Data Mining: an Introduction

An Introduction to Data MiningData Mining and Machine Learning in a nutshell 1

DATA MINING AND MACHINE LEARNINGIN A NUTSHELL

AN INTRODUCTION TO DATA MINING

Mohammad-Ali Abbasihttp://www.public.asu.edu/~mabbasi2/

SCHOOL OF COMPUTING, INFORMATICS, AND DECISION SYSTEMS ENGINEERINGARIZONA STATE UNIVERSITY

http://dmml.asu.edu/

http://www.public.asu.edu/~mabbasi2/


INTRODUCTION

• Data production rate has been increased dramatically (Big Data) and we are able store much more data than before– E.g., purchase data, social media data, mobile phone

data• Businesses and customers need useful or

actionable knowledge and gain insight from raw data for various purposes– It’s not just searching data or databases

Data mining helps us to extract new information and uncover hidden patterns out of the stored and streaming data


DATA MINING

• Extracting or “mining” knowledge from large amounts of data, or big data

• Data-driven discovery and modeling of hidden patterns in big data

• Extracting implicit, previously unknown, unexpected, and potentially useful information/knowledge from data

The process of discovering hidden patterns in large data sets

It utilizes methods at the intersection of artificial intelligence, machine learning, statistics, and database systems


DATA MINING STORIES

• “My bank called and said that they saw that I bought two surfboards at Laguna Beach, California.” - credit card fraud detection

• The NSA is using data mining to analyze telephone call data to track al’Qaeda activities

• Walmart uses data mining to control product distribution based on typical customer buying patterns at individual stores


DATA MINING VS. DATABASES

• Data mining is the process of extracting hidden and actionable patterns from data

• Database systems store and manage data – Queries return part of stored data – Queries do not extract hidden patterns

• Examples of querying databases– Find all employees with income more than $250K– Find top spending customers in last month– Find all students from engineering college with

GPA more than average


EXAMPLES OF DATA MINING APPLICATIONS

• Identifying fraudulent transactions of a credit card or spam emails– You are given a user’s purchase history and a new

transaction, identify whether the transaction is fraud or not;

– Determine whether a given email is spam or not• Extracting purchase patterns from existing records– beer dippers (80%)⇒

• Forecasting future sales and needs according to some given samples

• Extracting groups of like-minded people in a given network


BASIC DATA MINING TASKS

• Classification– Assign data into predefined classes• Spam Detection, fraudulent credit card detection

• Regression– Predict a real value for a given data instance• Predict the price for a given house

• Clustering– Group similar items together into some clusters• Detect communities in a given social network


DATA


DATA INSTANCES

• A collection of properties and features related to an object or person– A patient’s medical record– A user’s profile– A gene’s information

• Instances are also called examples, records, data points, or observations

Data Instance:

Features or Attributes Class Label


DATA TYPES

• Nominal (categorical)– No comparison is defined– E.g., {male, female}

• Ordinal– Comparable but the difference is not defined– E.g., {Low, medium, high}

• Interval– Deduction and addition is defined but not division– E.g., 3:08 PM, calendar dates

• Ratio– E.g., Height, weight, money quantities


SAMPLE DATASEToutlook temperature humidity windy playsunny 85 85 FALSE nosunny 80 90 TRUE no

overcast 83 86 FALSE yesrainy 70 96 FALSE yesrainy 68 80 FALSE yesrainy 65 70 TRUE no

overcast 64 65 TRUE yessunny 72 95 FALSE nosunny 69 70 FALSE yesrainy 75 80 FALSE yessunny 75 70 TRUE yes

overcast 72 90 TRUE yesovercast 81 75 FALSE yes

rainy 71 91 TRUE no

Nominal OrdinalInterval


DATA QUALITY

When making data ready for data mining algorithms, data quality need to be assured• Noise– Noise is the distortion of the data

• Outliers– Outliers are data points that are considerably different

from other data points in the dataset• Missing Values– Missing feature values in data instances

• Duplicate data


DATA PREPROCESSING

• Aggregation– when multiple attributes need to be combined into a single

attribute or when the scale of the attributes change• Discretization

– From continues values to discrete values• Feature Selection

– Choose relevant features• Feature Extraction

– Creating a mapping of new features from original features • Sampling

– Random Sampling– Sampling with or without replacement– Stratified Sampling


CLASSIFICATION


CLASSIFICATION

Learning patterns from labeled data and classify new data with labels (categories)– For example, we want to classify an e-mail as

