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G54DMT – Data Mining Techniques and Applications Dr. Jaume Bacardit

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1 G54DMT – Data Mining Techniques and Applications Dr. Jaume Bacardit Topic 1: Preliminaries

2 Outline of the topic General data mining definitions and concepts Handling datasets Repositories of datasets Experimental evaluation of data mining methods Information theory Playing a bit with Weka

3 Dataset structure It most cases we will treat a dataset as a table with rows and columns Instances Attributes

4 Instances and attributes Instances are the atomic elements of information from a dataset – Also known as records or prototypes Each instance is composed of a certain number of attributes – Also known as features or variables – In a dataset attributes can be of different types Continuous (or Integer) Discrete (i.e. being able to take a value from a finite set)

5 Supervised learning Many times the datasets got a special attribute, the class or output If they do, the task of the data mining process consists in generating a model that can predict the class/output for a new instance based on the values for the rest of attributes In order to generate this model, we will use a corpus of data for which we already know the answer, the training set

6 Example of dataset Witten and Frank, 2005 (

7 Process of supervised learning Learning Algorithm Inference Engine Models Training Set New Instance Annotated Instance

8 Types of supervised learning If the special attribute is discrete – We call it class – The dataset is a classification problem If the special attribute is continuous – We call it output – The dataset is a regression problem Also called modelling or function aproximation

9 Rule Learning CN2, RISE, GAssist, BioHEL X Y 0 1 1 If (X 0.75) or (X>0.75 and Y<0.25) then  If (X>0.75 and Y>0.75) then  If (X<0.25 and Y<0.25) then  Everything else 

10 A decision tree (ID3/C4.5) age? overcast student?credit rating? <=30 >40 noyes 31..40 no fairexcellent yesno

11 Linear Classification (Logistic Regression) x x x x xx x x x x o o o o o o o o oo o o o

12 Support Vector Machines (SVM) Support Vectors Small Margin Large Margin

13 Unsupervised learning When we do not have/not take into account the class/output attribute If the goal is to identify aggregations of instances – Clustering problem If the goal is to detect strong patterns in the data – Association rules/Itemset mining

14 Clustering (K-Means, EM) Partitional clusteringHierarchical clustering

15 Association rules mining (Apriori, FP-growth) Witten and Frank, 2005 (

16 Reinforcement learning When the system is being given a reward or punishment whether its prediction was correct or not The DM system is not being told what is exactly right or wrong, just the reward RL methods work prediction by prediction – This is why many times they are called online systems

17 Dataset handling and format In DM most datasets are represented as simple plain text files (or sometimes excel sheets) More sophisticated (and efficient) methods exist We need to decide how to specify the dataset structure (i.e. the metadata) and the content (the instances)

18 ARFF format ARFF = Attribute-Relation File Format File format from the WEKA DM package

19 HDF5 Much more complex file format designed for scientific data handling It can store heterogeneous and hierarchical organized data It has been designed for efficiency Presentation slides

20 Repositories of datasets UCI repository – – Probably the most famous collection of datasets in ML! – Currently has 235 datasets Kaggle – It is not a static repository of datasets, but a site that manages Data Mining competitions – Example of the modern concept of crowdsourcing

21 Repositories of datasets KDNuggets – PSPbenchmarks – – Datasets derived from Protein Structure Prediction problems – Interesting benchmarks because they can be parametrised in a very large variety of ways Pascal Large Scale Learning Challenge –

22 Experimental Evaluation We have Data Mining methods and datasets How can we know that the patterns they extract are meaningful? How can we know how well do they perform and which method is the best? We need to follow a principled protocol to make sure that the results and conclusions we extract are sound

23 Verifying that the model is sound The dataset, before the data mining process, is partitioned into two non-overlapped parts: – Training set. Will be used to generate the model – Test set. Will be used to validate the model We can compute the performance metric (more on the next slides) on both sets. If the metric for the training set is much higher than in the test set, we have a case of overlearning That is, the DM method has not modelled the problem, only the training set

24 Performance metrics: Classification Problems Accuracy: C/D – C = number of correctly classified examples. D is size of instance set – Simplest and most widespread metric – But what if some classes got more examples than others? The majority class would get more benefit out of this metric

25 (Garcia et al., 2009) C = number of classes, x i = examples from class I X ii =examples correctly classified from class i Performance metrics: classification problems Cohen’s Kappa – Computes the agreement between two distributions of categorical variables (i.e. real and predicted classes) – Takes into account agreement by chance – Hence, it may be more suitable for multi-class problems There are more metrics (e.g. ROC curves)

26 Performance metrics Regression problems – RMSD RMSD Metrics for clustering problems Association rule mining – Support (percentage of instances covered by the pattern) – Confidence (agreement between predicate and consequent of the rule)

27 Performance estimation methodologies We have to partition the dataset into training and test, but how is this partitioning done? If this partitioning is wrong we will not obtain a good estimation of the method’s performance

