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DataMiningMTAT.03.183 Descriptiveanalysis,preprocessing, visualisation... JaakVilo 2017Spring Characterisedata use Big_University_DB mine characteristics as "Science_Students" in relevance to name,gender,major,birth_date,residence,pho ne#,gpa from student where statusin graduate JaakViloandotherauthors UT:DataMining2009 2 Knowledge Discovery (KDD) Process • • This is a view from typical database systems and data Pattern Evaluation warehousing communities Data mining plays an essential role in the knowledge discovery Data Mining process Task-relevant Data Selection Data Warehouse Data Cleaning Data Integration Databases Jiawei Han, Micheline Kamber, and Jian Pei DataMining:ConceptsandTechniques 3 Why Data Preprocessing? n Data in the real world is dirty n incomplete: lacking attribute values, lacking certain attributes of interest, or containing only aggregate data n n noisy: containing errors or outliers n n e.g., occupation=“ ” e.g., Salary=“-10” inconsistent: containing discrepancies in codes or names n n n February 22, 2017 e.g., Age=“42” Birthday=“03/07/1997” e.g., Was rating “1,2,3”, now rating “A, B, C” e.g., discrepancy between duplicate records Data Mining: Concepts and Techniques 4 Why Is Data Dirty? n Incomplete data may come from n n n n Noisy data (incorrect values) may come from n n n n Faulty data collection instruments Human or computer error at data entry Errors in data transmission Inconsistent data may come from n n n “Not applicable” data value when collected Different considerations between the time when the data was collected and when it is analyzed. Human/hardware/software problems Different data sources Functional dependency violation (e.g., modify some linked data) Duplicate records also need data cleaning February 22, 2017 Data Mining: Concepts and Techniques 5 Why Is Data Preprocessing Important? n No quality data, no quality mining results! n Quality decisions must be based on quality data n n n n e.g., duplicate or missing data may cause incorrect or even misleading statistics. Data warehouse needs consistent integration of quality data Data extraction, cleaning, and transformation comprises the majority of the work of building a data warehouse Garbage in, garbage out February 22, 2017 Data Mining: Concepts and Techniques 6 High quality data requirements n n n n n n n n n High-quality data needs to pass a set of quality criteria. Those include: Accuracy: an aggregated value over the criteria of integrity, consistency, and density Integrity: an aggregated value over the criteria of completeness and validity Completeness: achieved by correcting data containing anomalies Validity: approximated by the amount of data satisfying integrity constraints Consistency: concerns contradictions and syntactical anomalies Uniformity: directly related to irregularities and in compliance with the set 'unit of measure' Density: the quotient of missing values in the data and the number of total values ought to be known http://en.wikipedia.org/wiki/Data_cleansing February 22, 2017 n Data Mining: Concepts and Techniques 7 Multi-Dimensional Measure of Data Quality n n A well-accepted multidimensional view: n Accuracy n Completeness n Consistency n Timeliness n Believability n Value added n Interpretability n Accessibility Broad categories: n Intrinsic, contextual, representational, and accessibility February 22, 2017 Data Mining: Concepts and Techniques 8 Major Tasks in Data Preprocessing n Data cleaning n n Data integration n n Normalization and aggregation Data reduction n n Integration of multiple databases, data cubes, or files Data transformation n n Fill in missing values, smooth noisy data, identify or remove outliers, and resolve inconsistencies Obtains reduced representation in volume but produces the same or similar analytical results Data discretization n Part of data reduction but with particular importance, especially for numerical data February 22, 2017 Data Mining: Concepts and Techniques 9 Forms of Data Preprocessing February 22, 2017 Data Mining: Concepts and Techniques 10 Chapter 2: Data Preprocessing n Why preprocess the data? n Descriptive data summarization n Data cleaning n Data integration and transformation n Data reduction n Discretization and concept