"legitimate" or "spam"

Classifier


CLASSIFICATION: THE PROCESS

• In classification, we are given a set of labeled examples

• These examples are records/instances in the format (x, y) where x is a vector and y is the class attribute, commonly a scalar

• The classification task is to build model that maps x to y

• Our task is to find a mapping f such that f(x) = y


CLASSIFICATION: THE PROCESS


CLASSIFICATION: AN EMAIL EXAMPLE

• A set of emails is given where users have manually identified spam versus non-spam

• Our task is to use a set of features such as words in the email (x) to identify spam/non-spam status of the email (y)

• In this case, classes are y = {spam, non-spam}

• What would it be dealt with in a social setting?


CLASSIFICATION ALGORITHMS

• Decision tree learning

• Naive Bayes learning

• K-nearest neighbor classifier


DECISION TREE

• A decision tree is learned from the dataset (training data with known classes) and later applied to predict the class attribute value of new data (test data with unknown classes) where only the feature values are known


DECISION TREE INDUCTION


ID3, A DECISION TREE ALGORITHM

Use information gain (entropy) to determine how well an attribute separates the training data according to the class attribute value

– p+ is the proportion of positive examples in D

– p- is the proportion of negative examples in D

In a dataset containing ten examples, 7 have a positive class attribute value and 3 have a negative class attribute value [7+, 3-]:

If the numbers of positive and negative examples in the set are equal, then the entropy is 1


DECISION TREE: EXAMPLE 1outlook temperature humidity windy play

sunny 85 85 FALSE no

sunny 80 90 TRUE no

overcast 83 86 FALSE yes

rainy 70 96 FALSE yes


rainy 65 70 TRUE no

overcast 64 65 TRUE yes

sunny 72 95 FALSE no

sunny 69 70 FALSE yes


sunny 75 70 TRUE yes

overcast 72 90 TRUE yes

overcast 81 75 FALSE yes

rainy 71 91 TRUE no


DECISION TREE: EXAMPLE 2

Learned Decision Tree 1 Learned Decision Tree 2

Class Labels


NAIVE BAYES CLASSIFIER

For two random variables X and Y, Bayes theorem states that,

class variable the instance features

Then class attribute value for instance X

Assuming that variables are independent


NBC: AN EXAMPLE


NEAREST NEIGHBOR CLASSIFIER

• k-nearest neighbor employs the neighbors of a data point to perform classification

• The instance being classified is assigned the label that the majority of k neighbors’ labels

• When k = 1, the closest neighbor’s label is used as the predicted label for the instance being classified

• For determining the neighbors, distance is computed based on some distance metric, e.g., Euclidean distance


K-NN: ALGORITHM

1. The dataset, number of neighbors (k), and the instance i is given

2. Compute the distance between i and all other data points in the dataset

3. Pick k closest neighbors4. The class label for the data point i is the one

that the majority holds (if there are more than one class, select one of them randomly)


K-NEAREST NEIGHBOR: EXAMPLE

• Depending on the k, different labels can be predicted for the green circle• In our example k = 3 and k = 5 generate different labels for the instance• K= 10 we can choose either triangle or rectangle

k = 3

k = 5k = 10Class label = ?


K-NEAREST NEIGHBOR: EXAMPLE

Data instance Outlook Temperature Humidity Similarity Label K Prediction2 1 1 1 3 N 1 N1 1 0 1 2 N 2 N4 0 1 1 2 Y 3 N3 0 0 1 1 Y 4 ?5 1 0 0 1 Y 5 Y6 0 0 0 0 N 6 ?7 0 0 0 0 Y 7 Y

Similarity between row 8 and other data instances;(Similarity = 1 if attributes have the same value, otherwise similarity = 0)


EVALUATING CLASSIFICATION PERFORMANCE

• As the class labels are discrete, we can measure the accuracy by dividing number of correctly predicted labels (C) by the total number of instances (N)• Accuracy = C/N• Error rate = 1 - Accuracy

• More sophisticated approaches of evaluation will be discussed later


REGRESSION


REGRESSION

Regression analysis includes techniques of modeling and analyzing the relationship between a dependent variable and one or more independent variables• Regression analysis is widely used for

prediction and forecasting• It can be used to infer

relationships between the independent and dependent variables


REGRESSION

In regression, we deal with real numbers as class values (Recall that in classification, class values or labels are categories)

y ≈ f(X)

