Programme: II B.Com BA Course Title: Business Data Mining Content: Unit I – Data Preprocessing Ms. S. Valarmathi Assistant Professor B.Com (CA) Department KPR College of Arts Science and Research 1 II B.Com BA Data mining & Data Preprocessing Data Preprocessing • • • • • Why preprocess the data? Data cleaning Data integration and transformation Data reduction Discretization and concept hierarchy generation • Summary II B.Com BA Data mining & Data Preprocessing Why Data Preprocessing? • Data in the real world is dirty – incomplete: lacking attribute values, lacking certain attributes of interest, or containing only aggregate data • e.g., occupation=“” – noisy: containing errors or outliers • e.g., Salary=“-10” – inconsistent: containing discrepancies in codes or names • 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 II B.Com BA Data mining & Data Preprocessing Why Is Data Dirty? • Incomplete data comes from – n/a data value when collected – different consideration between the time when the data was collected and when it is analyzed. – human/hardware/software problems • Noisy data comes from the process of data – collection – entry – transmission • Inconsistent data comes from – Different data sources – Functional dependency violation II B.Com BA Data mining & Data Preprocessing Why Is Data Preprocessing Important? • No quality data, no quality mining results! – Quality decisions must be based on quality data • 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. —Bill Inmon II B.Com BA Data mining & Data Preprocessing Multi-Dimensional Measure of Data Quality • A well-accepted multidimensional view: – – – – – – – – Accuracy Completeness Consistency Timeliness Believability Value added Interpretability Accessibility • Broad categories: – intrinsic, contextual, representational, and accessibility. II B.Com BA Data mining & Data Preprocessing Major Tasks in Data Preprocessing • Data cleaning – Fill in missing values, smooth noisy data, identify or remove outliers, and resolve inconsistencies • Data integration – Integration of multiple databases, data cubes, or files • Data transformation – Normalization and aggregation • Data reduction – Obtains reduced representation in volume but produces the same or similar analytical results • Data discretization – Part of data reduction but with particular importance, especially for numerical data II B.Com BA Data mining & Data Preprocessing Data Preprocessing • • • • • Why preprocess the data? Data cleaning Data integration and transformation Data reduction Discretization and concept hierarchy generation • Summary II B.Com BA Data mining & Data Preprocessing Data Cleaning • Importance – “Data cleaning is one of the three biggest problems in data warehousing”—Ralph Kimball – “Data cleaning is the number one problem in data warehousing”—DCI survey • Data cleaning tasks – – – – II B.Com BA Fill in missing values Identify outliers and smooth out noisy data Correct inconsistent data Resolve redundancy caused by data integration Data mining & Data Preprocessing Missing Data • Data is not always available – E.g., many tuples have no recorded value for several attributes, such as customer income in sales data • Missing data may be due to – equipment malfunction – inconsistent with other recorded data and thus deleted – data not entered due to misunderstanding – 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. II B.Com BA Data mining & Data Preprocessing How to Handle Missing Data? • 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. • Fill in the missing value manually: tedious + infeasible? • Fill in it automatically with – a global constant : e.g., “unknown”, a new class?! – the attribute mean – the attribute mean for all samples belonging to the same class: smarter – the most probable value: inference-based such as Bayesian formula or decision tree II B.Com BA Data mining & Data Preprocessing Data preparation - What is Data? • Collection of data objects and their attributes • An attribute is a property or characteristic of an object – Examples: eye color of a person, temperature, etc. – Attribute is also known as variable, field, characteristic, or feature • A collection of attributes describe an object Attributes Objects – Object is also known as record, point, case, sample, entity, or instance 10 II B.Com BA Data mining & Data Preprocessing Tid Refund Marital