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Data Mining. Lecture 6. Course Syllabus. Case Study 1 : Working and experiencing on the properties of The Retail Banking Data Mart (Week 4 –Assignment1) Data Analysis Techniques ( Week 5 ) Statistical Background Trends/ Outliers/Normalizations Principal Component Analysis

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Data Mining

Lecture 6

Course Syllabus

  • Case Study 1: Working and experiencing on the properties of The Retail Banking Data Mart (Week 4 –Assignment1)

  • Data Analysis Techniques (Week 5)

    • Statistical Background

    • Trends/ Outliers/Normalizations

    • Principal Component Analysis

    • Discretization Techniques

  • Case Study 2: Working and experiencing on the properties of discretization infrastructure of The Retail Banking Data Mart (Week 5 –Assignment 2)

  • Lecture Talk: Searching/Matching Engine

Course Syllabus

  • Clustering Techniques (Week 6)

    • K-Means Clustering

    • Condorcet Clustering

    • Other Clustering Techniques

  • Case Study 3: Working and experiencing on the properties of the clustering infrastructure for The Retail Banking (Week 6 – Assignment3)

  • Lecture Talk: Different Perspectives on Searching/Matching



  • Three types of attributes:

    • Nominal — values from an unordered set, e.g., color, profession

    • Ordinal — values from an ordered set, e.g., military or academic rank

    • Continuous — real numbers, e.g., integer or real numbers

  • Discretization:

    • Divide the range of a continuous attribute into intervals

    • Some classification algorithms only accept categorical attributes.

    • Reduce data size by discretization

    • Prepare for further analysis

Discretization and Concept Hierarchy

  • Discretization

    • Reduce the number of values for a given continuous attribute by dividing the range of the attribute into intervals

    • Interval labels can then be used to replace actual data values

    • Supervised vs. unsupervised

    • Split (top-down) vs. merge (bottom-up)

    • Discretization can be performed recursively on an attribute

  • Concept hierarchy formation

    • Recursively reduce the data by collecting and replacing low level concepts (such as numeric values for age) by higher level concepts (such as young, middle-aged, or senior)

Discretization and Concept Hierarchy Generation for Numeric Data

  • Typical methods: All the methods can be applied recursively

    • Binning (covered above)

      • Top-down split, unsupervised,

    • Histogram analysis (covered above)

      • Top-down split, unsupervised

    • Clustering analysis (covered above)

      • Either top-down split or bottom-up merge, unsupervised

    • Entropy-based discretization: supervised, top-down split

    • Interval merging by 2 Analysis: unsupervised, bottom-up merge

    • Segmentation by natural partitioning: top-down split, unsupervised

Entropy-Based Discretization

  • Given a set of samples S, if S is partitioned into two intervals S1 and S2 using boundary T, the information gain after partitioning is

  • Entropy is calculated based on class distribution of the samples in the set. Given m classes, the entropy of S1 is

    • where pi is the probability of class i in S1

  • The boundary that minimizes the entropy function over all possible boundaries is selected as a binary discretization

  • The process is recursively applied to partitions obtained until some stopping criterion is met

  • Such a boundary may reduce data size and improve classification accuracy

Interval Merge by 2 Analysis

  • Merging-based (bottom-up) vs. splitting-based methods

  • Merge: Find the best neighboring intervals and merge them to form larger intervals recursively

  • ChiMerge [Kerber AAAI 1992, See also Liu et al. DMKD 2002]

    • Initially, each distinct value of a numerical attr. A is considered to be one interval

    • 2 tests are performed for every pair of adjacent intervals

    • Adjacent intervals with the least 2 values are merged together, since low 2 values for a pair indicate similar class distributions

    • This merge process proceeds recursively until a predefined stopping criterion is met (such as significance level, max-interval, max inconsistency, etc.)

2 Test

  • Χ2 (chi-square) test

  • The larger the Χ2 value, the more likely the variables are related

  • The cells that contribute the most to the Χ2 value are those whose actual count is very different from the expected count

  • Correlation does not imply causality

Chi-Square Calculation: An Example

  • Χ2 (chi-square) calculation (numbers in parenthesis are expected counts calculated based on the data distribution in the two categories)

  • It shows that like_science_fiction and play_chess are correlated in the group

Segmentation by Natural Partitioning

  • A simply 3-4-5 rule can be used to segment numeric data into relatively uniform, “natural” intervals.