Regressorsx1, x2, …, xm

Dependent variabley R

Our task is to find the relation between y and the vector (x1, x2, …, xm)


LINEAR REGRESSION

In linear regression, we assume the relation between the class attribute y and feature set x to be linear

where w represents the vector of regression coefficients• The problem of regression can be solved by

estimating w and using the provided dataset and the labels y– The least squares is often used to solve the problem


SOLVING LINEAR REGRESSION PROBLEMS

• The problem of regression can be solved by estimating w and using the dataset provided and the labels y– “Least squares” is a popular method to solve

regression problems


LEAST SQUARES

Find W such that minimizing ǁY - XWǁ2 for regressors X and labels Y


LEAST SQUARES


REGRESSION COEFFICIENTS

• When there is only one independent variable:y = w0 + w1x

• Two independent variablesy = w0 + w1x1 + w2x2


LINEAR REGRESSION: EXAMPLE

Years of experience Salary ($K)

3 30

8 57

9 64

13 72

3 36

6 43

11 59

21 90

1 20

16 83


EVALUATING REGRESSION PERFORMANCE

• The labels cannot be predicted precisely• It is needed to set a margin to accept or reject

the predictions– For example, when the observed temperature is

71 any prediction in the range of 71±0.5 can be considered as correct prediction


CLUSTERING


CLUSTERING

• Clustering is a form of unsupervised learning– The clustering algorithms do not have examples

showing how the samples should be group together• The clustering algorithms look for patterns or

structures in the data that are of interest• Clustering algorithms group together similar

items

Grouping together items that are similar in some way – according to some criteria


CLUSTERING: EXAMPLE


MEASURING SIMILARITY IN CLUSTERING ALGORITHMS

• The goal is to group together similar items• Different similarity measures can be used to

find similar items• Usually similarity measures are critical to

clustering algorithms

The most popular (dis)similarity measure for continuous features are Euclidean Distance and Pearson Linear Correlation


EUCLIDEAN DISTANCE – A DISSIMILAR MEASURE

• Here n is the number of dimensions in the data vector


PEARSON LINEAR CORRELATION

• We’re shifting the expression profiles down (subtracting the means) and scaling by the standard deviations (i.e., making the data have mean = 0 and std = 1)

• Always between –1 and +1 (perfectly anti-correlated and perfectly correlated)


SIMILARITY MEASURES: MORE DEFINITIONS


CLUSTERING

• Distance-based algorithms

– K-Means

• Hierarchical algorithms


K-MEANS

k-means clustering aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean• Finding the global optimal of k partitions is

computationally expensive (NP-hard). However, there are efficient heuristic algorithms that are commonly employed and converge quickly to an optimum that might not be global.


K-MEANS

• Given a set of observations (x1, x2, …, xn), where each observation is a d-dimensional real vector, k-means clustering aims to partition the n observations into k sets (k ≤ n) S = {S1, S2, …, Sk} so as to minimize the within-cluster sum of squares:

where μi is the mean of points in Si


K-MEANS: ALGORITHM

Given data points xi and an initial set of k centroids m1

(1),…,mk(1), the algorithm proceeds as

follows:• Assignment step: Assign each data point to the

cluster Si with the closest centroid each data point goes into exactly one cluster)

• Update step: Calculate the new means to be the centroid of the data points in the cluster


K-MEANS: AN EXAMPLE

Data point X Y

1 1 12 2 13 1 24 2 25 4 46 4 57 5 48 5 5

Cluster 1 Cluster 2Step Data point Centroid Data point Centroid

1 1 (1.0, 1.0) 2 (2.0, 1.0)


RUNNING K-MEANS ON IRIS DATASET


HIERARCHICAL CLUSTERING

Hierarchical clustering is a method of cluster analysis which seeks to build a hierarchy of clusters. • Strategies for hierarchical clustering generally fall

into two types:– Agglomerative: This is a "bottom up" approach: each

observation starts in its own cluster, and pairs of clusters are merged as one moves up the hierarchy.

– Divisive: This is a "top down" approach: all observations start in one cluster, and splits are performed recursively as one moves down the hierarchy.