hierarchy generation n Summary February 22, 2017 Data Mining: Concepts and Techniques 11 • 0.480.030.060.050.430.190.160.350.250.07 0.290.140.960.020.110.220.800.050.540.36 0.230.280.020.100.480.310.360.210.330.45 0.640.040.480.560.160.580.330.110.420.06 0.000.230.240.000.540.020.260.200.180.01 0.170.170.040.970.250.040.340.010.500.15 0.430.050.500.160.520.820.230.090.020.21 0.130.170.330.260.000.330.570.430.090.43 0.240.080.080.540.080.020.020.010.350.62 0.100.030.140.780.300.070.080.480.570.30 JaakViloandotherauthors UT:DataMining2009 12 1,20# 1,00# 0,80# 0,60# Series1# 0,40# 0,20# 0,00# 0# JaakViloandotherauthors 20# 40# 60# 80# UT:DataMining2009 100# 120# 13 1,20# 1,00# 0,80# 0,60# Series1# 0,40# 0,20# 0,00# 0# JaakViloandotherauthors 20# 40# 60# 80# UT:DataMining2009 100# 120# 14 JaakViloandotherauthors UT:DataMining2009 15 1,20# 1,00# 0,80# 0,60# 0,40# 0,20# 0,00# 0# 20# 40# 60# 80# 100# 120# 16 Series1# UT:DataMining2009 JaakViloandotherauthors Mining Data Descriptive Characteristics n Motivation n n Data dispersion characteristics n n n To better understand the data: central tendency, variation and spread median, max, min, quantiles, outliers, variance, etc. Numerical dimensions correspond to sorted intervals n Data dispersion: analyzed with multiple granularities of precision n Boxplot or quantile analysis on sorted intervals Dispersion analysis on computed measures n Folding measures into numerical dimensions n Boxplot or quantile analysis on the transformed cube February 22, 2017 Data Mining: Concepts and Techniques 17 Measuring the Central Tendency 1 n xi n Mean (algebraic measure) (sample vs. population): x = å n i =1 n n n Weighted arithmetic mean: N n Trimmed mean: chopping extreme values x= Median: A holistic measure n x å µ= åw x i =1 n i i åw i =1 i Middle value if odd number of values, or average of the middle two values otherwise n n Estimated by interpolation (for grouped data): median = L1 + ( Mode n Value that occurs most frequently in the data n Unimodal, bimodal, trimodal n Empirical formula: February 22, 2017 n / 2 - (å f )l f median )c mean - mode = 3 ´ (mean - median ) Data Mining: Concepts and Techniques 18 • • HistogramsandProbabilityDensityFunctions ProbabilityDensityFunctions – • FrequencyHistograms – – – • Totalareaundercurveintegratesto1 Y-axisiscounts Simpleinterpretation Can'tbedirectlyrelatedtoprobabilitiesordensityfunctions RelativeFrequencyHistograms – – – – Dividecountsbytotalnumberofobservations Y-axisisrelativefrequency Canbeinterpretedasprobabilitiesforeachrange Can'tbedirectlyrelatedtodensityfunction • • Barheightssumto1butwon'tintegrateto1unlessbarwidth=1 DensityHistograms – – – – Dividecountsby(totalnumberofobservationsXbarwidth) Y-axisisdensityvalues BarheightXbarwidthgivesprobabilityforeachrange Canbedirectlyrelatedtodensityfunction • Barareassumto1 http://www.geog.ucsb.edu/~joel/g210_w07/lecture_notes/lect04/oh07_04_1.html JaakViloandotherauthors UT:DataMining2009 19 JaakViloandotherauthors UT:DataMining2009 20 JaakViloandotherauthors UT:DataMining2009 21 JaakViloandotherauthors UT:DataMining2009 22 histograms • equalsub-intervals,knownas`bins‘ • breakpoints • binwidth JaakViloandotherauthors UT:DataMining2009 23 The data are (the log of) wing spans of aircraft built in from 1956 - 1984. JaakViloandotherauthors UT:DataMining2009 24 JaakViloandotherauthors UT:DataMining2009 25 JaakViloandotherauthors UT:DataMining2009 26 2-dimensionaldata:dot-plot February 22, 2017 DataMining:ConceptsandTechniques 27 Histogramvskerneldensity • propertiesofhistogramswiththesetwoexamples: – theyarenotsmooth – dependonendpointsofbins – dependonwidthofbins • Wecanalleviatethefirsttwoproblemsbyusing kerneldensityestimators. • Toremovethedependenceontheendpointsofthe bins,wecentreeachoftheblocksateachdatapoint ratherthanfixingtheendpointsoftheblocks. JaakViloandotherauthors UT:DataMining2009 28 block of width 1 and height 1/12 (the dotted boxes) as they are 12 data points, and then add them up JaakViloandotherauthors UT:DataMining2009 29 • Blocks- itisstilldiscontinuousaswehave usedadiscontinuouskernelasourbuilding block • Ifweuseasmoothkernelforourbuilding block,thenwewillhaveasmoothdensity estimate. JaakViloandotherauthors UT:DataMining2009 30 • It'simportanttochoosethemostappropriate bandwidthasavaluethatistoosmallortoolargeis