28 Performace estimation methodologies: Holdout Simply dividing the dataset into two non- overlaped sets (e.g. 2/3 of the dataset for training, 1/3 of the set for test). Most simple method and computationally cheap The performance is computed on the test set Its reliability greatly depends on how the sets are partitioned

29 Performace estimation methodologies: K-fold cross-validation Divide the dataset into K strata Iterate K times: – Use sets 1.. K-1 for training and the set K for test – Use sets 1..K-2,K for training and the set K-1 for test – etc Computer the performance estimation as the average of the metric for each of the K test sets More robust estimator, but computationally more costlier If each of the K strata has the same class distribution as the whole dataset, this method is called stratified K-fold cross- validation

30 Performance estimation methodologies Leave-one-out cross-validation – Extreme case of cross-validation, where K=D, the size of the dataset – Training sets will have size D-1 and test sets will have only one instance – Mostly used in datasets of small size Bootstrap – Generate a sample with replacement from the dataset with size D. Use it as training set – Use the instances never selected as test set – Repeat this process a high number of times

31 Performance estimation methodologies But which method is best? Two criteria to take into account – Bias: Difference between the estimation and the true error – Variance of the estimation’s sample Formal and experimental analysis of some of these methods Formal and experimental analysis of some of these methods Experimental study for microarray data

32 Who is the best? At the end of an experimentation we will have tested N methods on D datasets, thus we will have a NxD table of performance metrics How can we identify the best method? – Highest average performance across the D datasets? – Highest average rank across the D datasets? Also, is the best method significantly better than the others? For this we need statistical test (next slide) Best study nowadays on statistical tests Most of the tests described in the next slides can be found in many statistical packages (e.g. R)R

33 Statistical tests Procedure for making decisions about data Each test defines an hypothesis (H 0 ) about the observed data – “The accuracy differences I observe between A and B are just by pure chance and the methods perform equally” – Or in a more statistical way “The two sets of data observations A and B belong to the same distribution” Then, the probability of H 0 being true given the observed data is calculated If the probability (p-value) is smaller than a certain threshold, H 0 is rejected and the observed differences are statistically significant

34 Traditional approach: Student T- testStudent T- test Tests whether the difference between two distributions is significant or not Generates a p-value, in this case the probability that the two distributions are not significantly different P-values of 0.05 or 0.01 are typical thresholds Can only applied if the distributions have the same variance and are normal. These conditions are hardly ever achieved

35 Wilcoxon test Non-parametric tests, which is not affected by the normality of the distribution It ranks the absolute differences in performance, dataset by dataset Next, it sums the ranks separately for the positive and negative differences A p-value will be generated depending on which sum of ranks is smaller and the number of datasets

36 Multiple pair-wise comparisons? Both the t-test and the Wilcoxon test are used to compare two methods What if we have more than two methods in our comparison? – You can hold individually that A is better than B and better than C with 95% confidence and but it is better than both B and C at the same time? – The p-values do not hold anymore We need to apply a correction for multiple tests (e.g. Bonferroni, Holm, etc.)BonferroniHolm

37 The Friedman test Designed explicitly to compare multiple methods Based on the average rank of each method across the datasets This test just says if the performance of the methods included is similar or not Can be used when having more than 10 datasets and more than 5 methods Once the test has determined that there are significant performance differences, a post-hoc test is used to spot them

38 Two types of post-hoc test Comparing every method to each other (e.g. the Nemenyi test) Comparing a control method against the others (e.g. the Holm test) – E.g. the best method against the others – This latter kind of test gives less information but are also more powerful (i.e. less conservative) Both are based on ranks

39 Using R to compute statistical tests R is an open source statistical computing package R It is extremely powerful, but not the most simple tool to use in the world…. It has build-in functions for most of the tests described in the previous slides Example from the command line….

40 Data for the test A plain text file with rows consisting of: – Example file CV has already been computed Let’s load the data in R: $ R > data<-read.table("rchA.dat") > data V1 V2 V3 1 C4_5 rchA_1_q2 0.664884 2 C4_5 rchA_2_q2 0.690657 3 C4_5 rchA_3_q2 0.731942 4 C4_5 rchA_4_q2 0.756022 5 C4_5 rchA_5_q2 0.733984

41 T-test > pairwise.t.test(data$V3,data$V1,,paired=T) Pairwise comparisons using t tests with non-pooled SD data: data$V3 and data$V1 C4_5 HEL+ LCS+ HEL+ 0.00056 - - LCS+ 0.00038 0.53291 - NB 0.53291 0.52834 0.53291 P value adjustment method: holm

42 Wilcoxon test > pairwise.wilcox.test(data$V3,data$V1,paired=T) Pairwise comparisons using Wilcoxon rank sum test data: data$V3 and data$V1 C4_5 HEL+ LCS+ HEL+ 0.00038 - - LCS+ 0.00032 0.72586 - NB 0.72586 0.72586 0.72586 P value adjustment method: holm > pairwise.wilcox.test(data$V3,data$V1,paired=T)$p.value C4_5 HEL+ LCS+ HEL+ 0.0003814697 NA NA LCS+ 0.0003204346 0.7258606 NA NB 0.7258605957 0.7258606 0.7258606 > write.table(pairwise.wilcox.test(data$V3,data$V1,paired=T)$p.value,"wilcox.dat”) Saving the results to a file