Status Taxable Income Cheat 1 Yes Single 125K No 2 No Married 100K No 3 No Single 70K No 4 Yes Married 120K No 5 No Divorced 95K Yes 6 No Married No 7 Yes Divorced 220K No 8 No Single 85K Yes 9 No Married 75K No 10 No Single 90K Yes 60K Attribute Values • Attribute values are numbers or symbols assigned to an attribute • Distinction between attributes and attribute values – Same attribute can be mapped to different attribute values • Example: height can be measured in feet or meters – Different attributes can be mapped to the same set of values • Example: Attribute values for ID and age are integers • But properties of attribute values can be different – ID has no limit but age has a maximum and minimum value II B.Com BA Data mining & Data Preprocessing Types of Attributes • 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 • II B.Com BA Examples: temperature in Kelvin, length, time, counts Data mining & Data Preprocessing 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 II B.Com BA Data mining & Data Preprocessing Attribute Type Description Examples 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 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 Ratio II B.Com BA Data mining & Data Preprocessing Operations Attribute Level Transformation Comments Nominal Any permutation of values If all employee ID numbers were reassigned, would it make any difference? Ordinal An order preserving change of values, i.e., new_value = f(old_value) where f is a monotonic function. Interval new_value =a * old_value + b where a and b are constants An attribute encompassing the notion of good, better best can be represented equally well by the values {1, 2, 3} or by { 0.5, 1, 10}. Thus, the Fahrenheit and Celsius temperature scales differ in terms of where their zero value is and the size of a unit (degree). Ratio new_value = a * old_value Length can be measured in meters or feet. 19 II B.Com BA Data mining & Data Preprocessing 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. II B.Com BA Data mining & Data Preprocessing Types of data sets • Record – Data Matrix – Document Data – Transaction Data • Graph – World Wide Web – Molecular Structures • Ordered – – – – II B.Com BA Spatial Data Temporal Data Sequential Data Genetic Sequence Data Data mining & Data Preprocessing Important Characteristics of Structured Data – Dimensionality • Curse of Dimensionality – Sparsity • Only presence counts – Resolution • Patterns depend on the scale II B.Com BA Data mining & Data Preprocessing Record Data • Data that consists of a collection of records, each of which consists of a fixed set of attributes Tid Refund Marital Status Taxable Income Cheat 1 Yes Single 125K No 2 No Married 100K No 3 No Single 70K No 4 Yes Married 120K No 5 No Divorced 95K Yes 6 No Married No 7 Yes Divorced 220K No 8 No Single 85K Yes 9 No Married 75K No 10 No Single 90K Yes 10 II B.Com BA Data mining & Data Preprocessing 60K 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 Projection of x Load II B.Com BA Projection of y load Distance Load Thickness 10.23 5.27 15.22 2.7 1.2 12.65 6.25 16.22 2.2 1.1 Data mining & Data Preprocessing Document Data • Each document becomes a `term' vector, – each term is a component (attribute) of the vector, – the value of each component is the number of times the corresponding term occurs in the document. team coach pla y ball score game wi n lost timeout season II B.Com BA Document 1 3 0 5 0 2 6 0 2 0 2 Document 2 0 7 0 2 1 0 0 3 0 0 Document 3 0 1 0 0 1 2 2 0 3 0 Data mining & Data Preprocessing Transaction Data • A special type of record data, where – each record (transaction) involves a set of items. – For example, consider a grocery store. The set of products purchased by a customer during one shopping trip constitute a transaction, while the individual products that were purchased are the items. TID Items II B.Com BA 1 Bread, Coke, Milk 2 3 4 5 Beer, Bread Beer, Coke, Diaper, Milk Beer, Bread, Diaper, Milk Coke, Diaper, Milk Data mining & Data Preprocessing Graph Data • Examples: Generic graph and HTML Links 2 1 5 2 <a href="papers/papers.html#bbbb"> Data Mining </a> <li> <a href="papers/papers.html#aaaa"> Graph Partitioning </a> <li> <a href="papers/papers.html#aaaa"> Parallel Solution of Sparse Linear System of Equations </a> <li> <a href="papers/papers.html#ffff"> N-Body Computation and Dense Linear System Solvers 