notuseful. • Ifweuseanormal(Gaussian)kernelwithbandwidth orstandarddeviationof0.1(whichhasarea1/12 undertheeachcurve)thenthekerneldensity estimateissaidtoundersmoothedasthebandwidth istoosmallinthefigurebelow. • Itappearsthatthereare4modesinthisdensitysomeofthesearesurelyartificesofthedata. JaakViloandotherauthors UT:DataMining2009 31 JaakViloandotherauthors UT:DataMining2009 32 JaakViloandotherauthors UT:DataMining2009 33 • Chooseoptimalbandwith –Methodstoestimateit • AMISE=AsymptoticMeanIntegratedSquaredError • optimalbandwidth=argminAMISE JaakViloandotherauthors UT:DataMining2009 34 • Theoptimalvalueofthebandwidthforourdatasetis about0.25. • Fromtheoptimallysmoothedkerneldensity estimate,therearetwomodes.Asthesearethelog ofaircraftwingspan,itmeansthattherewerea groupofsmaller,lighterplanesbuilt,andtheseare clusteredaround2.5(whichisabout12m). • Whereasthelargerplanes,maybeusingjetengines astheseusedonacommercialscalefromaboutthe 1960s,aregroupedaround3.5(about33m). JaakViloandotherauthors UT:DataMining2009 35 JaakViloandotherauthors UT:DataMining2009 36 • Thepropertiesofkerneldensityestimators are,ascomparedtohistograms: – smooth – noendpoints – dependonbandwidth JaakViloandotherauthors UT:DataMining2009 37 KernelDensityestimation- links • Wikipedia: http://en.wikipedia.org/wiki/Kernel_density_estimation • RicardoGutierrez-Osuna http://research.cs.tamu.edu/prism/lectures/pr/pr_l7.pdf • TutorialandJavaappletfortesting: – http://parallel.vub.ac.be/research/causalModels/tutorial/kde.html • SimpleinteractivewebdemoatU.Tartu: – https://courses.cs.ut.ee/demos/kernel-density-estimation/ – http://kde.tume-maailm.pri.ee/ – JaakViloandotherauthors UT:DataMining2009 38 JaakViloandotherauthors UT:DataMining2009 39 R– example(dueK.Tretjakov) d=c(1,2,2,2,2,1,2,2,2,3,2,3,4,5,4,3,2,3,4,4,5,6,7); kernelsmooth<- function(data,sigma,x){ result=0; for(dindata){ result=result+exp(-(x-d)^2/2/sigma^2); } result/sqrt(2*pi)/sigma; } x=seq(min(d),max(d),by=0.1); y=sapply(x,function(x){kernelsmooth(d,1,x)}); hist(d); lines(x,y); JaakViloandotherauthors UT:DataMining2009 40 http://parallel.vub.ac.be/research/causalModels/tutorial/kde.html JaakViloandotherauthors UT:DataMining2009 41 JaakViloandotherauthors UT:DataMining2009 42 JaakViloandotherauthors UT:DataMining2009 43 http://kde.tume-maailm.pri.ee/ JaakViloandotherauthors UT:DataMining2009 44 http://kde.tume-maailm.pri.ee/ JaakViloandotherauthors UT:DataMining2009 45 http://kde.tume-maailm.pri.ee/ JaakViloandotherauthors UT:DataMining2009 46 Aggregation,analysisand visualizationofgeodata • • • • • • http://sightsmap.com Severallargecrowd-sourceddatasets: – ThewholePanoramiophotobankusedbyGooglemaps – ThewholeWikipedia,geotagsandwikipediaarticlelogs – Foursquare – ...More Aggregatedata,calculatepopularitesofplaces,calculatetypetags Translateandcategorizetitlesanddescriptionstogettypes Improveaggregationalgorithmsbylearning Visualizeheatmaps,typetags,aggregatedsources By: Tanel Tammet By: Tanel Tammet By: Tanel Tammet By: Tanel Tammet By: Tanel Tammet By: Tanel Tammet JaakViloandotherauthors UT:DataMining2009 53 • http://176.32.89.45/~hideaki/res/kernel.html JaakViloandotherauthors UT:DataMining2009 54 http://jmlr.csail.mit.edu/proceedings/papers/v2/kontkanen07a/kontkanen07a.pdf JaakViloandotherauthors UT:DataMining2009 55 JaakViloandotherauthors UT:DataMining2009 56 JaakViloandotherauthors UT:DataMining2009 57 MorelinksonRandkerneldensity • http://en.wikipedia.org/wiki/Kernel_density_estimation • http://sekhon.berkeley.edu/stats/html/density.html • http://stat.ethz.ch/R-manual/Rpatched/library/stats/html/density.html • http://www.google.com/search?q=kernel+density+estimation+R JaakViloandotherauthors UT:DataMining2009 58 JaakViloandotherauthors UT:DataMining2009 59 JaakViloandotherauthors UT:DataMining2009 60 JaakViloandotherauthors UT:DataMining2009 61 JaakViloandotherauthors UT:DataMining2009 62 Author: Gea Pajula JaakViloandotherauthors UT:DataMining2009 63 Symmetric vs. Skewed Data n Median, mean and mode of symmetric, positively and negatively skewed data February 22, 2017 Data Mining: Concepts and Techniques 64 Measuring the Dispersion of Data n Quartiles, outliers and boxplots n Quartiles: Q1 (25th percentile), Q3 (75th percentile) n Inter-quartile range: IQR = Q3 – Q1 n Five number