Data Analysis and Mining

Data Analysis and Mining

اسلاید 1: Chapter 18: Data Analysis and Mining

اسلاید 2: Chapter 18: Data Analysis and Mining Decision Support SystemsData Analysis and OLAPData Warehousing Data Mining

اسلاید 3: Decision Support SystemsDecision-support systems are used to make business decisions, often based on data collected by on-line transaction-processing systems.Examples of business decisions:What items to stock?What insurance premium to change?To whom to send advertisements?Examples of data used for making decisionsRetail sales transaction detailsCustomer profiles (income, age, gender, etc.)

اسلاید 4: Decision-Support Systems: OverviewData analysis tasks are simplified by specialized tools and SQL extensionsExample tasksFor each product category and each region, what were the total sales in the last quarter and how do they compare with the same quarter last yearAs above, for each product category and each customer categoryStatistical analysis packages (e.g., : S++) can be interfaced with databasesStatistical analysis is a large field, but not covered hereData mining seeks to discover knowledge automatically in the form of statistical rules and patterns from large databases.A data warehouse archives information gathered from multiple sources, and stores it under a unified schema, at a single site.Important for large businesses that generate data from multiple divisions, possibly at multiple sitesData may also be purchased externally

اسلاید 5: Data Analysis and OLAPOnline Analytical Processing (OLAP)Interactive analysis of data, allowing data to be summarized and viewed in different ways in an online fashion (with negligible delay)Data that can be modeled as dimension attributes and measure attributes are called multidimensional data.Measure attributes measure some valuecan be aggregated upone.g. the attribute number of the sales relationDimension attributesdefine the dimensions on which measure attributes (or aggregates thereof) are viewede.g. the attributes item_name, color, and size of the sales relation

اسلاید 6: Cross Tabulation of sales by item-name and colorThe table above is an example of a cross-tabulation (cross-tab), also referred to as a pivot-table.Values for one of the dimension attributes form the row headersValues for another dimension attribute form the column headersOther dimension attributes are listed on topValues in individual cells are (aggregates of) the values of the dimension attributes that specify the cell.

اسلاید 7: Relational Representation of Cross-tabsCross-tabs can be represented as relationsWe use the value all is used to represent aggregatesThe SQL:1999 standard actually uses null values in place of all despite confusion with regular null values

اسلاید 8: Data CubeA data cube is a multidimensional generalization of a cross-tabCan have n dimensions; we show 3 below Cross-tabs can be used as views on a data cube

اسلاید 9: Online Analytical ProcessingPivoting: changing the dimensions used in a cross-tab is called Slicing: creating a cross-tab for fixed values onlySometimes called dicing, particularly when values for multiple dimensions are fixed.Rollup: moving from finer-granularity data to a coarser granularity Drill down: The opposite operation - that of moving from coarser-granularity data to finer-granularity data

اسلاید 10: Hierarchies on DimensionsHierarchy on dimension attributes: lets dimensions to be viewed at different levels of detailE.g. the dimension DateTime can be used to aggregate by hour of day, date, day of week, month, quarter or year

اسلاید 11: Cross Tabulation With HierarchyCross-tabs can be easily extended to deal with hierarchiesCan drill down or roll up on a hierarchy

اسلاید 12: OLAP ImplementationThe earliest OLAP systems used multidimensional arrays in memory to store data cubes, and are referred to as multidimensional OLAP (MOLAP) systems.OLAP implementations using only relational database features are called relational OLAP (ROLAP) systemsHybrid systems, which store some summaries in memory and store the base data and other summaries in a relational database, are called hybrid OLAP (HOLAP) systems.

اسلاید 13: OLAP Implementation (Cont.)Early OLAP systems precomputed all possible aggregates in order to provide online responseSpace and time requirements for doing so can be very high2n combinations of group byIt suffices to precompute some aggregates, and compute others on demand from one of the precomputed aggregatesCan compute aggregate on (item-name, color) from an aggregate on (item-name, color, size) For all but a few “non-decomposable” aggregates such as medianis cheaper than computing it from scratch Several optimizations available for computing multiple aggregatesCan compute aggregate on (item-name, color) from an aggregate on (item-name, color, size)Can compute aggregates on (item-name, color, size), (item-name, color) and (item-name) using a single sorting of the base data

اسلاید 14: Extended Aggregation in SQL:1999The cube operation computes union of group by’s on every subset of the specified attributesE.g. consider the queryselect item-name, color, size, sum(number) from sales group by cube(item-name, color, size) This computes the union of eight different groupings of the sales relation: { (item-name, color, size), (item-name, color), (item-name, size), (color, size), (item-name), (color), (size), ( ) } where ( ) denotes an empty group by list.For each grouping, the result contains the null value for attributes not present in the grouping.

