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Database Systems Research on Data Mining Carlos Ordonez University of Houston USA Javier García-García UNAM Mexico Reference: Ordonez, C, Garcia-Garcia, J, Database Systems Research on Data Mining, Proc. ACM SIGMOD 2010, p (tutorial).

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Global Outline 1. Data mining models and algorithms (JG,15 min) 1.1 Preprocess to get Data set 1.2 Data set 1.3 Data Mining Models 1.4 Data Mining Algorithms 2.Processing alternatives (JG, 35 min) 2.1 Inside DBMS: SQL 2.2 Outside DBMS: MapReduce 2.3 Example 3. Storage and Optimizations (CO, 35 min) 3.1 Layouts: Horizontal and Vertical 3.2 Optimizations: Algorithmic and Systems 2/60

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1. Data Mining Models & Algorithms Data set preparation Data set Data mining models and patterns Algorithms 3/60

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1.1 Data set preparation [CDHHL1999,KDD] [GCBLRVPP1997,JDMKD] [O2004,DMKD] In practice, 80% of project time –significant SQL code writing; some tools help query writing –iterative: between modeling and data set prep Little attention in research literature –query optimization mostly in OLAP context –new operators: PIVOT, horizontal aggregations –research issue: can algorithms directly analyze 3NF tables? 4/60

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Data set preparation [GO2010,DKE] [OG2008,DSS] Overall goal: getting data set for analysis Database processing generally required –normalized (many 3NF) databases cannot be directly analyzed –joins, aggregations and pivoting (transposing) Data cleaning –remove outliers –null replacement –repair referential integrity Data transformation: categorical columns; rescale; code 5/60

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Typical queries to create data set join and aggregations 6/60

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1.2 Data set Data set with n records Each has attributes: numeric, discrete or both (mixed) Focus of the tutorial, d dimensions Generally, High d makes problem mathematically more difficult Extra column G/Y 7/60

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Example of data set horizontal layout n=5, d=3 and G/Y iX1X2X3G /60

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1.3 Data Mining Models [STA1998,SIGMOD] Models, coming mostly from statistics and machine learning –based on matrix computations, probability and calculus –time dimension not considered Patterns, mostly combinatorial –association rules, cubes, sequences and graphs –important, but not considered in tutorial –quite different algorithms from models –no strong statistical foundation 9/60

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Common data mining models [DLR1977,RSS] Unsupervised: –math: simpler –task: clustering, dimensionality reduction –models: KM, EM, PCA/SVD, FA –statistical tests overlap both Supervised –math: tuning and validation than unsupervised –task: classification, regression –models: decision trees, Naïve Bayes, Bayes, linear/logistic regression, SVM, neural nets 10/60

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Data mining models characteristics Multidimensional –tens, hundreds of dimensions –feature selection and dimensionality reduction Represented & computed with matrices & vectors –data set: set of vectors or set of records; all numeric, mixed attributes –model: numeric=matrices, discrete: histograms –intermediate computations: matrices and histograms 11/60

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Why is it hard? 12/60

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Data mining Major tasks Model computation –focus of most research –generally requires matrix computations –complex and slow algorithms (iterative) –large n makes it slower Scoring data set –assumes model exists –useful for tuning, testing and model exchange –fast: generally requires only one pass over X –research issue: not studied enough in literature 13/60

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1.4 Data Mining Algorithms input and output Input: data set X with n records, d dimensions Output: model, quality Parameters (representative; vary a lot): –k (clusters, principal components, discrete states) –epsilon for stopping (accuracy, convergence, local optima) –feature/variable selection (algorithm dependent, step-wise or now bayesian statistics) 14/60

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Data Mining Algorithms [ZRL1996,SIGMOD] Behavior with respect to data set X: –one pass, few passes –multiple passes, convergence, bigger issue (most algorithms) Time complexity: Research issues: –preserve time complexity in SQL/MapReduce –incremental learning 15/60

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2. Processing alternatives 2.1 Inside DBMS (SQL) 2.2 Outside DBMS (MapReduce) 2.3 Example 16/60

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2.1 Inside DBMS Assumption: –data records are in the DBMS; exporting slow –row-based storage (not column-based) Programming alternatives: –SQL and UDFs: SQL code generation (JDBC), precompiled UDFs. Extra: SP, embedded SQL, cursors –Internal C Code (direct access to file system and mem) DBMS advantages: –important: storage, queries, security –maybe: recovery, concurrency control, integrity, transactions 17/60

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Inside DBMS SQL code: CREATE + SELECT, Consider Layout [CDDHW2009,VLDB] CREATE TABLE –Row storage: Clustered (to group rows of pivoted tables), Block size (for large tables) –Index: primary (gen. for pk, critical for joins), secondary (may help joins & searches) SELECT –Basic mechanism to write queries; standard across DBMSs, arbitrarily complex queries, including arithmetic expressions 18/60 Vertical layout: A(i,j,v), B(i,j,v) A*B: SELECT A.i, B.j, sum(A.v * B.v) FROM A JOIN B ON A.j = B.i GROUP BY A.i, B.j

