Know Your Data in data mining applications

DATA MINING Lecture 3: KnowYour Data Slides Adapted from Jiawei Han et al. and Jianlin Cheng DEPARTMENTOFCOMPUTER SCIENCE,UNIVERSITYOF COLORADO,COLORADO SPRINGS. CS4434/5434ANDDASE4435 DATAMINING, FALL2023 DR.OLUWATOSIN OLUWADARE,2023

2 Data Mining: Concepts and Techniques — Chapter 2 — Jiawei Han, Micheline Kamber, and Jian Pei University of Illinois at Urbana-Champaign Simon Fraser University ©2011 Han, Kamber, and Pei. All rights reserved.

3 Chapter 2: Getting to Know Your Data  Data Objects and Attribute Types  Basic Statistical Descriptions of Data  Data Visualization  Measuring Data Similarity and Dissimilarity  Summary

4 Types of Data Sets  Record  Relational records  Data matrix, e.g., numerical matrix, crosstabs  Document data: text documents: term- frequency vector  Transaction data  Graph and network  World Wide Web  Social or information networks  Molecular Structures  Ordered  Video data: sequence of images  Temporal data: time-series  Sequential Data: transaction sequences  Genetic sequence data  Spatial, image and multimedia:  Spatial data: maps  Image data:  Video data: Document 1 season timeout lost wi n game score ball pla y coach team Document 2 Document 3 3 0 5 0 2 6 0 2 0 2 0 0 7 0 2 1 0 0 3 0 0 1 0 0 1 2 2 0 3 0 TID Items 1 Bread, Coke, Milk 2 Beer, Bread 3 Beer, Coke, Diaper, Milk 4 Beer, Bread, Diaper, Milk 5 Coke, Diaper, Milk

5 Important Characteristics of Structured Data  Dimensionality  Curse of dimensionality  Sparsity  Only presence counts  Resolution  Patterns depend on the scale  Distribution  Centrality and dispersion

6 Data Objects  Data sets are made up of data objects.  A data object represents an entity.  Examples:  sales database: customers, store items, sales  medical database: patients, treatments  university database: students, professors, courses  Also called samples , examples, instances, data points, objects, tuples.  Data objects are described by attributes.  Database rows -> data objects; columns ->attributes.

7 Attributes  Attribute (or dimensions, features, variables): a data field, representing a characteristic or feature of a data object.  E.g., customer _ID, name, address  Types:  Nominal  Binary  Numeric: quantitative  Interval-scaled  Ratio-scaled

Data Attributes  Attribute refers to the characteristic of the data object.  The nouns defining the characteristics are used interchangeably: Attribute, dimension, feature, and variable. 8 Field Data Warehousing Database and Data Mining Statistic Machine Learning Characteristic term Used Feature Attribute Variable Dimension

9 Attribute Types  Nominal: categories, states, or “names of things”  Hair_color = {auburn, black, blond, brown, grey, red, white}  marital status, occupation, ID numbers, zip codes  Binary  Nominal attribute with only 2 states (0 and 1)  Symmetric binary: both outcomes equally important  e.g., cat or dog  Asymmetric binary: outcomes not equally important.  e.g., medical test (positive vs. negative)  Convention: assign 1 to most important outcome (e.g., HIV positive)  the positive (1) and negative (0) outcomes of a disease test.  Ordinal  Values have a meaningful order (ranking) but magnitude between successive values is not known.  Size = {small, medium, large}, grades, army rankings

10 Numeric Attribute Types  Quantity (integer or real-valued)  Interval  Measured on a scale of equal-sized units  Values have order  E.g., temperature in C˚or F˚, calendar dates  No true zero-point  Ratio  Inherent zero-point  We can speak of values as being an order of magnitude larger than the unit of measurement (10 K˚ is twice as high as 5 K˚).  e.g., temperature in Kelvin, length, counts, monetary quantities