43 Friedman and post hoc tests Code for the Holm and Nemenyi post hoc testsHolm Nemenyi Code for accuracy (between 0 and 1) > source("fried+holm.r”) > fried.holm("rchA.dat") Friedman rank sum test data: data$V3, data$V1 and data$V2 Friedman chi-squared = 22.4667, df = 3, p-value = 5.216e-05 [1] "Average ranks" C4_5 HEL+ LCS+ NB 3.666667 1.722222 2.166667 2.444444 [1] "Control is HEL+" [1] "Confidence level of 0.950000" [1] "HEL+ is significantly better than C4_5" [1] "Confidence level of 0.990000" [1] "HEL+ is significantly better than C4_5"

44 Evaluation pipeline (summary) N datasets, M methods – Method can mean anything (mining, preprocessing, etc.) For each of the N datasets – Partition it into training and test sets – For each of the K pairs of (Training k n,Test k n ) sets For each of the M methods – model = Train Method M using set Training k n – Metric[N][M][K] = Test model using set Test k n – Metric[N][M] = Average across k pairs Compute average ranks of each method across datasets Run statistical tests using Metric matrix – There are overall statistical significant performance differences? – Individual tests one-vs-rest or all-vs-all

45 Basic Information Theory Shannon’s Entropy Shannon’s Entropy – Measure of the information content in discrete data – Metric inspired by statistical information transmission “How many bits per symbol (in average) would it take to transmit a message given the frequencies of each symbol?”

46 Shannon’s Entropy If we are tossing a coin and want to send a sequence of tosses – If heads and tails have the same probability it would take one bit per toss – If heads have a very small probability compared to tails we could just send a list of the heads and say that everything else is a tail Each head message would be long, but there would be very few of them, so overall it would take less than one bit to transmit a symbol (in average).

47 Other information theory metrics Conditional Entropy – Entropy of a certain variable given that we know all about a related variable Information gain – How many bits would I save from transmitting Y if I know about X? – IG(Y|X) = H(Y) – H(Y|X) Mutual information – Assesses the interrelationship between two variables

48 Why is it useful for in data mining? We have a continuous variable where each data point is associated to a class – 10 red dots, 10 blue dots – H(X) = -(0.5log(0.5)+0.5log(0.5))=1 What if we split this variable in two? – Where to split? – The point where we obtain maximum IG. Conditional variable X is the splitting point

49 Different cut points H(X;left) = 0.469, H(X;right) = 0.469, IG=0.531 H(X;left) = 0, H(X;right) = 0.863, IG=0.384 H(X;left) = 0.863, H(X;right)=0, IG=0.384

50 Let’s play a bit with Weka Download the WEKA GUI from herehere Dataset for this demo Dataset What I am going to show are just some of the steps from this tutorialthis tutorial

51 Weka from the command line…. $ java weka.classifiers.trees.J48 -t dataset.arff J48 pruned tree ------------------ att16 <= 1.28221 | att1 <= 1.33404 | | att3 <= 1.37681: 3 (6.0) | | att3 > 1.37681: 2 (4.0/1.0) | att1 > 1.33404 | | att17 <= 1.52505 | | | att5 <= 1.34135: 3 (3.0) | | | att5 > 1.34135 | | | | att8 <= 1.3391: 3 (4.0/1.0) | | | | att8 > 1.3391: 2 (19.0/1.0) | | att17 > 1.52505: 2 (18.0) att16 > 1.28221: 3 (938.0/456.0) Number of Leaves : 7 Size of the tree : 13 Time taken to build model: 0.11 seconds Time taken to test model on training data: 0.05 seconds === Error on training data === Correctly Classified Instances 533 53.7298 % Incorrectly Classified Instances 459 46.2702 % Kappa statistic 0.0746 Mean absolute error 0.4774 Root mean squared error 0.4885 Relative absolute error 95.4706 % Root relative squared error 97.7091 % Total Number of Instances 992 === Confusion Matrix === a b <-- classified as 39 457 | a = 2 2 494 | b = 3 === Stratified cross-validation === Correctly Classified Instances 491 49.496 % Incorrectly Classified Instances 501 50.504 % Kappa statistic -0.0101 Mean absolute error 0.4992 Root mean squared error 0.5111 Relative absolute error 99.8304 % Root relative squared error 102.214 % Total Number of Instances 992 === Confusion Matrix === a b <-- classified as 141 355 | a = 2 146 350 | b = 3

52 KEEL Knowledge Extration using Evolutionary Learning Another data mining platform with integrated graphical design of experiments Download prototype Manual Instructions about integrating new methods into it (slides,paper)slidespaper

53 Questions?

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