اسلاید 15: Extended Aggregation (Cont.)Relational representation of cross-tab that we saw earlier, but with null in place of all, can be computed byselect item-name, color, sum(number) from sales group by cube(item-name, color)The function grouping() can be applied on an attributeReturns 1 if the value is a null value representing all, and returns 0 in all other cases. select item-name, color, size, sum(number), grouping(item-name) as item-name-flag, grouping(color) as color-flag, grouping(size) as size-flag, from sales group by cube(item-name, color, size)Can use the function decode() in the select clause to replace such nulls by a value such as allE.g. replace item-name in first query by decode( grouping(item-name), 1, ‘all’, item-name)

اسلاید 16: Extended Aggregation (Cont.)The rollup construct generates union on every prefix of specified list of attributes E.g. select item-name, color, size, sum(number) from sales group by rollup(item-name, color, size)Generates union of four groupings: { (item-name, color, size), (item-name, color), (item-name), ( ) }Rollup can be used to generate aggregates at multiple levels of a hierarchy.E.g., suppose table itemcategory(item-name, category) gives the category of each item. Then select category, item-name, sum(number) from sales, itemcategory where sales.item-name = itemcategory.item-name group by rollup(category, item-name)would give a hierarchical summary by item-name and by category.

اسلاید 17: Extended Aggregation (Cont.)Multiple rollups and cubes can be used in a single group by clauseEach generates set of group by lists, cross product of sets gives overall set of group by listsE.g., select item-name, color, size, sum(number) from sales group by rollup(item-name), rollup(color, size) generates the groupings {item-name, ()} X {(color, size), (color), ()} = { (item-name, color, size), (item-name, color), (item-name), (color, size), (color), ( ) }

اسلاید 18: RankingRanking is done in conjunction with an order by specification. Given a relation student-marks(student-id, marks) find the rank of each student.select student-id, rank( ) over (order by marks desc) as s-rank from student-marksAn extra order by clause is needed to get them in sorted orderselect student-id, rank ( ) over (order by marks desc) as s-rank from student-marks order by s-rankRanking may leave gaps: e.g. if 2 students have the same top mark, both have rank 1, and the next rank is 3dense_rank does not leave gaps, so next dense rank would be 2

اسلاید 19: Ranking (Cont.)Ranking can be done within partition of the data.“Find the rank of students within each section.”select student-id, section, rank ( ) over (partition by section order by marks desc) as sec-rank from student-marks, student-section where student-marks.student-id = student-section.student-id order by section, sec-rankMultiple rank clauses can occur in a single select clauseRanking is done after applying group by clause/aggregation

اسلاید 20: Ranking (Cont.)Other ranking functions: percent_rank (within partition, if partitioning is done)cume_dist (cumulative distribution) fraction of tuples with preceding valuesrow_number (non-deterministic in presence of duplicates)SQL:1999 permits the user to specify nulls first or nulls last select student-id, rank ( ) over (order by marks desc nulls last) as s-rank from student-marks

اسلاید 21: Ranking (Cont.)For a given constant n, the ranking the function ntile(n) takes the tuples in each partition in the specified order, and divides them into n buckets with equal numbers of tuples.E.g.:select threetile, sum(salary) from ( select salary, ntile(3) over (order by salary) as threetile from employee) as s group by threetile

اسلاید 22: WindowingUsed to smooth out random variations. E.g.: moving average: “Given sales values for each date, calculate for each date the average of the sales on that day, the previous day, and the next day”Window specification in SQL:Given relation sales(date, value) select date, sum(value) over (order by date between rows 1 preceding and 1 following) from salesExamples of other window specifications:between rows unbounded preceding and currentrows unbounded precedingrange between 10 preceding and current rowAll rows with values between current row value –10 to current valuerange interval 10 day precedingNot including current row