5 II B.Com BA Data mining & Data Preprocessing Chemical Data • Benzene Molecule: C6H6 II B.Com BA Data mining & Data Preprocessing Ordered Data • Sequences of transactions Items/Events An element of the sequence II B.Com BA CS590D Data mining & Data Preprocessing Ordered Data • Genomic sequence data GGTTCCGCCTTCAGCCCCGCGCC CGCAGGGCCCGCCCCGCGCCGTC GAGAAGGGCCCGCCTGGCGGGCG GGGGGAGGCGGGGCCGCCCGAGC CCAACCGAGTCCGACCAGGTGCC CCCTCTGCTCGGCCTAGACCTGA GCTCATTAGGCGGCAGCGGACAG GCCAAGTAGAACACGCGAAGCGC TGGGCTGCCTGCTGCGACCAGGG II B.Com BA Data mining & Data Preprocessing Ordered Data • Spatio-Temporal Data Average Monthly Temperature of land and ocean CS590D II B.Com BA Data mining & Data Preprocessing 31 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 II B.Com BA Data mining & Data Preprocessing 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 II B.Com BA Two Sine Waves + Noise Data mining & Data Preprocessing Outliers • Outliers are data objects with characteristics that are considerably different than most of the other data objects in the data set CS590D II B.Com BA Data mining & Data Preprocessing 34 Missing Values • Reasons for missing values – Information is not collected (e.g., people decline to give their age and weight) – Attributes may not be applicable to all cases (e.g., annual income is not applicable to children) • Handling missing values – – – – II B.Com BA Eliminate Data Objects Estimate Missing Values Ignore the Missing Value During Analysis Replace with all possible values (weighted by their probabilities) Data mining & Data Preprocessing Duplicate Data • Data set may include data objects that are duplicates, or almost duplicates of one another – Major issue when merging data from heterogeous sources • Examples: – Same person with multiple email addresses • Data cleaning – Process of dealing with duplicate data issues II B.Com BA Data mining & Data Preprocessing Noisy Data • Noise: random error or variance in a measured variable • Incorrect attribute values may due to – – – – – faulty data collection instruments data entry problems data transmission problems technology limitation inconsistency in naming convention • Other data problems which requires data cleaning – duplicate records – incomplete data – inconsistent data II B.Com BA Data mining & Data Preprocessing How to Handle Noisy Data? • Binning method: – first sort data and partition into (equi-depth) bins – then one can smooth by bin means, smooth by bin median, smooth by bin boundaries, etc. • Clustering – detect and remove outliers • Combined computer and human inspection – detect suspicious values and check by human (e.g., deal with possible outliers) • Regression – smooth by fitting the data into regression functions II B.Com BA Data mining & Data Preprocessing Simple Discretization Methods: Binning • Equal-width (distance) partitioning: – Divides the range into N intervals of equal size: uniform grid – if A and B are the lowest and highest values of the attribute, the width of intervals will be: W = (B –A)/N. – The most straightforward, but outliers may dominate presentation – Skewed data is not handled well. • Equal-depth (frequency) partitioning: – Divides the range into N intervals, each containing approximately same number of samples – Good data scaling – Managing categorical attributes can be tricky. II B.Com BA Data mining & Data Preprocessing Binning Methods for Data Smoothing • Sorted data (e.g., by price) – 4, 8, 9, 15, 21, 21, 24, 25, 26, 28, 29, 34 • Partition into (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 II B.Com BA Data mining & Data Preprocessing Cluster Analysis II B.Com BA Data mining & Data Preprocessing Regression y Y1 Y1’ y=x+1 X1 II B.Com BA Data mining & Data Preprocessing x Data Preprocessing • • • • • Why preprocess the data? Data cleaning Data integration and transformation Data reduction Discretization and concept hierarchy generation • Summary II B.Com BA Data mining & Data Preprocessing Data Integration • Data integration: – combines data from multiple sources into a coherent store • Schema integration – integrate metadata from different sources – Entity identification problem: identify real world entities from multiple data sources, e.g., A.cust-id B.cust-# • Detecting and resolving data value conflicts – for the same real world entity, attribute values from different sources are different – possible