    • If an interval covers 3, 6, 7 or 9 distinct values at the most significant digit, partition the range into 3 equi-width intervals

    • If it covers 2, 4, or 8 distinct values at the most significant digit, partition the range into 4 intervals

    • If it covers 1, 5, or 10 distinct values at the most significant digit, partition the range into 5 intervals


-$351-$159profit $1,838 $4,700

Step 1:

Min Low (i.e, 5%-tile) High(i.e, 95%-0 tile) Max

Step 2:


(-$1,000 - $2,000)

Step 3:

(-$1,000 - 0)

($1,000 - $2,000)

(0 -$ 1,000)

($2,000 - $5, 000)

($1,000 - $2, 000)

(-$400 - 0)

(0 - $1,000)

(0 -


($1,000 -


(-$400 -


($2,000 -


($200 -


($1,200 -


(-$300 -


($3,000 -


($1,400 -


($400 -


(-$200 -


($4,000 -


($600 -


($1,600 -


($1,800 -


($800 -


(-$100 -


Example of 3-4-5 Rule

(-$400 -$5,000)

Step 4:

Concept Hierarchy Generation for Categorical Data

  • Specification of a partial/total ordering of attributes explicitly at the schema level by users or experts

    • street < city < state < country

  • Specification of a hierarchy for a set of values by explicit data grouping

    • {Urbana, Champaign, Chicago} < Illinois

  • Specification of only a partial set of attributes

    • E.g., only street < city, not others

  • Automatic generation of hierarchies (or attribute levels) by the analysis of the number of distinct values

    • E.g., for a set of attributes: {street, city, state, country}

15 distinct values


365 distinct values

province_or_ state

3567 distinct values


674,339 distinct values


Automatic Concept Hierarchy Generation

  • Some hierarchies can be automatically generated based on the analysis of the number of distinct values per attribute in the data set

    • The attribute with the most distinct values is placed at the lowest level of the hierarchy

    • Exceptions, e.g., weekday, month, quarter, year

Case Study 2 Discretization

Case Study 2 Discretization

What is Cluster Analysis?

  • 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

Examples of Clustering Applications

  • 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

Quality: What Is Good Clustering?

  • 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

Measure the Quality of Clustering

  • 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.

Requirements of Clustering in Data Mining

  • Scalability

  • Ability to deal with different types of attributes

  • Ability to handle dynamic data

  • Discovery of clusters with arbitrary shape

  • Minimal requirements for domain knowledge to determine input parameters

  • Able to deal with noise and outliers

  • Insensitive to order of input records

  • High dimensionality

  • Incorporation of user-specified constraints

  • Interpretability and usability

Data Structures

  • Data matrix

    • (two modes)

  • Dissimilarity matrix

    • (one mode)

Type of data in clustering analysis

  • Interval-scaled variables

  • Binary variables

  • Nominal, ordinal, and ratio variables

  • Variables of mixed types

Interval-valued variables

  • Standardize data

    • Calculate the mean absolute deviation:

    • where

    • Calculate the standardized measurement (z-score)

  • Using mean absolute deviation is more robust than using standard deviation

Similarity and Dissimilarity Between Objects

  • Distances are normally used to measure the similarity or dissimilarity between two data objects

  • Some popular ones include: Minkowski distance:

    • where i = (xi1, xi2, …, xip) and j = (xj1, xj2, …, xjp) are two p-dimensional data objects, and q is a positive integer

  • If q = 1, d is Manhattan distance

Similarity and Dissimilarity Between Objects (Cont.)

  • If q = 2, d is Euclidean distance:

    • Properties

      • d(i,j) 0

      • d(i,i)= 0

      • d(i,j)= d(j,i)

      • d(i,j) d(i,k)+ d(k,j)

  • Also, one can use weighted distance, parametric Pearson product moment correlation, or other disimilarity measures

Major Clustering Approaches (I)

  • 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: DBSCAN, OPTICS, DenClue

Major Clustering Approaches (II)

  • 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

Typical Alternatives to Calculate the Distance between Clusters

  • Single link: smallest distance between an element in one cluster and an element in the other, i.e., dis(Ki, Kj) = min(tip, tjq)

  • Complete link: largest distance between an element in one cluster and an element in the other, i.e., dis(Ki, Kj) = max(tip, tjq)

  • Average: avg distance between an element in one cluster and an element in the other, i.e., dis(Ki, Kj) = avg(tip, tjq)

  • Centroid: distance between the centroids of two clusters, i.e., dis(Ki, Kj) = dis(Ci, Cj)

  • Medoid: distance between the medoids of two clusters, i.e., dis(Ki, Kj) = dis(Mi, Mj)

    • Medoid: one chosen, centrally located object in the cluster

Centroid: the “middle” of a cluster

Radius: square root of average distance from any point of the cluster to its centroid

Diameter: square root of average mean squared distance between all pairs of points in the cluster

Centroid, Radius and Diameter of a Cluster (for numerical data sets)

Week 6-End

  • assignment 2 (please share your ideas with your group)

    • choose freely a dataset my advice:

    • use Weka

      - apply different discretization strategies that you have learned in class (equi–width, equi-depth, entropy based, merging, splitting,...)

Week 6-End

  • read

    • Course Text Book Chapter 7

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