اسلاید 23: Windowing (Cont.)Can do windowing within partitionsE.g. Given a relation transaction (account-number, date-time, value), where value is positive for a deposit and negative for a withdrawal“Find total balance of each account after each transaction on the account”select account-number, date-time, sum (value ) over (partition by account-number order by date-time rows unbounded preceding) as balance from transaction order by account-number, date-time

اسلاید 24: Data WarehousingData sources often store only current data, not historical dataCorporate decision making requires a unified view of all organizational data, including historical dataA data warehouse is a repository (archive) of information gathered from multiple sources, stored under a unified schema, at a single siteGreatly simplifies querying, permits study of historical trendsShifts decision support query load away from transaction processing systems

اسلاید 25: Data Warehousing

اسلاید 26: Design IssuesWhen and how to gather dataSource driven architecture: data sources transmit new information to warehouse, either continuously or periodically (e.g. at night)Destination driven architecture: warehouse periodically requests new information from data sourcesKeeping warehouse exactly synchronized with data sources (e.g. using two-phase commit) is too expensiveUsually OK to have slightly out-of-date data at warehouseData/updates are periodically downloaded form online transaction processing (OLTP) systems.What schema to useSchema integration

اسلاید 27: More Warehouse Design IssuesData cleansingE.g. correct mistakes in addresses (misspellings, zip code errors)Merge address lists from different sources and purge duplicatesHow to propagate updatesWarehouse schema may be a (materialized) view of schema from data sourcesWhat data to summarizeRaw data may be too large to store on-lineAggregate values (totals/subtotals) often sufficeQueries on raw data can often be transformed by query optimizer to use aggregate values

اسلاید 28: Warehouse SchemasDimension values are usually encoded using small integers and mapped to full values via dimension tablesResultant schema is called a star schemaMore complicated schema structures Snowflake schema: multiple levels of dimension tablesConstellation: multiple fact tables

اسلاید 29: Data Warehouse Schema

اسلاید 30: Data MiningData mining is the process of semi-automatically analyzing large databases to find useful patterns Prediction based on past historyPredict if a credit card applicant poses a good credit risk, based on some attributes (income, job type, age, ..) and past historyPredict if a pattern of phone calling card usage is likely to be fraudulentSome examples of prediction mechanisms:ClassificationGiven a new item whose class is unknown, predict to which class it belongsRegression formulaeGiven a set of mappings for an unknown function, predict the function result for a new parameter value

اسلاید 31: Data Mining (Cont.)Descriptive PatternsAssociationsFind books that are often bought by “similar” customers. If a new such customer buys one such book, suggest the others too.Associations may be used as a first step in detecting causationE.g. association between exposure to chemical X and cancer, ClustersE.g. typhoid cases were clustered in an area surrounding a contaminated wellDetection of clusters remains important in detecting epidemics

اسلاید 32: Classification RulesClassification rules help assign new objects to classes. E.g., given a new automobile insurance applicant, should he or she be classified as low risk, medium risk or high risk?Classification rules for above example could use a variety of data, such as educational level, salary, age, etc. person P, P.degree = masters and P.income > 75,000  P.credit = excellent person P, P.degree = bachelors and (P.income  25,000 and P.income  75,000)  P.credit = goodRules are not necessarily exact: there may be some misclassificationsClassification rules can be shown compactly as a decision tree.

اسلاید 33: Decision Tree

اسلاید 34: Construction of Decision TreesTraining set: a data sample in which the classification is already known. Greedy top down generation of decision trees.Each internal node of the tree partitions the data into groups based on a partitioning attribute, and a partitioning condition for the nodeLeaf node:all (or most) of the items at the node belong to the same class, or all attributes have been considered, and no further partitioning is possible.