reasons: different representations, different scales, e.g., metric vs. British units II B.Com BA Data mining & Data Preprocessing Handling Redundancy in Data Integration • Redundant data occur often when integration of multiple databases – The same attribute may have different names in different databases – One attribute may be a “derived” attribute in another table, e.g., annual revenue • Redundant data may be able to be detected by correlational analysis • Careful integration of the data from multiple sources may help reduce/avoid redundancies and inconsistencies and improve mining speed and quality II B.Com BA Data mining & Data Preprocessing Data Transformation • Smoothing: remove noise from data • Aggregation: summarization, data cube construction • Generalization: concept hierarchy climbing • Normalization: scaled to fall within a small, specified range – min-max normalization – z-score normalization – normalization by decimal scaling • Attribute/feature construction – New attributes constructed from the given ones II B.Com BA Data mining & Data Preprocessing Data Transformation: Normalization • min-max normalization v minA v' (new _ maxA new _ minA) new _ minA maxA minA • z-score normalization v meanA v' stand_devA • normalization by decimal scaling v v' j 10 II B.Com BA Where j is the smallest integer such that Max(| v ' |)<1 Data mining & Data Preprocessing Z-Score (Example) v’ v 0.18 0.60 0.52 0.25 0.80 0.55 0.92 0.21 0.64 0.20 0.63 0.70 0.67 0.58 0.98 0.81 0.10 0.82 0.50 3.00 II B.Com BA v’ v -0.84 -0.14 -0.27 -0.72 0.20 -0.22 0.40 -0.79 -0.07 -0.80 -0.09 0.04 -0.02 -0.17 0.50 0.22 -0.97 0.24 -0.30 3.87 Avg sdev 0.68 0.59 20 40 5 70 32 8 5 15 250 32 18 10 -14 22 45 60 -5 7 2 4 Data mining & Data Preprocessing -.26 .11 .55 4 -.05 -.48 -.53 -.35 3.87 -.05 -.30 -.44 -.87 -.23 .20 .47 -.71 -.49 -.58 -.55 Avg sdev 34.3 55.9 Data Preprocessing • • • • • • • Aggregation Sampling Dimensionality Reduction Feature subset selection Feature creation Discretization and Binarization Attribute Transformation II B.Com BA Data mining & Data Preprocessing 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 II B.Com BA Data mining & Data Preprocessing Aggregation Variation of Precipitation in Australia Standard Deviation of Average Monthly Precipitation II B.Com BA Data mining & Data Preprocessing Standard Deviation of Average Yearly Precipitation Data Preprocessing • • • • • Why preprocess the data? Data cleaning Data integration and transformation Data reduction Discretization and concept hierarchy generation • Summary II B.Com BA Data mining & Data Preprocessing Data Reduction Strategies • A data warehouse may store terabytes of data – Complex data analysis/mining may take a very long time to run on the complete data set • Data reduction – 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 – – – – – II B.Com BA Data cube aggregation Dimensionality reduction — remove unimportant attributes Data Compression Numerosity reduction — fit data into models Discretization and concept hierarchy generation Data mining & Data Preprocessing Data Cube Aggregation • The lowest level of a data cube – the aggregated data for an individual entity of interest – e.g., a customer in a phone calling data warehouse. • Multiple levels of aggregation in data cubes – Further reduce the size of data to deal with • Reference appropriate levels – Use the smallest representation which is enough to solve the task • Queries regarding aggregated information should be answered using data cube, when possible II B.Com BA Data mining & Data Preprocessing Dimensionality Reduction • Feature selection (i.e., attribute subset selection): – Select a minimum set of features such that the probability distribution of different classes given the values for those features is as close as possible to the original distribution given the values of all features – reduce # of patterns in the patterns, easier to understand • Heuristic methods (due to exponential # of choices): – – – – II B.Com BA step-wise forward selection step-wise backward elimination combining forward selection and backward elimination decision-tree induction Data mining & Data Preprocessing Example of Decision Tree Induction Initial attribute set: {A1, A2, A3, A4, A5, A6} A4 ? A6? A1? Class 1 > II B.Com BA Class 2 Class 1 Reduced attribute set: {A1, A4, A6} Data mining & Data Preprocessing Class 