11 Discrete vs. Continuous Attributes  Discrete Attribute  Has only a finite or countably infinite set of values  E.g., zip codes, profession, or the set of words in a collection of documents  Sometimes, represented as integer variables  Note: Binary attributes are a special case of discrete attributes  Continuous Attribute  Has real numbers as attribute values  E.g., 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

13 Basic Statistical Descriptions of Data  Motivation  To better understand the data: central tendency, variation and spread  Data dispersion characteristics  median, max, min, quantiles, outliers, variance, etc.  Numerical dimensions correspond to sorted intervals  Data dispersion: analyzed with multiple granularities of precision  Boxplot or quantile analysis on sorted intervals  Dispersion analysis on computed measures  Folding measures into numerical dimensions  Boxplot or quantile analysis on the transformed cube

14 Measuring the Central Tendency  Mean (algebraic measure) (sample vs. population): Note: n is sample size and N is population size.  Weighted arithmetic mean:  Trimmed mean: chopping extreme values  Median:  Middle value if odd number of values, or average of the middle two values otherwise  Estimated by interpolation (for grouped data):  Mode  Value that occurs most frequently in the data  Unimodal, bimodal, trimodal  Empirical formula:    n i i x n x 1 1      n i i n i i i w x w x 1 1 width freq l freq n L median median ) ) ( 2 / ( 1     ) ( 3 median mean mode mean     N x   

May 8, 2024 Data Mining: Concepts and Techniques 15 Symmetric vs. Skewed Data  Median, mean and mode of symmetric, positively and negatively skewed data positively skewed negatively skewed symmetric

16 Measuring the Dispersion of Data  Quartiles, outliers and boxplots  Quartiles: Q1 (25th percentile), Q3 (75th percentile)  Inter-quartile range: IQR = Q3 – Q1  Five number summary: min, Q1, median, Q3, max  Boxplot: ends of the box are the quartiles; median is marked; add whiskers, and plot outliers individually  Outlier: usually, a value higher/lower than Q3 + 1.5 x IQR or Q1 – 1.5 x IQR  Variance and standard deviation (sample: s, population: σ)  Variance: (algebraic, scalable computation)  Standard deviation s (or σ) is the square root of variance s2 (or σ2)             n i n i i i n i i x n x n x x n s 1 1 2 2 1 2 2 ] ) ( 1 [ 1 1 ) ( 1 1         n i i n i i x N x N 1 2 2 1 2 2 1 ) ( 1   

17 Boxplot Analysis  Five-number summary of a distribution  Minimum, Q1, Median, Q3, Maximum  Boxplot  Data is represented with a box  The ends of the box are at the first and third quartiles, i.e., the height of the box is IQR  The median is marked by a line within the box  Whiskers: two lines outside the box extended to Minimum and Maximum  Outliers: points beyond a specified outlier threshold, plotted individually

Boxplot Analysis Example  Distribution A is positively skewed, because the whisker and half-box are longer on the right side of the median than on the left side.  Distribution B is approximately symmetric, because both half-boxes are almost the same length (0.11 on the left side and 0.10 on the right side).  Distribution C is negatively skewed because the whisker and half-box are longer on the left side of the median than on the right side. 18 https://www150.statcan.gc.ca/n1/edu/power-pouvoir/ch12/5214889-eng.htm

May 8, 2024 Data Mining: Concepts and Techniques 19 Visualization of Data Dispersion: 3-D Boxplots

20 Properties of Normal Distribution Curve  The normal (distribution) curve  From μ–σ to μ+σ: contains about 68% of the measurements (μ: mean, σ: standard deviation)  From μ–2σ to μ+2σ: contains about 95% of it  From μ–3σ to μ+3σ: contains about 99.7% of it

Standard deviation in a Normal Distribution 21 Images/google

22 Graphic Displays of Basic Statistical Descriptions  Boxplot: graphic display of five-number summary  Histogram: x-axis are values, y-axis repres. frequencies  Quantile plot: each value xi is paired with fi indicating that approximately 100 fi % of data are  xi  Quantile-quantile (q-q) plot: graphs the quantiles of one univariant distribution against the corresponding quantiles of another  Scatter plot: each pair of values is a pair of coordinates and plotted as points in the plane