HIERARCHICAL ALGORITHMS

• Initially n data points are considered as either 1 or n clusters in hierarchical clustering

• These clusters are gradually split or merged (divisive or agglomerative hierarchical clustering algorithms), depending on the type of an algorithm

• Until the desired number of clusters are reached


HIERARCHICAL AGGLOMERATIVE CLUSTERING

• Start with each data point as a cluster• Keep merging the most similar pairs of data

points/clusters until only one big cluster left• This is called a bottom-up or agglomerative

method

This produces a binary tree or dendrogram– The final cluster is the root and each data point is a

leaf– The height of the bars indicate how close the points

are


HIERARCHICAL CLUSTERING: AN EXAMPLE


MERGING THE DATA POINTS IN HIERARCHICAL CLUSTERING

• Average Linkage– Each cluster ci is associated with a mean vector i

which is the mean of all the data items in the cluster– The distance between two clusters ci and cj is then

just d(i , j )• Single Linkage– The minimum of all pairwise distances between

points in the two clusters• Complete Linkage– The maximum of all pairwise distances between

points in the two clusters


LINKAGE IN HIERARCHICAL CLUSTERING: EXAMPLE

Single Linkage Average Linkage

Complete Linkage


EVALUATING THE CLUSTERINGS

• Evaluation with ground truth• Evaluation without ground truth

When we are given objects of two different kinds, the perfect clustering would be that objects of the same type are clustered together.


EVALUATION WITH GROUND TRUTH

When ground truth is available, the evaluator has prior knowledge of what a clustering should be– That is, we know the correct clustering

assignments.

• Measures– Precision and Recall, or F-Measure– Purity– Normalized Mutual Information (NMI)


PRECISION AND RECALL

• True Positive (TP) : – when similar points are assigned to the

same clusters– This is considered a correct decision.

• True Negative (TN) : – when dissimilar points are assigned to

different clusters– This is considered a correct decision

• False Negative (FN) :

– when similar points are assigned to different clusters

– This is considered an incorrect decision• False Positive (FP) :

– when dissimilar points are assigned to the same clusters

– This is considered an incorrect decision


PRECISION AND RECALL: EXAMPLE 1


F-MEASURE

• To consolidate precision and recall into one measure, we can use the harmonic mean of precision of recall

Computed for the same example, we get F = 0.54


PURITY• In purity, we assume the majority of a cluster

represents the cluster• Hence, we use the label of the majority against

the label of each member to evaluate the algorithm

• The purity is then defined as the fraction of instances that have labels equal to the cluster’s majority label

where Lj defines label j (ground truth) and Mi defines the majority label for cluster i

• Purity can be easily tampered; consider points being singleton clusters (of size 1) or very large clusters.

• In both cases, purity does not make much sense.


MUTUAL INFORMATION

The mutual information of two random variables is a quantity that measures the mutual dependence of the two random variables

• p(x,y) is the joint probability distribution function of X and Y, • p(x) and p(y) are the marginal probability distribution

functions of X and Y respectively


NORMALIZED MUTUAL INFORMATION

Normalized Mutual Information has been derived from information theory where the Mutual Information (MI) between the clusterings found and the labels is normalized by the upper bound of (MI) which is a mean of the entropies (H) of labels and clusterings found


NORMALIZED MUTUAL INFORMATION

• NMI values close to one indicate high similarity between clusterings found and labels

• Values close to zero indicate high dissimilarity between them

• where l and h are labels and found clusterings, • nh and nl are the number of data points in the clusters h and l, respectively, • nh,l is the number of points in clusters h and labeled l, • n is the size of the dataset


NORMALIZED MUTUAL INFORMATION: EXAMPLE

Partition a: [1,1,1,1,1,1,1, 2,2,2,2,2,2,2] Partition b: [1,1,1,1,1,2,2, 1,2,2,2,2,2,2]

nh

h=1 6

h=2 8

nl

l=1 7

l=2 7

nh,l l=1 l=2

h=1 5 1

h=2 2 6n = 14


EVALUATION WITHOUT GROUND TRUTH

• Use domain experts

• Use quality measures such as SSE

– SSE: the sum of the squared error for all clusters

• Use more than two clustering algorithms and

compare the results and pick the algorithm

with better quality measure


TEXT MINING


TEXT MINING

• In social media, most of the data that is available online is in text format

• In general, the way to perform data mining is to convert text data into tabular format and then perform data mining on this data

