Course on Data Mining 5815504

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Course on Data Mining (581550-4)
Intro/Ass. Rules
Clustering
Episodes
KDD Process
Text Mining
Appl./Summary
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Course on Data Mining (581550-4)
Today 14.11.2001

• Today's subject
• Classification, clustering
• Next week's program
• Lecture Data mining process
• Exercise Classification, clustering
• Seminar Classification, clustering

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Classification and clustering

• Classification and prediction
• Clustering and similarity

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Cluster analysis

• What is cluster analysis?
• Similarity and dissimilarity
• Types of data in cluster analysis
• Major clustering methods
• Partitioning methods
• Hierarchical methods
• Outlier analysis
• Summary

Overview
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What is cluster analysis?

• Cluster a collection of data objects
• similar to one another within the same cluster
• dissimilar to the objects in the other clusters
• Aim of clustering to group a set of data objects
  into clusters

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Typical uses of clustering

• As a stand-alone tool to get insight into data
  distribution
• As a preprocessing step for other algorithms

Used as?
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Applications of clustering

• Marketing discovering of distinct customer
  groups in a purchase database
• Land use identifying 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

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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
• the similarity measure used
• implementation of the similarity measure
• The quality of a clustering method is also
  measured by its ability to discover some or all
  of the hidden patterns

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Requirements of clustering in data mining (1)

• Scalability
• Ability to deal with different types of
  attributes
• Discovery of clusters with arbitrary shape
• Minimal requirements for domain knowledge to
  determine input parameters

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Requirements of clustering in data mining (2)

• Ability to deal with noise and outliers
• Insensitivity to order of input records
• High dimensionality
• Incorporation of user-specified constraints
• Interpretability and usability

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Similarity and dissimilarity between objects (1)

• There is no single definition of similarity or
  dissimilarity between data objects
• The definition of similarity or dissimilarity
  between objects depends on
• the type of the data considered
• what kind of similarity we are looking for

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Similarity and dissimilarity between objects (2)

• Similarity/dissimilarity between objects is often
  expressed in terms of a distance measure d(x,y)
• Ideally, every distance measure should be a
  metric, i.e., it should satisfy the following
  conditions

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Type of data in cluster analysis

• Interval-scaled variables
• Binary variables
• Nominal, ordinal, and ratio variables
• Variables of mixed types
• Complex data types

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Interval-scaled variables (1)

• Continuous measurements of a roughly linear scale
• For example, weight, height and age
• The measurement unit can affect the cluster
  analysis
• To avoid dependence on the measurement unit, we
  should standardize the data

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Interval-scaled variables (2)

• To standardize the measurements
• calculate the mean absolute deviation
• where and
• calculate the standardized measurement (z-score)

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Interval-scaled variables (3)

• One group of popular distance measures for
  interval-scaled variables are Minkowski distances
• where i (xi1, xi2, , xip) and j (xj1, xj2,
  , xjp) are two p-dimensional data objects, and q
  is a positive integer

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Interval-scaled variables (4)

• If q 1, the distance measure is Manhattan (or
  city block) distance
• If q 2, the distance measure is Euclidean
  distance

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Binary variables (1)

• A binary variable has only two states 0 or 1
• A contingency table for binary data

Object j
Object i
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Binary variables (2)

• Simple matching coefficient (invariant
  similarity, if the binary variable is symmetric)
• Jaccard coefficient (noninvariant similarity, if
  the binary variable is asymmetric)

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Binary variables (3)

• Example dissimilarity between binary variables
• a patient record table
• eight attributes, of which
• gender is a symmetric attribute, and
• the remaining attributes are asymmetric binary

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Binary variables (4)

• Let the values Y and P be set to 1, and the value
  N be set to 0
• Compute distances between patients based on the
  asymmetric variables by using Jaccard coefficient

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Nominal variables

• A generalization of the binary variable in that
  it can take more than 2 states, e.g., red,
  yellow, blue, green
• Method 1 simple matching
• m of matches, p total of variables
• Method 2 use a large number of binary variables
• create a new binary variable for each of the M
  nominal states

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Ordinal variables

• An ordinal variable can be discrete or continuous
• Order of values is important, e.g., rank
• Can be treated like interval-scaled
• replacing xif by their rank
• map the range of each variable onto 0, 1 by
  replacing i-th object in the f-th variable by
• compute the dissimilarity using methods for
  interval-scaled variables

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Ratio-scaled variables

• A positive measurement on a nonlinear scale,
  approximately at exponential scale
• for example, AeBt or Ae-Bt
• Methods
• treat them like interval-scaled variables not a
  good choice! (why?)
• apply logarithmic transformation yif log(xif)
• treat them as continuous ordinal data and treat
  their rank as interval-scaled

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Variables of mixed types (1)

• A database may contain all the six types of
  variables
• One may use a weighted formula to combine their
  effects
• where