2 Data Compression • String compression – There are extensive theories and well-tuned algorithms – Typically lossless – But only limited manipulation is possible without expansion • Audio/video compression – Typically lossy compression, with progressive refinement – Sometimes small fragments of signal can be reconstructed without reconstructing the whole • Time sequence is not audio – Typically short and vary slowly with time II B.Com BA Data mining & Data Preprocessing Data Compression Compressed Data Original Data lossless Original Data Approximated II B.Com BA Data mining & Data Preprocessing Wavelet Transformation Haar2 Daubechie4 • Discrete wavelet transform (DWT): linear signal processing, multiresolutional analysis • Compressed approximation: store only a small fraction of the strongest of the wavelet coefficients • Similar to discrete Fourier transform (DFT), but better lossy compression, localized in space • Method: – Length, L, must be an integer power of 2 (padding with 0s, when necessary) – Each transform has 2 functions: smoothing, difference – Applies to pairs of data, resulting in two set of data of length L/2 – Applies two functions recursively, until reaches the desired length II B.Com BA Data mining & Data Preprocessing DWT for Image Compression • Image Low Pass Low Pass Low Pass II B.Com BA High Pass High Pass High Pass Data mining & Data Preprocessing 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 II B.Com BA Data mining & Data Preprocessing Dimensionality Reduction • Purpose: – Avoid curse of dimensionality – Reduce amount of time and memory required by data mining algorithms – Allow data to be more easily visualized – May help to eliminate irrelevant features or reduce noise • Techniques – Principle Component Analysis – Singular Value Decomposition – Others: supervised and non-linear techniques II B.Com BA Data mining & Data Preprocessing Dimensionality Reduction: PCA • Goal is to find a projection that captures the largest amount of variation in data x2 e x1 II B.Com BA Data mining & Data Preprocessing Dimensionality Reduction: PCA • Find the eigenvectors of the covariance matrix • The eigenvectors define the new space x2 e x1 II B.Com BA Data mining & Data Preprocessing Principal Component Analysis • Given N data vectors from k-dimensions, find c ≤ k orthogonal vectors that can be best used to represent data – The original data set is reduced to one consisting of N data vectors on c principal components (reduced dimensions) • Each data vector is a linear combination of the c principal component vectors • Works for numeric data only • Used when the number of dimensions is large II B.Com BA Data mining & Data Preprocessing Dimensionality Reduction: PCA Dimensions Dimensions==206 120 160 10 40 80 II B.Com BA Data mining & Data Preprocessing Dimensionality Reduction: ISOMAP • Construct a neighbourhood graph • For each pair of points in the graph, compute the shortest path distances – geodesic distances II B.Com BA By: Tenenbaum, de Silva, Langford (2000) Data mining & Data Preprocessing Feature Subset Selection • Another way to reduce dimensionality of data • Redundant features – duplicate much or all of the information contained in one or more other attributes – Example: purchase price of a product and the amount of sales tax paid • Irrelevant features – contain no information that is useful for the data mining task at hand – Example: students' ID is often irrelevant to the task of predicting students' GPA II B.Com BA Data mining & Data Preprocessing Feature Subset Selection • Techniques: – Brute-force approch: • Try all possible feature subsets as input to data mining algorithm – Embedded approaches: • Feature selection occurs naturally as part of the data mining algorithm – Filter approaches: • Features are selected before data mining algorithm is run – Wrapper approaches: • Use the data mining algorithm as a black box to find best subset of attributes II B.Com BA Data mining & Data Preprocessing Feature Creation • Create new attributes that can capture the important information in a data set much more efficiently than the original attributes • Three general methodologies: – Feature Extraction • domain-specific – Mapping Data to New Space – Feature Construction • combining features II B.Com BA Data mining & Data Preprocessing Mapping Data to a New Space Fourier transform Wavelet