summary: min, Q1, M, Q3, max n Boxplot: ends of the box are the quartiles, median is marked, whiskers, and plot outlier individually n n Outlier: usually, a value higher/lower than 1.5 x IQR Variance and standard deviation (sample: s, population: σ) n Variance: (algebraic, scalable computation) 1 n 1 n 2 1 n 2 2 s = ( xi - x ) = [å xi - (å xi ) ] å n - 1 i =1 n - 1 i =1 n i =1 2 n 1 s = N 2 n 1 ( x µ ) = å i N i =1 2 n åx i =1 i 2 - µ2 Standard deviation s (or σ) is the square root of variance s2 (or σ2) February 22, 2017 Data Mining: Concepts and Techniques 65 Boxplot Analysis n Five-number summary of a distribution: Minimum, Q1, M, Q3, Maximum n Boxplot n n n n 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 IRQ The median is marked by a line within the box Whiskers: two lines outside the box extend to Minimum and Maximum February 22, 2017 Data Mining: Concepts and Techniques 66 BoxPlots • Tukey77:JohnW.Tukey,"ExploratoryData Analysis".Addison-Wesley,Reading,MA. 1977. • http://informationandvisualization.de/blog/box-plot • JaakViloandotherauthors UT:DataMining2009 67 JaakViloandotherauthors UT:DataMining2009 68 JaakViloandotherauthors UT:DataMining2009 69 1.5 x IQR – Inter Quartile range JaakViloandotherauthors UT:DataMining2009 70 JaakViloandotherauthors UT:DataMining2009 71 Gea Pajula JaakViloandotherauthors UT:DataMining2009 72 Visualization of Data Dispersion: Boxplot Analysis February 22, 2017 Data Mining: Concepts and Techniques 73 February 22, 2017 Data Mining: Concepts and Techniques 74 February 22, 2017 Data Mining: Concepts and Techniques 75 Violin plot 76 Violin plot – R vertical kernel density http://gallery.r-enthusiasts.com/graph/Violin_plot,43 77 Combining plots… February 22, 2017 Data Mining: Concepts and Techniques 79 Properties of Normal Distribution Curve n The normal (distribution) curve n From μ–σ to μ+σ: contains about 68% of the measurements (μ: mean, σ: standard deviation) n From μ–2σ to μ+2σ: contains about 95% of it n From μ–3σ to μ+3σ: contains about 99.7% of it February 22, 2017 Data Mining: Concepts and Techniques 80 February 22, 2017 Data Mining: Concepts and Techniques 81 n Example of plots-containing article: n http://www.kgs.ku.edu/Magellan/WaterLevels/ CD/Reports/OFR04_57/rep00.htm February 22, 2017 Data Mining: Concepts and Techniques 82 Quantile-Quantile (q-q) Plots n n n http://onlinestatbook.com/2/advanced_graphs/q-q_plots.html http://www.itl.nist.gov/div898/handbook/eda/section3/eda33o.htm A q-q plot is a plot of the quantiles of the first data set against the quantiles of the second data set. By a quantile, we mean the fraction (or percent) of points below the given value. That is, the 0.3 (or 30%) quantile is the point at which 30% percent of the data fall below and 70% fall above that value. February 22, 2017 Data Mining: Concepts and Techniques 83 Cumulative Distribution Function (CDF) February 22, 2017 Data Mining: Concepts and Techniques 84 February 22, 2017 Data Mining: Concepts and Techniques 85 n n n These 2 batches do not appear to have come from populations with a common distribution. The batch 1 values are significantly higher than the corresponding batch 2 values. The differences are increasing from values 525 to 625. Then the values for the 2 batches get closer again. February 22, 2017 Data Mining: Concepts and Techniques 86 February 22, 2017 Data Mining: Concepts and Techniques 87 The advantages of the q-q plot are: n n The sample sizes do not need to be equal. Many distributional aspects can be simultaneously tested. For example, shifts in location, shifts in scale, changes in symmetry, and the presence of outliers can all be detected from this plot. For example, if the two data sets come from populations whose distributions differ only by a shift in location, the points should lie along a straight line that is displaced either up or down from the 45-degree reference line. February 22, 2017 Data Mining: Concepts and Techniques 88 February 22, 2017 Data Mining: Concepts and Techniques 89 A Q–Q plot comparing the distributions of standardizeddaily maximum temperatures at 25 stations in the US state of Ohio in March and in July. The curved pattern suggests that the central quantiles are more closely spaced in July than in March, and that the March distribution is skewed to