1. Topics Related to Data Mining

2. Information Retrieval
Relevance Ranking Using Terms
Relevance Using Hyperlinks
Synonyms., Homonyms, and Ontologies
Indexing of Documents
Measuring Retrieval Effectiveness
Information Retrieval and Structured Data

3. Information Retrieval Systems
Information retrieval (IR) systems use a simpler data model than database systems
Information organized as a collection of documents
Documents are unstructured, no schema
Information retrieval locates relevant documents, on the basis of user input such as keywords or example documents
e.g., find documents containing the words “database systems”
Can be used even on textual descriptions provided with non-textual data such as images

4. Keyword Search
In full text retrieval, all the words in each document are considered to be keywords.
We use the word term to refer to the words in a document
Information-retrieval systems typically allow query expressions formed using keywords and the logical connectives and, or, and not
Ands are implicit, even if not explicitly specified
Ranking of documents on the basis of estimated relevance to a query is critical
Relevance ranking is based on factors such as
Term frequency
Frequency of occurrence of query keyword in document
Inverse document frequency
How many documents the query keyword occurs in
Fewer  give more importance to keyword
Hyperlinks to documents
More links to a document  document is more important

5. Relevance Ranking Using Terms
TF-IDF (Term frequency/Inverse Document frequency) ranking:
Let n(d) = number of terms in the document d
n(d, t) = number of occurrences of term t in the document d.
Relevance of a document d to a term t
The log factor is to avoid excessive weight to frequent terms
Relevance of document to query Q
n(d, t)
TF (d, t) = log
1 +
n(d)
TF (d, t) 
r (d, Q) =
n(t)
tQ
IDF=1/n(t), n(t) is the number of documents that contain the term t

6. Relevance Ranking Using Terms (Cont.)
Most systems add to the above model
Words that occur in title, author list, section headings, etc. are given greater importance
Words whose first occurrence is late in the document are given lower importance
Very common words such as “a”, “an”, “the”, “it” etc are eliminated
Called stop words
Proximity: if keywords in query occur close together in the document, the document has higher importance than if they occur far apart
Documents are returned in decreasing order of relevance score
Usually only top few documents are returned, not all

7. Synonyms and Homonyms Synonyms Homonyms
E.g. document: “motorcycle repair”, query: “motorcycle maintenance”
need to realize that “maintenance” and “repair” are synonyms
System can extend query as “motorcycle and (repair or maintenance)”
Homonyms
E.g. “object” has different meanings as noun/verb
Can disambiguate meanings (to some extent) from the context
Extending queries automatically using synonyms can be problematic
Need to understand intended meaning in order to infer synonyms
Or verify synonyms with user
Synonyms may have other meanings as well

8. Indexing of Documents
An inverted index maps each keyword Ki to a set of documents Si that contain the keyword
Documents identified by identifiers
Inverted index may record
Keyword locations within document to allow proximity based ranking
Counts of number of occurrences of keyword to compute TF
and operation: Finds documents that contain all of K1, K2, ..., Kn.
Intersection S1 S2 .....  Sn
or operation: documents that contain at least one of K1, K2, …, Kn
union, S1S2 .....  Sn,.
Each Si is kept sorted to allow efficient intersection/union by merging
“not” can also be efficiently implemented by merging of sorted lists

9. Word-Level Inverted File
lexicon
posting

10. Measuring Retrieval Effectiveness
Information-retrieval systems save space by using index structures that support only approximate retrieval. May result in:
false negative (false drop) - some relevant documents may not be retrieved.
false positive - some irrelevant documents may be retrieved.
For many applications a good index should not permit any false drops, but may permit a few false positives.
Relevant performance metrics:
precision - what percentage of the retrieved documents are relevant to the query.
recall - what percentage of the documents relevant to the query were retrieved.