23 Histogram Analysis  Histogram: Graph display of tabulated frequencies, shown as bars  It shows what proportion of cases fall into each of several categories  Differs from a bar chart in that it is the area of the bar that denotes the value, not the height as in bar charts, a crucial distinction when the categories are not of uniform width  The categories are usually specified as non-overlapping intervals of some variable. The categories (bars) must be adjacent 0 5 10 15 20 25 30 35 40 10000 30000 50000 70000 90000

Homework 1  Homework 1 has been posted at the course web site and on Canvas.  Due Sept. 12, 2023  Submit it to Canvas May 8, 2024 Data Mining: Concepts and Techniques 24

25 Histograms Often Tell More than Boxplots  The two histograms shown in the left may have the same boxplot representation  The same values for: min, Q1, median, Q3, max  But they have rather different data distributions

Data Mining: Concepts and Techniques 26 Quantile Plot  Displays all of the data (allowing the user to assess both the overall behavior and unusual occurrences)  Plots quantile information  For a data xi data sorted in increasing order, fi indicates that approximately 100 fi% of the data are below or equal to the value xi

27 Quantile-Quantile (Q-Q) Plot  Graphs the quantiles of one univariate distribution against the corresponding quantiles of another  View: Is there is a shift in going from one distribution to another?  Example shows unit price of items sold at Branch 1 vs. Branch 2 for each quantile. Unit prices of items sold at Branch 1 tend to be lower than those at Branch 2.

28 Scatter plot  Provides a first look at bivariate data to see clusters of points, outliers, etc  Each pair of values is treated as a pair of coordinates and plotted as points in the plane

29 Positively and Negatively Correlated Data  The left half fragment is positively correlated  The right half is negative correlated

32 Similarity and Dissimilarity  Similarity  Numerical measure of how alike two data objects are  Value is higher when objects are more alike  Often falls in the range [0,1]  Dissimilarity (e.g., distance)  Numerical measure of how different two data objects are  Lower when objects are more alike  Minimum dissimilarity is often 0  Upper limit varies  Proximity refers to a similarity or dissimilarity

33 Data Matrix and Dissimilarity Matrix  Data matrix  n data points with p dimensions  Two modes  Dissimilarity matrix  n data points, but registers only the distance  A triangular matrix  Single mode                   np x ... nf x ... n1 x ... ... ... ... ... ip x ... if x ... i1 x ... ... ... ... ... 1p x ... 1f x ... 11 x                 0 ... ) 2 , ( ) 1 , ( : : : ) 2 , 3 ( ) ... n d n d 0 d d(3,1 0 d(2,1) 0

34 Proximity Measure for Nominal Attributes  Can take 2 or more states, e.g., red, yellow, blue, green (generalization of a binary attribute)  Method 1: Simple matching  m: # of matches, p: total # of variables  Method 2: Use a large number of binary attributes  creating a new binary attribute for each of the M nominal states p m p j i d   ) , (

Class Example: Method 1 35                 0 ... ) 2 , ( ) 1 , ( : : : ) 2 , 3 ( ) ... n d n d 0 d d(3,1 0 d(2,1) 0 p m p j i d   ) , (

36 Proximity Measure for Binary Attributes  A contingency table for binary data  Distance measure for symmetric binary variables:  Distance measure for asymmetric binary variables:  Jaccard coefficient (similarity measure for asymmetric binary variables):  Note: Jaccard coefficient is the same as “coherence”: Object i Object j

Variables (q, r, s ,t)  q is the number of attributes that equal 1 for both objects i and j,  r is the number of attributes that equal 1 for object i but equal 0 for object j,  s is the number of attributes that equal 0 for object i but equal 1 for object j, and  t is the number of attributes that equal 0 for both objects i and j. 37