the right compared to the July distribution. The data cover the period 1893–2001. February 22, 2017 Data Mining: Concepts and Techniques 90 n Parametric modeling usually involves making assumptions about the shape of data, or the shape of residuals from a regression fit. Verifying such assumptions can take many forms, but an exploration of the shape using histograms and qq plots is very effective. The q-q plot does not have any design parameters such as the number of bins for a histogram. February 22, 2017 Data Mining: Concepts and Techniques 91 February 22, 2017 Data Mining: Concepts and Techniques 92 Kemmeren et.al. (Mol. Cell, 2002) Randomized expression data Yeast 2-hybrid studies Known (literature) PPI MPK1 YLR350w SNF4 YCL046W SNF7 YGR122W. Scatter plot n n 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 February 22, 2017 Data Mining: Concepts and Techniques 94 February 22, 2017 Data Mining: Concepts and Techniques 95 Pearson Correlation 96 Not Correlated Data February 22, 2017 Data Mining: Concepts and Techniques 97 Abalone data set – P. Danelson hw. 98 Bias vs Variance Scott Fortmann-Roe http://scott.fortmann-roe.com/docs/BiasVariance.html 99 Several sets of (x, y) points, with the Pearson correlation coefficient of x and y for each set. Note that the correlation reflects the noisiness and direction of a linear relationship (top row), but not the slope of that relationship (middle), nor many aspects of nonlinear relationships (bottom). N.B.: the figure in the center has a slope of 0 but in that case the correlation coefficient is undefined because the variance of Y is zero. 100 Numerical summary? February 22, 2017 Data Mining: Concepts and Techniques 101 Anscombe’s quartet February 22, 2017 Data Mining: Concepts and Techniques 102 February 22, 2017 Data Mining: Concepts and Techniques 103 February 22, 2017 Data Mining: Concepts and Techniques 104 February 22, 2017 Data Mining: Concepts and Techniques 105 February 22, 2017 Data Mining: Concepts and Techniques 106 February 22, 2017 Data Mining: Concepts and Techniques 107 February 22, 2017 Data Mining: Concepts and Techniques 108 February 22, 2017 Data Mining: Concepts and Techniques 109 Loess Curve n n Adds a smooth curve to a scatter plot in order to provide better perception of the pattern of dependence Loess curve is fitted by setting two parameters: a smoothing parameter, and the degree of the polynomials that are fitted by the regression February 22, 2017 Data Mining: Concepts and Techniques 110 Graphic Displays of Basic Statistical Descriptions n n n n n n Histogram: (shown before) Boxplot: (covered before) 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 Loess (local regression) curve: add a smooth curve to a scatter plot to provide better perception of the pattern of dependence February 22, 2017 Data Mining: Concepts and Techniques 111 Chapter 2: Data Preprocessing n Why preprocess the data? n Descriptive data summarization n Data cleaning n Data integration and transformation n Data reduction n Discretization and concept hierarchy generation n Summary February 22, 2017 Data Mining: Concepts and Techniques 112 Data Cleaning n n Importance n “Data cleaning is one of the three biggest problems in data warehousing”—Ralph Kimball n “Data cleaning is the number one problem in data warehousing”—DCI survey Data cleaning tasks n Fill in missing values n Identify outliers and smooth out noisy data n Correct inconsistent data n Resolve redundancy caused by data integration February 22, 2017 Data Mining: Concepts and Techniques 113 Missing Data n Data is not always available n n Missing data may be due to n equipment malfunction n inconsistent with other recorded data and thus deleted n data not entered due to misunderstanding n n n E.g., many tuples have no recorded value for several attributes, such as customer income in sales data certain data may not be considered important at the time of entry not register history or changes of the data Missing data may need to be inferred. February 22, 2017 Data Mining: Concepts and Techniques 114 February 22, 2017 Data Mining: Concepts and Techniques 115 How to Handle Missing Data? n Ignore the tuple: usually done when class label is missing (assuming the tasks in classification—not effective when the percentage of missing values