اسلاید 35: Best SplitsPick best attributes and conditions on which to partitionThe purity of a set S of training instances can be measured quantitatively in several ways. Notation: number of classes = k, number of instances = |S|, fraction of instances in class i = pi.The Gini measure of purity is defined as[Gini (S) = 1 -  When all instances are in a single class, the Gini value is 0It reaches its maximum (of 1 –1 /k) if each class the same number of instances. ki- 1p2i

اسلاید 36: Best Splits (Cont.)Another measure of purity is the entropy measure, which is defined as entropy (S) = – When a set S is split into multiple sets Si, I=1, 2, …, r, we can measure the purity of the resultant set of sets as:purity(S1, S2, ….., Sr) = The information gain due to particular split of S into Si, i = 1, 2, …., r Information-gain (S, {S1, S2, …., Sr) = purity(S ) – purity (S1, S2, … Sr)ri= 1|Si||S|purity (Si)ki- 1pilog2 pi

اسلاید 37: Best Splits (Cont.)Measure of “cost” of a split: Information-content (S, {S1, S2, ….., Sr})) = – Information-gain ratio = Information-gain (S, {S1, S2, ……, Sr}) Information-content (S, {S1, S2, ….., Sr})The best split is the one that gives the maximum information gain ratiolog2ri- 1|Si||S||Si||S|

اسلاید 38: Finding Best SplitsCategorical attributes (with no meaningful order):Multi-way split, one child for each valueBinary split: try all possible breakup of values into two sets, and pick the bestContinuous-valued attributes (can be sorted in a meaningful order)Binary split:Sort values, try each as a split pointE.g. if values are 1, 10, 15, 25, split at 1,  10,  15Pick the value that gives best splitMulti-way split:A series of binary splits on the same attribute has roughly equivalent effect

اسلاید 39: Decision-Tree Construction AlgorithmProcedure GrowTree (S ) Partition (S ); Procedure Partition (S) if ( purity (S ) > p or |S| < s ) then return; for each attribute A evaluate splits on attribute A; Use best split found (across all attributes) to partition S into S1, S2, …., Sr, for i = 1, 2, ….., r Partition (Si );

اسلاید 40: Other Types of ClassifiersNeural net classifiers are studied in artificial intelligence and are not covered here Bayesian classifiers use Bayes theorem, which saysp (cj | d ) = p (d | cj ) p (cj ) p ( d ) where p (cj | d ) = probability of instance d being in class cj, p (d | cj ) = probability of generating instance d given class cj, p (cj ) = probability of occurrence of class cj, and p (d ) = probability of instance d occuring

اسلاید 41: Naïve Bayesian ClassifiersBayesian classifiers requirecomputation of p (d | cj )precomputation of p (cj ) p (d ) can be ignored since it is the same for all classesTo simplify the task, naïve Bayesian classifiers assume attributes have independent distributions, and thereby estimatep (d | cj) = p (d1 | cj ) * p (d2 | cj ) * ….* (p (dn | cj )Each of the p (di | cj ) can be estimated from a histogram on di values for each class cj the histogram is computed from the training instances Histograms on multiple attributes are more expensive to compute and store

اسلاید 42: RegressionRegression deals with the prediction of a value, rather than a class. Given values for a set of variables, X1, X2, …, Xn, we wish to predict the value of a variable Y. One way is to infer coefficients a0, a1, a1, …, an such that Y = a0 + a1 * X1 + a2 * X2 + … + an * Xn Finding such a linear polynomial is called linear regression. In general, the process of finding a curve that fits the data is also called curve fitting.The fit may only be approximatebecause of noise in the data, or because the relationship is not exactly a polynomialRegression aims to find coefficients that give the best possible fit.

اسلاید 43: Association RulesRetail shops are often interested in associations between different items that people buy. Someone who buys bread is quite likely also to buy milkA person who bought the book Database System Concepts is quite likely also to buy the book Operating System Concepts.Associations information can be used in several ways. E.g. when a customer buys a particular book, an online shop may suggest associated books.Association rules: bread  milk DB-Concepts, OS-Concepts  NetworksLeft hand side: antecedent, right hand side: consequentAn association rule must have an associated population; the population consists of a set of instancesE.g. each transaction (sale) at a shop is an instance, and the set of all transactions is the population

اسلاید 44: Association Rules (Cont.)Rules have an associated support, as well as an associated confidence. Support is a measure of what fraction of the population satisfies both the antecedent and the consequent of the rule.E.g. suppose only 0.001 percent of all purchases include milk and screwdrivers. The support for the rule is milk  screwdrivers is low.Confidence is a measure of how often the consequent is true when the antecedent is true. E.g. the rule bread  milk has a confidence of 80 percent if 80 percent of the purchases that include bread also include milk.