11. Measuring Retrieval Effectiveness (Cont.)
Recall vs. precision tradeoff:
Can increase recall by retrieving many documents (down to a low level of relevance ranking), but many irrelevant documents would be fetched, reducing precision
Measures of retrieval effectiveness:
Recall as a function of number of documents fetched, or
Precision as a function of recall
Equivalently, as a function of number of documents fetched
E.g. “precision of 75% at recall of 50%, and 60% at a recall of 75%”
Problem: which documents are actually relevant, and which are not

12. Information Retrieval and Structured Data
Information retrieval systems originally treated documents as a collection of words
Information extraction systems infer structure from documents, e.g.:
Extraction of house attributes (size, address, number of bedrooms, etc.) from a text advertisement
Extraction of topic and people named from a new article
Relations or XML structures used to store extracted data
System seeks connections among data to answer queries
Question answering systems

13. Probabilities and Statistic

14. Probabilities Event E is defined as a any subset of1. 2.
Event E is defined as a any subset of
f(x) is called a probability distribution function (pdf)

15. Conditional Probabilities
Conditional probability of E, provided that G occurred is
E and G are independent if and only if .
Expected Value
Expected value of X is
For continuous function f(x), the E(X) is
E(X+Y) = E(X)+E(Y)
E(aX+b) = aE(X)+b

16. Variance Var(X) = E(X-E(X))2 2
Var(X) = E(X-E(X))
It indicates how values of random variable are distributed around its expected value
Standard deviation of X is defined as
VAR(X+Y) = VAR(X) + VAR(Y)
VAR(aX+b) = VAR(X)b
P(|S - E(S)| r) VAR(S)/r (Chebyshev’s Ineequality) 2 2 2

17. Random Distributions Normal Bernoulli E(X) = μ 2 Var(X) = σ E(X) = np
Var(X) = np(1-p)

18. Normal Distributions
E(x) =

19. Random Distributions Geometric E(X) = 1/p; VAR(X) =(1-p)/p Poisson2
E(X) = 1/p; VAR(X) =(1-p)/p
Poisson
E(X)=VAR(X)=m
P(X=x) = 1/(b-a)
Uniform 2
E(X)=(b-a)/2; VAR(X)= (b-a) /12

20. Data and their characteristics

21. There are different types of attributes
Nominal
Examples: ID numbers, eye color, zip codes
Ordinal
Examples: rankings (e.g., taste of potato chips on a scale from 1-10), grades, height in {tall, medium, short}
Interval
Examples: calendar dates, temperatures in Celsius or Fahrenheit.
Ratio
Examples: temperature in Kelvin, length, time, counts

22. Properties of Attribute Values
The type of an attribute depends on which of the following properties it possesses:
Distinctness: = 
Order: < >
Addition:
Multiplication: * /
Nominal attribute: distinctness
Ordinal attribute: distinctness & order
Interval attribute: distinctness, order & addition
Ratio attribute: all 4 properties

23. Attribute Type Description Examples Operations Nominal
The values of a nominal attribute are just different names, i.e., nominal attributes provide only enough information to distinguish one object from another. (=, )
zip codes, employee ID numbers, eye color, sex: {male, female}
mode, entropy, contingency correlation, 2 test
Ordinal
The values of an ordinal attribute provide enough information to order objects. (<, >)
hardness of minerals, {good, better, best}, grades, street numbers
median, percentiles, rank correlation, run tests, sign tests
Interval
For interval attributes, the differences between values are meaningful, i.e., a unit of measurement exists. (+, - )
calendar dates, temperature in Celsius or Fahrenheit
mean, standard deviation, Pearson's correlation, t and F tests
Ratio
For ratio variables, both differences and ratios are meaningful. (*, /)
temperature in Kelvin, monetary quantities, counts, age, mass, length, electrical current
geometric mean, harmonic mean, percent variation

24. Discrete and Continuous Attributes
Discrete Attribute
Has only a finite or countably infinite set of values
Examples: zip codes, counts, or the set of words in a collection of documents
Often represented as integer variables.
Note: binary attributes are a special case of discrete attributes
Continuous Attribute
Has real numbers as attribute values
Examples: temperature, height, or weight.
Practically, real values can only be measured and represented using a finite number of digits.
Continuous attributes are typically represented as floating-point variables.

25. Data Matrix
If data objects have the same fixed set of numeric attributes, then the data objects can be thought of as points in a multi-dimensional space, where each dimension represents a distinct attribute
Such data set can be represented by an m by n matrix, where there are m rows, one for each object, and n columns, one for each attribute

26. Data Quality What kinds of data quality problems?
How can we detect problems with the data?
What can we do about these problems?
Examples of data quality problems:
Noise and outliers
missing values
duplicate data

27. Noise Noise refers to modification of original values
Examples: distortion of a person’s voice when talking on a poor phone and “snow” on television screen
Two Sine Waves
Two Sine Waves + Noise

28. Outliers
Outliers are data objects with characteristics that are considerably different than most of the other data objects in the data set