per attribute varies considerably. n Fill in the missing value manually: tedious + infeasible? n Fill in it automatically with n a global constant : e.g., “unknown”, a new class?! n the attribute mean n the attribute mean for all samples belonging to the same class: smarter n the most probable value: inference-based such as Bayesian formula or decision tree February 22, 2017 Data Mining: Concepts and Techniques 116 K-NN impute n K nearest neighbours imputation n Find K neighbours on available data points n Estimate the missing value (Hastie, Tibshirani, Troyanskaya, … Stanford 19992001) n February 22, 2017 Data Mining: Concepts and Techniques 117 Noisy Data n n n Noise: random error or variance in a measured variable Incorrect attribute values may due to n faulty data collection instruments n data entry problems n data transmission problems n technology limitation n inconsistency in naming convention Other data problems which requires data cleaning n duplicate records n incomplete data n inconsistent data February 22, 2017 Data Mining: Concepts and Techniques 118 How to Handle Noisy Data? n n n n Binning n first sort data and partition into (equal-frequency) bins n then one can smooth by bin means, smooth by bin median, smooth by bin boundaries, etc. Regression n smooth by fitting the data into regression functions Clustering n detect and remove outliers Combined computer and human inspection n detect suspicious values and check by human (e.g., deal with possible outliers) February 22, 2017 Data Mining: Concepts and Techniques 119 Simple Discretization Methods: Binning n Equal-width (distance) partitioning n Divides the range into N intervals of equal size: uniform grid n if A and B are the lowest and highest values of the attribute, the width of intervals will be: W = (B –A)/N. n n The most straightforward, but outliers may dominate presentation n Skewed data is not handled well Equal-depth (frequency) partitioning n Divides the range into N intervals, each containing approximately same number of samples n Good data scaling n Managing categorical attributes can be tricky February 22, 2017 Data Mining: Concepts and Techniques 120 Binning Methods for Data Smoothing Sorted data for price (in dollars): 4, 8, 9, 15, 21, 21, 24, 25, 26, 28, 29, 34 * Partition into equal-frequency (equi-depth) bins: - Bin 1: 4, 8, 9, 15 - Bin 2: 21, 21, 24, 25 - Bin 3: 26, 28, 29, 34 * Smoothing by bin means: - Bin 1: 9, 9, 9, 9 - Bin 2: 23, 23, 23, 23 - Bin 3: 29, 29, 29, 29 * Smoothing by bin boundaries: - Bin 1: 4, 4, 4, 15 - Bin 2: 21, 21, 25, 25 - Bin 3: 26, 26, 26, 34 q February 22, 2017 Data Mining: Concepts and Techniques 121 Regression y Y1 y=x+1 Y1’ X1 February 22, 2017 Data Mining: Concepts and Techniques x 122 Cluster Analysis G1 G3 G2 February 22, 2017 Data Mining: Concepts and Techniques 123 Data Cleaning as a Process n n n Data discrepancy detection n Use metadata (e.g., domain, range, dependency, distribution) n Check field overloading n Check uniqueness rule, consecutive rule and null rule n Use commercial tools n Data scrubbing: use simple domain knowledge (e.g., postal code, spell-check) to detect errors and make corrections n Data auditing: by analyzing data to discover rules and relationship to detect violators (e.g., correlation and clustering to find outliers) Data migration and integration n Data migration tools: allow transformations to be specified n ETL (Extraction/Transformation/Loading) tools: allow users to specify transformations through a graphical user interface Integration of the two processes n Iterative and interactive (e.g., Potter’s Wheels) February 22, 2017 Data Mining: Concepts and Techniques 124 Chapter 2: Data Preprocessing n Why preprocess the data? n Data cleaning n Data integration and transformation n Data reduction n Discretization and concept hierarchy generation n Summary February 22, 2017 Data Mining: Concepts and Techniques 125 Data Integration n n n n Data integration: n Combines data from multiple sources into a coherent store Schema integration: e.g., A.cust-id º B.cust-# n Integrate metadata from different sources Entity identification problem: n Identify real world entities from multiple data sources, e.g., Bill Clinton = William Clinton Detecting and resolving data value conflicts n For the same real