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Variables of mixed types (2)

• Contribution of variable f to distance d(i,j)
• if f is binary or nominal
• if f is interval-based use the normalized
  distance
• if f is ordinal or ratio-scaled
• compute ranks rif and
• and treat zif as interval-scaled

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Complex data types

• All objects considered in data mining are not
  relational gt complex types of data
• examples of such data are spatial data,
  multimedia data, genetic data, time-series data,
  text data and data collected from World-Wide Web
• Often totally different similarity or
  dissimilarity measures than above
• can, for example, mean using of string and/or
  sequence matching, or methods of information
  retrieval

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Major clustering methods

• Partitioning methods
• Hierarchical methods
• Density-based methods
• Grid-based methods
• Model-based methods (conceptual clustering,
  neural networks)

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Partitioning methods

• A partitioning method construct a partition of a
  database D of n objects into a set of k clusters
  such that
• each cluster contains at least one object
• each object belongs to exactly one cluster
• Given a k, find a partition of k clusters that
  optimizes the chosen partitioning criterion

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Criteria for judging the quality of partitions

• Global optimal exhaustively enumerate all
  partitions
• Heuristic methods
• k-means (MacQueen67) each cluster is
  represented by the center of the cluster
  (centroid)
• k-medoids (Kaufman Rousseeuw87) each cluster
  is represented by one of the objects in the
  cluster (medoid)

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K-means clustering method (1)

• Input to the algorithm the number of clusters k,
  and a database of n objects
• Algorithm consists of four steps
• partition object into k nonempty subsets/clusters
• compute a seed points as the centroid (the mean
  of the objects in the cluster) for each cluster
  in the current partition
• assign each object to the cluster with the
  nearest centroid
• go back to Step 2, stop when there are no more
  new assignments

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K-means clustering method (2)

• Alternative algorithm also consists of four
  steps
• arbitrarily choose k objects as the initial
  cluster centers (centroids)
• (re)assign each object to the cluster with the
  nearest centroid
• update the centroids
• go back to Step 2, stop when there are no more
  new assignments

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K-means clustering method - Example
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Strengths of K-means clustering method

• Relatively scalable in processing large data sets
• Relatively efficient O(tkn), where n is
  objects, k is clusters, and t is iterations.
  Normally, k, t ltlt n.
• Often terminates at a local optimum the global
  optimum may be found using techniques such as
  genetic algorithms

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Weaknesses of K-means clustering method

• Applicable only when the mean of objects is
  defined
• Need to specify k, the number of clusters, in
  advance
• Unable to handle noisy data and outliers
• Not suitable to discover clusters with non-convex
  shapes, or clusters of very different size

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Variations of K-means clustering method (1)

• A few variants of the k-means which differ in
• selection of the initial k centroids
• dissimilarity calculations
• strategies for calculating cluster centroids

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Variations of K-means clustering method (2)

• Handling categorical data k-modes (Huang98)
• replacing means of clusters with modes
• using new dissimilarity measures to deal with
  categorical objects
• using a frequency-based method to update modes of
  clusters
• A mixture of categorical and numerical data
  k-prototype method

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K-medoids clustering method

• Input to the algorithm the number of clusters k,
  and a database of n objects
• Algorithm consists of four steps
• arbitrarily choose k objects as the initial
  medoids (representative objects)
• assign each remaining object to the cluster with
  the nearest medoid
• select a nonmedoid and replace one of the medoids
  with it if this improves the clustering
• go back to Step 2, stop when there are no more
  new assignments

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Hierarchical methods

• A hierarchical method construct a hierarchy of
  clustering, not just a single partition of
  objects
• The number of clusters k is not required as an
  input
• Use a distance matrix as clustering criteria
• A termination condition can be used (e.g., a
  number of clusters)

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A tree of clusterings

• The hierarchy of clustering is ofter given as a
  clustering tree, also called a dendrogram
• leaves of the tree represent the individual
  objects
• internal nodes of the tree represent the clusters

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Two types of hierarchical methods (1)

• Two main types of hierarchical clustering
  techniques
• agglomerative (bottom-up)
• place each object in its own cluster (a
  singleton)
• merge in each step the two most similar clusters
  until there is only one cluster left or the
  termination condition is satisfied
• divisive (top-down)
• start with one big cluster containing all the
  objects
• divide the most distinctive cluster into smaller
  clusters and proceed until there are n clusters
  or the termination condition is satisfied

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Two types of hierarchical methods (2)
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Inter-cluster distances

• Three widely used ways of defining the
  inter-cluster distance, i.e., the distance
  between two separate clusters, are
• single linkage method (nearest neighbor)
• complete linkage method (furthest neighbor)
• average linkage method (unweighted pair-group
  average)

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Strengths of hierarchical methods