transform Two Sine Waves II B.Com BA Two Sine Waves + Noise Data mining & Data Preprocessing Frequency Discretization Using Class Labels • Entropy based approach 3 categories for both x and y II B.Com BA 5 categories for both x and y Data mining & Data Preprocessing Discretization Without Using Class Labels Data Equal frequency II B.Com BA Equal interval width K-means Data mining & Data Preprocessing Attribute Transformation • A function that maps the entire set of values of a given attribute to a new set of replacement values such that each old value can be identified with one of the new values – Simple functions: xk, log(x), ex, |x| – Standardization and Normalization CS590D II B.Com BA Data mining & Data Preprocessing Numerosity Reduction • Parametric methods – Assume the data fits some model, estimate model parameters, store only the parameters, and discard the data (except possible outliers) – Log-linear models: obtain value at a point in m-D space as the product on appropriate marginal subspaces • Non-parametric methods – Do not assume models – Major families: histograms, clustering, sampling II B.Com BA Data mining & Data Preprocessing Regression and Log-Linear Models • Linear regression: Data are modeled to fit a straight line – Often uses the least-square method to fit the line • Multiple regression: allows a response variable Y to be modeled as a linear function of multidimensional feature vector • Log-linear model: approximates discrete multidimensional probability distributions II B.Com BA Data mining & Data Preprocessing Regress Analysis and LogLinear Models • Linear regression: Y = + X – Two parameters , and specify the line and are to be estimated by using the data at hand. – using the least squares criterion to the known values of Y1, Y2, …, X1, X2, …. • Multiple regression: Y = b0 + b1 X1 + b2 X2. – Many nonlinear functions can be transformed into the above. • Log-linear models: – The multi-way table of joint probabilities is approximated by a product of lower-order tables. – Probability: p(a, b, c, d) = ab acad bcd II B.Com BA Data mining & Data Preprocessing Histograms • A popular data reduction technique • Divide data into buckets and store average (sum) for each bucket • Can be constructed optimally in one dimension using dynamic programming • Related to quantization problems. II B.Com BA 40 35 30 25 20 15 10 5 0 10000 20000 Data mining & Data Preprocessing 30000 40000 50000 60000 70000 80000 90000 100000 Clustering • Partition data set into clusters, and one can store cluster representation only • Can be very effective if data is clustered but not if data is “smeared” • Can have hierarchical clustering and be stored in multi-dimensional index tree structures • There are many choices of clustering definitions and clustering algorithms, further detailed in Chapter 8 II B.Com BA Data mining & Data Preprocessing Hierarchical Reduction • Use multi-resolution structure with different degrees of reduction • Hierarchical clustering is often performed but tends to define partitions of data sets rather than “clusters” • Parametric methods are usually not amenable to hierarchical representation • Hierarchical aggregation – An index tree hierarchically divides a data set into partitions by value range of some attributes – Each partition can be considered as a bucket – Thus an index tree with aggregates stored at each node is a hierarchical histogram II B.Com BA Data mining & Data Preprocessing Sampling • Allow a mining algorithm to run in complexity that is potentially sub-linear to the size of the data • Choose a representative subset of the data – Simple random sampling may have very poor performance in the presence of skew • Develop adaptive sampling methods – Stratified sampling: • Approximate the percentage of each class (or subpopulation of interest) in the overall database • Used in conjunction with skewed data • Sampling may not reduce database I/Os (page at a time). II B.Com BA Data mining & Data Preprocessing Sampling Raw Data II B.Com BA Data mining & Data Preprocessing Sampling Raw Data II B.Com BA Cluster/Stratified Sample Data mining & Data Preprocessing 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. II B.Com BA Data mining & Data Preprocessing 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 II B.Com BA Data mining & Data Preprocessing 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 