38 Dissimilarity between Binary Variables  Example  Gender is a symmetric attribute  The remaining attributes are asymmetric binary attributes  Let the values Y(yes) and P(positive) be 1, and the value N(no and negative) 0 Name Gender Fever Cough Test-1 Test-2 Test-3 Test-4 Jack M Y N P N N N Mary F Y N P N P N Jim M Y P N N N N

Calculate the Dissimilarity  d(Jack, Mary) = ?  d(Jack, Jim). = ?  d(Jim, Jack) = ?  q is the number of attributes that equal 1 for both objects i and j,  r is the number of attributes that equal 1 for object i but equal 0 for object j,  s is the number of attributes that equal 0 for object i but equal 1 for object j, and  t is the number of attributes that equal 0 for both objects i and j. 39 OR

40 Dissimilarity between Binary Variables  Example  Gender is a symmetric attribute  The remaining attributes are asymmetric binary attributes  Let the values Y(yes) and P(positive) be 1, and the value N(no and negative) 0 Name Gender Fever Cough Test-1 Test-2 Test-3 Test-4 Jack M Y N P N N N Mary F Y N P N P N Jim M Y P N N N N 75 . 0 2 1 1 2 1 ) , ( 67 . 0 1 1 1 1 1 ) , ( 33 . 0 1 0 2 1 0 ) , (                mary jim d jim jack d mary jack d

Comment on the Result  What does the measurement suggest?  These measurements suggest that Jim and Mary are unlikely to have a similar disease because they have the highest dissimilarity value among the three pairs.  Of the three patients, Jack and Mary are the most likely to have a similar disease. 41

42 Standardizing Numeric Data  Z-score:  X: raw score to be standardized, μ: mean of the population, σ: standard deviation  the distance between the raw score and the population mean in units of the standard deviation  negative when the raw score is below the mean, “+” when above  An alternative way: Calculate the mean absolute deviation where  standardized measure (z-score):  Using mean absolute deviation is more robust than using standard deviation . ) ... 2 1 1 nf f f f x x (x n m     |) | ... | | | (| 1 2 1 f nf f f f f f m x m x m x n s        f f if if s m x z       x z

43 Example: Data Matrix and Dissimilarity Matrix point attribute1 attribute2 x1 1 2 x2 3 5 x3 2 0 x4 4 5 Dissimilarity Matrix (with Euclidean Distance) x1 x2 x3 x4 x1 0 x2 3.61 0 x3 5.1 5.1 0 x4 4.24 1 5.39 0 Data Matrix

44 Distance on Numeric Data: Minkowski Distance  Minkowski distance: A popular distance measure where i = (xi1, xi2, …, xip) and j = (xj1, xj2, …, xjp) are two p-dimensional data objects, and h is the order (the distance so defined is also called L-h norm)  Properties  d(i, j) > 0 if i ≠ j, and d(i, i) = 0 (Positive definiteness)  d(i, j) = d(j, i) (Symmetry)  d(i, j)  d(i, k) + d(k, j) (Triangle Inequality)  A distance that satisfies these properties is a metric

45 Special Cases of Minkowski Distance  h = 1: Manhattan (city block, L1 norm) distance  E.g., the Hamming distance: the number of bits that are different between two binary vectors  h = 2: (L2 norm) Euclidean distance  h  . “supremum” (Lmax norm, L norm) distance.  This is the maximum difference between any component (attribute) of the vectors ) | | ... | | | (| ) , ( 2 2 2 2 2 1 1 p p j x i x j x i x j x i x j i d        | | ... | | | | ) , ( 2 2 1 1 p p j x i x j x i x j x i x j i d       

46 Example: Minkowski Distance Dissimilarity Matrices point attribute 1 attribute 2 x1 1 2 x2 3 5 x3 2 0 x4 4 5 L x1 x2 x3 x4 x1 0 x2 5 0 x3 3 6 0 x4 6 1 7 0 L2 x1 x2 x3 x4 x1 0 x2 3.61 0 x3 2.24 5.1 0 x4 4.24 1 5.39 0 L x1 x2 x3 x4 x1 0 x2 3 0 x3 2 5 0 x4 3 1 5 0 Manhattan (L1) Euclidean (L2) Supremum