اسلاید 45: Finding Association RulesWe are generally only interested in association rules with reasonably high support (e.g. support of 2% or greater)Naïve algorithmConsider all possible sets of relevant items.For each set find its support (i.e. count how many transactions purchase all items in the set).Large itemsets: sets with sufficiently high supportUse large itemsets to generate association rules.From itemset A generate the rule A - {b } b for each b  A.Support of rule = support (A).Confidence of rule = support (A ) / support (A - {b })

اسلاید 46: Finding SupportDetermine support of itemsets via a single pass on set of transactionsLarge itemsets: sets with a high count at the end of the passIf memory not enough to hold all counts for all itemsets use multiple passes, considering only some itemsets in each pass.Optimization: Once an itemset is eliminated because its count (support) is too small none of its supersets needs to be considered.The a priori technique to find large itemsets:Pass 1: count support of all sets with just 1 item. Eliminate those items with low supportPass i: candidates: every set of i items such that all its i-1 item subsets are largeCount support of all candidatesStop if there are no candidates

اسلاید 47: Other Types of AssociationsBasic association rules have several limitationsDeviations from the expected probability are more interestingE.g. if many people purchase bread, and many people purchase cereal, quite a few would be expected to purchase bothWe are interested in positive as well as negative correlations between sets of itemsPositive correlation: co-occurrence is higher than predictedNegative correlation: co-occurrence is lower than predictedSequence associations / correlationsE.g. whenever bonds go up, stock prices go down in 2 daysDeviations from temporal patternsE.g. deviation from a steady growthE.g. sales of winter wear go down in summerNot surprising, part of a known pattern. Look for deviation from value predicted using past patterns

اسلاید 48: ClusteringClustering: Intuitively, finding clusters of points in the given data such that similar points lie in the same clusterCan be formalized using distance metrics in several waysGroup points into k sets (for a given k) such that the average distance of points from the centroid of their assigned group is minimizedCentroid: point defined by taking average of coordinates in each dimension.Another metric: minimize average distance between every pair of points in a clusterHas been studied extensively in statistics, but on small data setsData mining systems aim at clustering techniques that can handle very large data setsE.g. the Birch clustering algorithm (more shortly)

اسلاید 49: Hierarchical ClusteringExample from biological classification (the word classification here does not mean a prediction mechanism) chordata mammalia reptilia leopards humans snakes crocodiles Other examples: Internet directory systems (e.g. Yahoo, more on this later)Agglomerative clustering algorithmsBuild small clusters, then cluster small clusters into bigger clusters, and so onDivisive clustering algorithmsStart with all items in a single cluster, repeatedly refine (break) clusters into smaller ones

اسلاید 50: Clustering AlgorithmsClustering algorithms have been designed to handle very large datasetsE.g. the Birch algorithmMain idea: use an in-memory R-tree to store points that are being clusteredInsert points one at a time into the R-tree, merging a new point with an existing cluster if is less than some  distance awayIf there are more leaf nodes than fit in memory, merge existing clusters that are close to each otherAt the end of first pass we get a large number of clusters at the leaves of the R-treeMerge clusters to reduce the number of clusters

اسلاید 51: Collaborative FilteringGoal: predict what movies/books/… a person may be interested in, on the basis ofPast preferences of the personOther people with similar past preferencesThe preferences of such people for a new movie/book/…One approach based on repeated clusteringCluster people on the basis of preferences for moviesThen cluster movies on the basis of being liked by the same clusters of peopleAgain cluster people based on their preferences for (the newly created clusters of) moviesRepeat above till equilibriumAbove problem is an instance of collaborative filtering, where users collaborate in the task of filtering information to find information of interest

اسلاید 52: Other Types of MiningText mining: application of data mining to textual documentscluster Web pages to find related pagescluster pages a user has visited to organize their visit historyclassify Web pages automatically into a Web directoryData visualization systems help users examine large volumes of data and detect patterns visuallyCan visually encode large amounts of information on a single screenHumans are very good a detecting visual patter