II B.Com BA Data mining & Data Preprocessing Sample Size 8000 points II B.Com BA 2000 Points Data mining & Data Preprocessing 500 Points Sample Size • What sample size is necessary to get at least one object from each of 10 groups. CS590D II B.Com BA Data mining & Data Preprocessing 90 Data Preprocessing • • • • • Why preprocess the data? Data cleaning Data integration and transformation Data reduction Discretization and concept hierarchy generation • Summary 113 II B.Com BA Data mining & Data Preprocessing Discretization • Three types of attributes: – Nominal — values from an unordered set – Ordinal — values from an ordered set – Continuous — 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 114 II B.Com BA Data mining & Data Preprocessing Discretization and Concept hierachy • 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 • Concept hierarchies – reduce the data by collecting and replacing low level concepts (such as numeric values for the attribute age) by higher level concepts (such as young, middle-aged, or senior) 115 II B.Com BA Data mining & Data Preprocessing Discretization and Concept Hierarchy Generation for Numeric Data • • • • • Binning (see sections before) Histogram analysis (see sections before) Clustering analysis (see sections before) Entropy-based discretization Segmentation by natural partitioning 116 II B.Com BA Data mining & Data Preprocessing Definition of Entropy • Entropy H(X ) P( x) log xAX 2 P( x) • Example: Coin Flip – – – – AX = {heads, tails} P(heads) = P(tails) = ½ ½ log2(½) = ½ * - 1 H(X) = 1 • What about a two-headed coin? • Conditional Entropy: H ( X | Y ) P( y ) H ( X | y ) yAY 117 II B.Com BA Data mining & Data Preprocessing Entropy-Based Discretization • Given a set of samples S, if S is partitioned into two intervals S1 and S2 using boundary T, the entropy after partitioning is |S | |S | H (S , T ) 1 |S| H ( S 1) 2 |S| H ( S 2) • 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, e.g., H ( S ) H (T , S ) • Experiments show that it may reduce data size and improve classification accuracy 118 II B.Com BA Data mining & Data Preprocessing 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 equiwidth 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 119 II B.Com BA Data mining & Data Preprocessing Example of 3-4-5 Rule count Step 1: Step 2: -$351 -$159 Min Low (i.e, 5%-tile) msd=1,000 profit Low=-$1,000 (-$1,000 - 0) (-$400 - 0) (-$200 -$100) (-$100 0) Max High=$2,000 ($1,000 - $2,000) (0 -$ 1,000) (-$4000 -$5,000) Step 4: (-$300 -$200) High(i.e, 95%-0 tile) $4,700 (-$1,000 - $2,000) Step 3: (-$400 -$300) $1,838 ($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) ($2,000 - $5, 000) ($2,000 $3,000) ($3,000 $4,000) ($4,000 $5,000) 120 Concept Hierarchy Generation for Categorical Data • Specification of a partial ordering of attributes explicitly at the schema level by users or experts – street<city<state<country • Specification of a portion of a hierarchy by explicit data grouping – {Urbana, Champaign, Chicago}<Illinois • Specification of a set of attributes. – System automatically generates partial ordering by analysis of the number of distinct values – E.g., street < city <state < country • Specification of only a partial set of attributes – E.g., only street < city, not others 121 II B.Com BA Data mining & Data Preprocessing Automatic Concept Hierarchy Generation • Some concept hierarchies can be automatically generated based on the analysis of the number of distinct values per attribute in the given data set – The attribute with the most distinct values is placed at the lowest level of the hierarchy – Note: Exception—weekday, month, quarter, year 15 distinct values country province_or_ state 65 distinct values city 3567 distinct values street II B.Com BA 674,339 distinct values Data mining & Data Preprocessing 122 Data Preprocessing • • • • • Why preprocess the data? Data cleaning Data integration and transformation Data reduction Discretization and concept hierarchy generation • Summary 123 II B.Com BA Data mining & Data Preprocessing Summary • Data preparation is a big issue for both warehousing and mining • Data preparation includes – Data cleaning and data integration – Data reduction and feature selection – Discretization • A lot a methods have been developed but still an active area of research 124 II B.Com BA Data mining & Data Preprocessing