world entity, attribute values from different sources are different n Possible reasons: different representations, different scales, e.g., metric vs. British units February 22, 2017 Data Mining: Concepts and Techniques 126 February 22, 2017 Data Mining: Concepts and Techniques 127 Handling Redundancy in Data Integration n Redundant data occur often when integration of multiple databases n n n n Object identification: The same attribute or object may have different names in different databases Derivable data: One attribute may be a “derived” attribute in another table, e.g., annual revenue Redundant attributes may be able to be detected by correlation analysis Careful integration of the data from multiple sources may help reduce/avoid redundancies and inconsistencies and improve mining speed and quality February 22, 2017 Data Mining: Concepts and Techniques 128 February 22, 2017 Data Mining: Concepts and Techniques 129 February 22, 2017 Data Mining: Concepts and Techniques 130 February 22, 2017 Data Mining: Concepts and Techniques 131 Normalisation n Making data comparable… February 22, 2017 Data Mining: Concepts and Techniques 132 0,8% 0,6% 0,4% 0,2% Series1% Series2% Series3% Series4% 0% 0% 20% 40% 60% 80% 100% 120% !0,2% !0,4% !0,6% February 22, 2017 Data Mining: Concepts and Techniques 133 Elements of microarray statistics Reference Test M = log2R – log2G = log2(R/G) A = 1/2 (log2R + log2G) JaakViloandotherauthors UT:DataMining2009 135 Normalisation can be used to transform data Expression Profiler 136 Chapter 2: Data Preprocessing n Why preprocess the data? n Data cleaning n Data integration and transformation n Data reduction n Discretization and concept hierarchy generation n Summary February 22, 2017 Data Mining: Concepts and Techniques 137 Data Reduction Strategies n n n Why data reduction? n A database/data warehouse may store terabytes of data n Complex data analysis/mining may take a very long time to run on the complete data set Data reduction n Obtain a reduced representation of the data set that is much smaller in volume but yet produce the same (or almost the same) analytical results Data reduction strategies n Data cube aggregation: n Dimensionality reduction — e.g., remove unimportant attributes n Data Compression n Numerosity reduction — e.g., fit data into models n Discretization and concept hierarchy generation February 22, 2017 Data Mining: Concepts and Techniques 138 Chapter 2: Data Preprocessing n Why preprocess the data? n Data cleaning n Data integration and transformation n Data reduction n Discretization and concept hierarchy generation n Summary February 22, 2017 Data Mining: Concepts and Techniques 139 Discretization n Three types of attributes: n Nominal — values from an unordered set, e.g., color, profession n Ordinal — values from an ordered set, e.g., military or academic rank n n Continuous — real numbers, e.g., integer or real numbers Discretization: n Divide the range of a continuous attribute into intervals n Some classification algorithms only accept categorical attributes. n Reduce data size by discretization n Prepare for further analysis February 22, 2017 Data Mining: Concepts and Techniques 140 Discretization and Concept Hierarchy n Discretization n Reduce the number of values for a given continuous attribute by dividing the range of the attribute into intervals n n Interval labels can then be used to replace actual data values n Supervised vs. unsupervised n Split (top-down) vs. merge (bottom-up) n Discretization can be performed recursively on an attribute Concept hierarchy formation n 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) February 22, 2017 Data Mining: Concepts and Techniques 141 E.g. n n n n 0-18 y 19-65 y 66-105 1580 8394 2700 0-20 21-40 41-60 61-105 1780 4200 4767 2900 Vs n n n n February 22, 2017 Data Mining: Concepts and Techniques 142 Segmentation by Natural Partitioning n A simply 3-4-5 rule can be used to segment numeric data into relatively uniform, “natural” intervals. n If an interval covers 3, 6, 7 or 9 distinct values at the most significant digit, partition the range into 3 equiwidth intervals n If it covers 2, 4, or 8 distinct values at the most significant digit, partition the range into 4 intervals n If it covers 1, 5, or 10 distinct values at the most