• Conceptually simple
• Theoretical properties are well understood
• When clusters are merged/split, the decision is
  permanent gt the number of different
  alternatives that need to be examined is reduced

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Weaknesses of hierarchical methods

• Merging/splitting of clusters is permanent gt
  erroneous decisions are impossible to correct
  later
• Divisive methods can be computational hard
• Methods are not (necessarily) scalable for large
  data sets

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Outlier analysis (1)

• Outliers
• are objects that are considerably dissimilar from
  the remainder of the data
• can be caused by a measurement or execution
  error, or
• are the result of inherent data variability
• Many data mining algorithms try
• to minimize the influence of outliers
• to eliminate the outliers

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Outlier analysis (2)

• Minimizing the effect of outliers and/or
  eliminating the outliers may cause information
  loss
• Outliers themselves may be of interest gt
  outlier mining
• Applications of outlier mining
• Fraud detection
• Customized marketing
• Medical treatments

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Summary (1)

• Cluster analysis groups objects based on their
  similarity
• Cluster analysis has wide applications
• Measure of similarity can be computed for various
  type of data
• Selection of similarity measure is dependent on
  the data used and the type of similarity we are
  searching for

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Summary (2)

• Clustering algorithms can be categorized into
• partitioning methods,
• hierarchical methods,
• density-based methods,
• grid-based methods, and
• model-based methods
• There are still lots of research issues on
  cluster analysis

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Seminar Presentations/Groups 7-8
Classification of spatial data
K. Koperski, J. Han, N. Stefanovic An Efficient
Two-Step Method of Classification of Spatial
Data", SDH98
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Seminar Presentations/Groups 7-8
WEBSOM
K. Lagus, T. Honkela, S. Kaski, T. Kohonen
Self-organizing Maps of Document Collections A
New Approach to Interactive Exploration,
KDD96 T. Honkela, S. Kaski, K. Lagus, T.
Kohonen WEBSOM Self-Organizing Maps of
Document Collections, WSOM97
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Course on Data Mining
Thanks to Jiawei Han from Simon Fraser
University for his slides which greatly helped
in preparing this lecture!
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References - clustering

• R. Agrawal, J. Gehrke, D. Gunopulos, and P.
  Raghavan. Automatic subspace clustering of high
  dimensional data for data mining applications.
  SIGMOD'98
• M. R. Anderberg. Cluster Analysis for
  Applications. Academic Press, 1973.
• M. Ankerst, M. Breunig, H.-P. Kriegel, and J.
  Sander. Optics Ordering points to identify the
  clustering structure, SIGMOD99.
• P. Arabie, L. J. Hubert, and G. De Soete.
  Clustering and Classification. World Scietific,
  1996
• M. Ester, H.-P. Kriegel, J. Sander, and X. Xu. A
  density-based algorithm for discovering clusters
  in large spatial databases. KDD'96.
• M. Ester, H.-P. Kriegel, and X. Xu. Knowledge
  discovery in large spatial databases Focusing
  techniques for efficient class identification.
  SSD'95.
• D. Fisher. Knowledge acquisition via incremental
  conceptual clustering. Machine Learning,
  2139-172, 1987.
• D. Gibson, J. Kleinberg, and P. Raghavan.
  Clustering categorical data An approach based on
  dynamic systems. In Proc. VLDB98.

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References - clustering

• S. Guha, R. Rastogi, and K. Shim. Cure An
  efficient clustering algorithm for large
  databases. SIGMOD'98.
• A. K. Jain and R. C. Dubes. Algorithms for
  Clustering Data. Printice Hall, 1988.
• L. Kaufman and P. J. Rousseeuw. Finding Groups in
  Data an Introduction to Cluster Analysis. John
  Wiley Sons, 1990.
• E. Knorr and R. Ng. Algorithms for mining
  distance-based outliers in large datasets.
  VLDB98.
• G. J. McLachlan and K.E. Bkasford. Mixture
  Models Inference and Applications to Clustering.
  John Wiley and Sons, 1988.
• P. Michaud. Clustering techniques. Future
  Generation Computer systems, 13, 1997.
• R. Ng and J. Han. Efficient and effective
  clustering method for spatial data mining.
  VLDB'94.
• E. Schikuta. Grid clustering An efficient
  hierarchical clustering method for very large
  data sets. Proc. 1996 Int. Conf. on Pattern
  Recognition, 101-105.
• G. Sheikholeslami, S. Chatterjee, and A. Zhang.
  WaveCluster A multi-resolution clustering
  approach for very large spatial databases.
  VLDB98.
• W. Wang, Yang, R. Muntz, STING A Statistical
  Information grid Approach to Spatial Data Mining,
  VLDB97.
• T. Zhang, R. Ramakrishnan, and M. Livny. BIRCH
  an efficient data clustering method for very
  large databases. SIGMOD'96.