• The process of converting text data into tabular data is called vectorization


TEXT MINING PROCESS

A set of linguistic, statistical, and machine learning techniques that model and structure the information content of textual sources for business intelligence, exploratory data analysis, research, or investigation


TEXT PREPROCESSING

Text preprocessing aims to make the input documents more consistent to facilitate text representation, which is necessary for most text analytics tasks• Methods:– Stop word removal

• Stop word removal eliminates words using a stop word list, in which the words are considered more general and meaningless – e.g. the, a, is, at, which

– Stemming• Stemming reduces inflected (or sometimes derived) words to

their stem, base or root form– For example, “watch”, “watching”, “watched” are represented as

“watch”


TEXT REPRESENTATION

• The most common way to model documents is to transform them into sparse numeric vectors and then deal with them with linear algebraic operations

• This representation is called “Bag of Words”

• Methods:– Vector space model– tf-idf


VECTOR SPACE MODEL

• In the vector space model, we start with a set of documents, D

• Each document is a set of words• The goal is to convert these textual documents

to vectors

• di : document i, wj,i : the weight for word j in document i

The weight can be set to 1 when the word exist in the document and 0 when it does not. Or we can set this weight to the number of times the word is observed in the document


VECTOR SPACE MODEL: AN EXAMPLE

• Documents:– d1: data mining and social media mining– d2: social network analysis– d3: data mining

• Reference vector:– (social, media, mining, network, analysis, data)

• Vector representation: analysis data media mining network sociald1 0 1 1 1 0 1d2 1 0 0 0 1 1d3 0 1 0 1 0 0


TF-IDF (TERM FREQUENCY-INVERSE DOCUMENT FREQUENCY)

tf-idf of term t, document d, and document corpus D is calculated as follows:

tf-idf(t, d, D) = tf (t, d) * idf (t, D)

The total number of documents in the corpus

The number of documents where the term t appears


TF-IDF: AN EXAMPLE

Consider words “apple” and “the” that appear 10 and 20 times in document 1 (d1), which contains 100 words. Consider |D| = 20 and word “apple” only appearing in d1 and word “the” appearing in all 20 documents


TF-IDF: AN EXAMPLE

• Documents:– d1: data mining and social media mining– d2: social network analysis– d3: data mining

• tf-idf representation:

analysis data media mining network socialdf(w) 1 2 1 2 1 2log(N/df(w)) 0.48 0.18 0.48 0.18 0.48 0.18d1, tf 0 1 1 2 0 1d2, tf 1 0 0 0 1 1d3, tf 0 1 0 1 0 0d1, tf-idf 0.00 0.18 0.48 0.35 0.00 0.18d2, tf-idf 0.48 0.00 0.00 0.00 0.48 0.18d3, tf-idf 0.00 0.18 0.00 0.18 0.00 0.00


SENTIMENT ANALYSIS

• Sentiment analysis or opinion mining refers to the application of natural language processing, computational linguistics, and text analytics to identify and extract subjective information in source materials

• It aims to determine the attitude of a speaker or a writer with respect to some topic or the overall contextual polarity of a document.


POLARITY ANALYSIS

• The basic task in opinion mining is classifying the polarity of a given document or text– The polarity could be positive, negative, or neutral

• Methods:– Naïve Bayes– Pointwise Mutual Information (PMI)


MEASURING POLARITY, NAÏVE BAYES

• Bayes’ rule:

• If we consider that the occurrence of features (words) in the document are independent


MEASURING POLARITY, MAXIMUM ENTROPY

• Z(d) is the normalization factor• is feature-weight parameter and shows the

importance of each feature• Fi,c is defined as a feature/class function for

feature fi and class c


MEASURING POLARITY, POINTWISE MUTUAL INFORMATION

• P(word) is the number of results returned by search engine in response to search for term word

• P(word1 word2) is the number of results for mutual search of word1 and word2 together


Mohammad-Ali Abbasi (Ali), Ali, is a Ph.D. student at Data Mining and Machine Learning Lab, Arizona State University. His research interests include Data Mining, Machine Learning, Social Computing, and Social Media Behavior Analysis.


http://dmml.asu.edu/

http://asu.edu/

http://asu.edu/



Data Mining: an Introduction

Data & Analytics