significant digit, partition the range into 5 intervals February 22, 2017 Data Mining: Concepts and Techniques 143 Example of 3-4-5 Rule count Step 1: Step 2: -$351 -$159 Min Low (i.e, 5%-tile) msd=1,000 profit High(i.e, 95%-0 tile) Low=-$1,000 $4,700 Max High=$2,000 (-$1,000 - $2,000) Step 3: (-$1,000 - 0) ($1,000 - $2,000) (0 -$ 1,000) (-$400 -$5,000) Step 4: (-$400 - 0) (-$400 -$300) (-$300 -$200) (-$200 -$100) (-$100 0) $1,838 February 22, 2017 ($1,000 - $2, 000) (0 - $1,000) (0 $200) ($1,000 $1,200) ($200 $400) ($1,200 $1,400) ($1,400 $1,600) ($400 $600) ($600 $800) ($800 $1,000) ($1,600 ($1,800 $1,800) $2,000) Data Mining: Concepts and Techniques ($2,000 - $5, 000) ($2,000 $3,000) ($3,000 $4,000) ($4,000 $5,000) 144 -351,976.00 .. 4,700,896.50 Example MIN= -351,976.00 MAX=4,700,896.50 LOW = 5th percentile -159,876 HIGH = 95th percentile 1,838,761 msd = 1,000,000 (most significant digit) LOW = -1,000,000 (round down) HIGH = 2,000,000 (round up) 3 value ranges 1. (-1,000,000 .. 0] 2. (0 .. 1,000,000] 3. (1,000,000 .. 2,000,000] Adjust with real MIN and MAX 1. 2. 3. 4. (-400,000 .. 0] (0 .. 1,000,000] (1,000,000 .. 2,000,000] (2,000,000 .. 5,000,000] February 22, 2017 Data Mining: Concepts and Techniques 145 Recursive … 1.1. (-400,000 .. -300,000 ] 1.2. (-300,000 .. -200,000 ] 1.3. (-200,000 .. -100,000 ] 1.4. (-100,000 .. 0 ] 2.1. (0 .. 200,000 ] 2.2. (200,000 .. 400,000 ] 2.3. (400,000 .. 600,000 ] 2.4. (600,000 .. 800,000 ] 2.5. (800,000 .. 1,000,000 ] 3.1. (1,000,000 .. 1,200,000 ] 3.2. (1,200,000 .. 1,400,000 ] 3.3. (1,400,000 .. 1,600,000 ] 3.4. (1,600,000 .. 1,800,000 ] 3.5. (1,800,000 .. 2,000,000 ] 4.1. (2,000,000 .. 3,000,000 ] 4.2. (3,000,000 .. 4,000,000 ] 4.3. (4,000,000 .. 5,000,000 ] JaakViloandotherauthors UT:DataMining2009 146 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} February 22, 2017 DataMining:ConceptsandTechniques 147 Automatic Concept Hierarchy Generation n Some hierarchies can be automatically generated based on the analysis of the number of distinct values per attribute in the data set n The attribute with the most distinct values is placed at the lowest level of the hierarchy n Exceptions, e.g., weekday, month, quarter, year 15 distinct values country province_or_ state 365 distinct values city 3567 distinct values street February 22, 2017 674,339 distinct values Data Mining: Concepts and Techniques 148 Chapter 2: Data Preprocessing n Why preprocess the data? n Data cleaning n Data integration and transformation n Data reduction n Discretization and concept hierarchy generation n Summary February 22, 2017 Data Mining: Concepts and Techniques 149 Summary n n n n Data preparation or preprocessing is a big issue for both data warehousing and data mining Discriptive data summarization is need for quality data preprocessing Data preparation includes n Data cleaning and data integration n Data reduction and feature selection n Discretization A lot a methods have been developed but data preprocessing still an active area of research February 22, 2017 Data Mining: Concepts and Techniques 150 References n D. P. Ballou and G. K. Tayi. Enhancing data quality in data warehouse environments. Communications of ACM, 42:73-78, 1999 n T. Dasu and T. Johnson. Exploratory Data Mining and Data Cleaning. John Wiley & Sons, 2003 n T. Dasu, T. Johnson, S. Muthukrishnan, V. Shkapenyuk. Mining Database Structure; Or, How to Build a Data Quality Browser. SIGMOD’02. n H.V. Jagadish et al., Special Issue on Data Reduction Techniques. Bulletin of the Technical Committee on Data Engineering, 20(4), December 1997 n D. Pyle. Data Preparation for Data Mining. Morgan Kaufmann, 1999 n E. Rahm and H. H. Do. Data Cleaning: Problems and Current Approaches. IEEE Bulletin of the Technical Committee on Data Engineering. Vol.23, No.4 n V. Raman and J. Hellerstein. Potters Wheel: An Interactive Framework for Data Cleaning and Transformation, VLDB’2001 n T. Redman. Data Quality: Management and Technology. Bantam Books, 1992 n Y. Wand and R. Wang. Anchoring data quality dimensions ontological foundations. Communications of ACM, 39:86-95, 1996 n R. Wang, V. Storey, and C. Firth. A framework for analysis of data quality research. IEEE Trans. Knowledge and Data Engineering, 7:623-640, 1995 February 22, 2017 Data Mining: Concepts and Techniques 151