29. Data Preprocessing Aggregation Sampling Dimensionality Reduction
Feature subset selection
Feature creation
Discretization and Binarization
Attribute Transformation

30. Aggregation
Combining two or more attributes (or objects) into a single attribute (or object)
Purpose
Data reduction
Reduce the number of attributes or objects
Change of scale
Cities aggregated into regions, states, countries, etc
More “stable” data
Aggregated data tends to have less variability

31. Sampling Sampling is the main technique employed for data selection.
It is often used for both the preliminary investigation of the data and the final data analysis.
Statisticians sample because obtaining the entire set of data of interest is too expensive or time consuming.
Sampling is used in data mining because processing the entire set of data of interest is too expensive or time consuming.

32. Sampling … The key principle for effective sampling is the following:
using a sample will work almost as well as using the entire data sets, if the sample is representative
A sample is representative if it has approximately the same property (of interest) as the original set of data

33. Types of Sampling Simple Random Sampling
There is an equal probability of selecting any particular item
Sampling without replacement
As each item is selected, it is removed from the population
Sampling with replacement
Objects are not removed from the population as they are selected for the sample.
In sampling with replacement, the same object can be picked up more than once
Stratified sampling
Split the data into several partitions; then draw random samples from each partition

34. Curse of Dimensionality
When dimensionality increases, data becomes increasingly sparse in the space that it occupies
Definitions of density and distance between points, which is critical for clustering and outlier detection, become less meaningful
Randomly generate 500 points
Compute difference between max and min distance between any pair of points

35. Discretization Using Class Labels
Entropy based approach
3 categories for both x and y
5 categories for both x and y

36. Discretization Without Using Class Labels
Data
Equal interval width
Equal frequency
K-means

37. Similarity and Dissimilarity
Numerical measure of how alike two data objects are.
Is higher when objects are more alike.
Often falls in the range [0,1]
Dissimilarity
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

38. Similarity/Dissimilarity for Simple Attributes
p and q are the attribute values for two data objects.

39. Euclidean Distance Euclidean Distance
Where n is the number of dimensions (attributes) and pk and qk are, respectively, the kth attributes (components) or data objects p and q.

40. Euclidean Distance
Distance Matrix

41. Minkowski Distance
Minkowski Distance is a generalization of Euclidean Distance
Where r is a parameter, n is the number of dimensions (attributes) and pk and qk are, respectively, the kth attributes (components) or data objects p and q.

42. Minkowski Distance
Distance Matrix

43. Common Properties of a Distance
Distances, such as the Euclidean distance, have some well known properties.
d(p, q)  0 for all p and q and d(p, q) = 0 only if p = q. (Positive definiteness)
d(p, q) = d(q, p) for all p and q. (Symmetry)
d(p, r)  d(p, q) + d(q, r) for all points p, q, and r. (Triangle Inequality)
where d(p, q) is the distance (dissimilarity) between points (data objects), p and q.
A distance that satisfies these properties is called a metric

44. Common Properties of a Similarity
Similarities, also have some well known properties.
s(p, q) = 1 (or maximum similarity) only if p = q.
s(p, q) = s(q, p) for all p and q. (Symmetry)
where s(p, q) is the similarity between points (data objects), p and q.

45. Similarity Between Binary Vectors
Common situation is that objects, p and q, have only binary attributes
Compute similarities using the following quantities
M01 = the number of attributes where p was 0 and q was 1
M10 = the number of attributes where p was 1 and q was 0
M00 = the number of attributes where p was 0 and q was 0
M11 = the number of attributes where p was 1 and q was 1
Simple Matching and Jaccard Coefficients
SMC = number of matches / number of attributes
= (M11 + M00) / (M01 + M10 + M11 + M00)
J = number of 11 matches / number of not-both-zero attributes values
= (M11) / (M01 + M10 + M11)

46. SMC versus Jaccard: Example
q =
M01 = 2 (the number of attributes where p was 0 and q was 1)
M10 = 1 (the number of attributes where p was 1 and q was 0)
M00 = 7 (the number of attributes where p was 0 and q was 0)
M11 = 0 (the number of attributes where p was 1 and q was 1)
SMC = (M11 + M00)/(M01 + M10 + M11 + M00) = (0+7) / ( ) = 0.7
J = (M11) / (M01 + M10 + M11) = 0 / ( ) = 0