& Spang, 2005] [Kostka Expression over samples in controls and cases Biological interpretations of DC: Dysregulation of pathways, mutation of transcriptional factors, etc. [Silva et al. , 1995], [Li, 2002], [Kostka & Spang, 2005], [Rosemary et al. , 2008], [Cho et al. 2009] etc. July 15, 2015 Mining Big Data 121

Differential Coexpression (DC) • Existing work on differential coexpression – Pairs of genes with differential coexpression • [Silva et al. , 1995], [Li, 2002], [Li et al. , 2003], [Lai et al. 2004] – Clustering based differential coexpression analysis • [Ihmels et al. , 2005], [Watson. , 2006] – Network based analysis of differential coexpression • [Zhang and Horvath, 2005], [Choi et al. , 2005], [Gargalovic et al. 2006], [Oldham et al. 2006], [Fuller et al. , 2007], [Xu et al. , 2008] – Beyond pair-wise (size-k) differential coexpression • [Kostka and Spang. , 2004], [Prieto et al. , 2006] – Gene-pathway differential coexpression • [Rosemary et al. , 2008] – Pathway-pathway differential coexpression • [Cho et al. , 2009] July 15, 2015 Mining Big Data 122

Existing DC work is “full-space” • Full-space differential coexpression Full-space measures: e. g. correlation difference • May have limitations due to the heterogeneity of – Causes of a disease (e. g. genetic difference) – Populations affected (e. g. demographic difference) Motivation: Such subspace patterns may be missed by fullspace models July 15, 2015 Mining Big Data 123

Extension to Subspace Differential Coexpression • Definition of Subspace Differential Coexpression Pattern – A set of k genes – – = {g 1, g 2 , …, gk} : Fraction of samples in class A, on which the k genes are coexpressed : Fraction of samples in class B, on which the k genes are coexpressed Problem: given n genes, find all the subsets of genes, s. t. SDC≥d as a measure of subspace differential coexpression Details in [Fang, Kuang, Pandey, Steinbach, Myers and Kumar, PSB 2010] July 15, 2015 Mining Big Data 124

Computational Challenge Problem: given n genes, find all the subsets of genes, s. t. SDC≥d Given n genes, there are 2 n candidates of SDC pattern! How to effectively handle the combinatorial search space? Similar motivation and challenge as biclustering, but here differential biclustering ! July 15, 2015 Mining Big Data 125

Direct Mining of Differential Patterns Refined SDC measure: “direct” >> A measure M is antimonotonic if V A, B: A B M(A) >= M(B) ≈ Details in [Fang, Kuang, Pandey, Steinbach, Myers and Kumar, PSB 2010] [Fang, Pandey, Gupta, Steinbach and Kumar, IEEE TKDE 2011] July 15, 2015 Mining Big Data 126

An Association-analysis Approach Refined SDC measure Disqualified A measure M is antimonotonic if V A, B: A B M(A) >= M(B) Advantages: 1) Systematic & direct 2) Completeness 3) Efficiency Prune all the supersets July 15, 2015 [ Agrawal et al. 1994] Mining Big Data 127

A 10 -gene Subspace DC Pattern Enriched with the TNF-α/NFk. B signaling pathway (6/10 overlap with the pathway, P-value: 1. 4*10 -5) ≈ 10% July 15, 2015 Suggests that the dysregulation of TNF-α/NFk. B pathway may be related to lung cancer ≈ 60% Mining Big Data www. ingenuity. com: enriched Ingenuity subnetwork 128

Data Mining Book For further details and sample chapters see www. cs. umn. edu/~kumar/dmbook July 15, 2015 Mining Big Data 129

References • • Book Computational Approaches for Protein Function Prediction, Gaurav Pandey, Vipin Kumar and Michael Steinbach, to be published by John Wiley and Sons in the Book Series on Bioinformatics in Fall 2007 • • Conferences/Workshops Association Analysis-based Transformations for Protein Interaction Networks: A Function Prediction Case Study, Gaurav Pandey, Michael Steinbach, Rohit Gupta, Tushar Garg and Vipin Kumar, to appear, ACM SIGKDD 2007 • Incorporating Functional Inter-relationships into Algorithms for Protein Function Prediction, Gaurav Pandey and Vipin Kumar, to appear, ISMB satellite meeting on Automated Function Prediction 2007 • Comparative Study of Various Genomic Data Sets for Protein Function Prediction and Enhancements Using Association Analysis, Rohit Gupta, Tushar Garg, Gaurav Pandey, Michael Steinbach and Vipin Kumar, To be published in the proceedings of the Workshop on Data Mining for Biomedical Informatics, held in conjunction with SIAM International Conference on Data Mining, 2007 • Identification of Functional Modules in Protein Complexes via Hyperclique Pattern Discovery, Hui Xiong, X. He, Chris Ding, Ya Zhang, Vipin Kumar and Stephen R. Holbrook, pp 221 -232, Proc. of the Pacific Symposium on Biocomputing, 2005 • Feature Mining for Prediction of Degree of Liver Fibrosis, Benjamin Mayer, Huzefa Rangwala, Rohit Gupta, Jaideep Srivastava, George Karypis, Vipin Kumar and Piet de Groen, Proc. Annual Symposium of American Medical Informatics Association (AMIA), 2005 • • Technical Reports Association Analysis-based Transformations for Protein Interaction Networks: A Function Prediction Case Study, Gaurav Pandey, Michael Steinbach, Rohit Gupta, Tushar Garg, Vipin Kumar, Technical Report 07 -007, March 2007, Department of Computer Science, University of Minnesota • Computational Approaches for Protein Function Prediction: A Survey, Gaurav Pandey, Vipin Kumar, Michael Steinbach, Technical Report 06 -028, October 2006, Department of Computer Science, University of Minnesota July 15, 2015 Mining Big Data 130