47 Ordinal Variables  An ordinal variable can be discrete or continuous  Order is important, e.g., rank  Can be treated like interval-scaled  replace 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 1 1    f if if M r z } ,..., 1 { f if M r 

48 Attributes of Mixed Type  A database may contain all attribute types  Nominal, symmetric binary, asymmetric binary, numeric, ordinal  One may use a weighted formula to combine their effects  f is binary or nominal: dij (f) = 0 if xif = xjf , or dij (f) = 1 otherwise  f is numeric: use the normalized distance  f is ordinal  Compute ranks rif and  Treat zif as interval-scaled ) ( 1 ) ( ) ( 1 ) , ( f ij p f f ij f ij p f d j i d        1 1    f if M r zif

49 Cosine Similarity  A document can be represented by thousands of attributes, each recording the frequency of a particular word (such as keywords) or phrase in the document.  Other vector objects: gene features in micro-arrays, …  Applications: information retrieval, biologic taxonomy, gene feature mapping, ...  Cosine measure: If d1 and d2 are two vectors (e.g., term-frequency vectors), then cos(d1, d2) = (d1  d2) /||d1|| ||d2|| , where  indicates vector dot product, ||d||: the length of vector d

50 Example: Cosine Similarity  cos(d1, d2) = (d1  d2) /||d1|| ||d2|| , where  indicates vector dot product, ||d|: the length of vector d  Ex: Find the similarity between documents 1 and 2. d1 = (5, 0, 3, 0, 2, 0, 0, 2, 0, 0) d2 = (3, 0, 2, 0, 1, 1, 0, 1, 0, 1) d1d2 = 5*3+0*0+3*2+0*0+2*1+0*1+0*1+2*1+0*0+0*1 = 25 ||d1||= (5*5+0*0+3*3+0*0+2*2+0*0+0*0+2*2+0*0+0*0)0.5=(42)0.5 = 6.481 ||d2||= (3*3+0*0+2*2+0*0+1*1+1*1+0*0+1*1+0*0+1*1)0.5=(17)0.5 = 4.12 cos(d1, d2 ) = 0.94

Summary  Data attribute types: nominal, binary, ordinal, interval-scaled, ratio- scaled  Many types of data sets, e.g., numerical, text, graph, Web, image.  Gain insight into the data by:  Basic statistical data description: central tendency, dispersion, graphical displays  Data visualization: map data onto graphical primitives  Measure data similarity  Above steps are the beginning of data preprocessing.  Many methods have been developed but still an active area of research. 52

References  W. Cleveland, Visualizing Data, Hobart Press, 1993  T. Dasu and T. Johnson. Exploratory Data Mining and Data Cleaning. John Wiley, 2003  U. Fayyad, G. Grinstein, and A. Wierse. Information Visualization in Data Mining and Knowledge Discovery, Morgan Kaufmann, 2001  L. Kaufman and P. J. Rousseeuw. Finding Groups in Data: an Introduction to Cluster Analysis. John Wiley & Sons, 1990.  H. V. Jagadish, et al., Special Issue on Data Reduction Techniques. Bulletin of the Tech. Committee on Data Eng., 20(4), Dec. 1997  D. A. Keim. Information visualization and visual data mining, IEEE trans. on Visualization and Computer Graphics, 8(1), 2002  D. Pyle. Data Preparation for Data Mining. Morgan Kaufmann, 1999  S. Santini and R. Jain,” Similarity measures”, IEEE Trans. on Pattern Analysis and Machine Intelligence, 21(9), 1999  E. R. Tufte. The Visual Display of Quantitative Information, 2nd ed., Graphics Press, 2001  C. Yu , et al., Visual data mining of multimedia data for social and behavioral studies, Information Visualization, 8(1), 2009 53

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