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Inside DBMS User-Defined Function (UDF) Classification: –Scalar UDF –Aggregate UDF –Table UDF Programming: –Called in a SELECT statement –C code or similar language –API provided by DBMS, in C/C++ –Data type mapping 19/60

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Inside DBMS UDF pros and cons Advantages: –arrays and flow control –flexibility in code writing and no side effects –No need to modify DBMS internal code –In general, simple data types Limitations: –OS and DBMS architecture dependent, not portable –No I/O capability, no side effects –Null handling and fixed memory allocation –Memory leaks with arrays (matrices): fenced/protected mode 20/60

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Inside DBMS Scalar UDF [DNPT2006,SAC] Memory allocation in the stack Returns one value of simple data type Basic SQL data types (e.g. int, float, char) May support UDT Call & return value with every row Useful for vector operations 21/60

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Inside DBMS Aggregate UDF [JM1998,SIGMOD] Table scan Memory allocation in the heap GROUP BY extend their power Also require handling nulls Advantage: parallel & multithreaded processing Drawback: returns a single value, not a table DBMSs: SQL Server, PostgreSQL,Teradata, Oracle, DB2, among others Useful for model computations 22/60

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Inside DBMS UDF: Aggregate User-Defined Function 1. Initialization: allocates variable storage 2. Accumulate: processes every record, aggregate some value (vector). Bottleneck. 3. Merge: consolidates partial results from multiple threads 4. Terminate: final processing, return result 23/60

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Inside DBMS Table UDF [BRKPHK2008,SIGMOD] Main difference with aggregate UDF: returns a table (instead of single value) Also, it can take several input values Called in the FROM clause in a SELECT Stream: no parallel processing, external file Computation power same as aggregate UDF Suitable for complex math operations and algorithms Since result is a table it can be joined DBMS: SQL Server,DB2, Oracle,PostgreSQL 24/60

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Inside DBMS Internal C code [LTWZ2005,SIGMOD], [MYC2005,VLDB] [SD2001,CIKM] Advantages: –access to file system (table record blocks), –physical operators (scan, join, sort, search) –main memory, data structures, libraries –hardware optimizations: multithreading, multicore, caching RAM, caching LI/L2 Disadvantages: –requires careful integration with rest of system –not available to end users and practitioners –may require exposing functionality with DM language or SQL 25/60

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Inside DBMS Physical Operators [DG1992,CACM] [SMAHHH2007,VLDB] [WH2009,SIGMOD] Serial DBMS (one CPU, maybe RAID): –table Scan –join: hash join, sort merge join, nested loop –external merge sort Parallel DBMS (shared-nothing): –even row distribution, hashing –parallel table scan –parallel joins: large/large (sort-merge, hash); large/short (replicate short) –distributed sort 26/60

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2.2 Outside DBMS Alternatives: –MapReduce –Packages, libraries, Java/C++ Issue: I/O bottleneck 27/60

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Outside DBMS MapReduce [DG2008,CACM] Parallel processing; simple; shared-nothing Functions are programmed in a high-level programming language (e.g. Java, Python); flexible. pairs processed in two phases: –map(): computation is distributed and evaluated in parallel; independent mappers –reduce(): partial results are combined/summarized Can be categorized as inside/outside DBMS, depending on level of integration with DBMS DBMS integration: Greenplum, Aster Data, Teradata... 28/60

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Outside DBMS MapReduce Files and Processing File Types: –Text Files: Common storage (e.g. CSV files.) –SequenceFiles: Efficient processing –Custom InputFormat (rarely used.) Processing: –Points are sorted by “key” before sending to reducers –Small files should be merged –Partial results are stored in file system –Intermediate files should be managed in SequenceFiles for efficiency 29/60

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Outside DBMS Packages, libraries, Java/C++ [ZHY2009,CIDR] [ZZY2010,ICDE] Statistical and data mining packages: –exported flat files; proprietary file formats –Memory-based (processing data records, models, internal data structures) Programming languages: –Arrays –flexibility of control statements Limitation: large number of records Packages: R, SAS, SPSS, KXEN,Matlab, WEKA 30/60

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2.3 Naïve Bayes Example Horizontal layout NB –one pass –Gaussian, sufficient statistics (NLQ) Example in: –SQL –UDF –MapReduce 31/60 Data Structures public double N; public double[] L; public double[] Q;

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Naïve Bayes SQL (2 passes, n L Q, triangular Q ) /*Inserting NL*/ SELECT g,sum(1.0) AS Ng /* N */,sum(X1) AS L_X1 /* L */,sum(X2) AS L_X2,sum(X3) AS L_X3 FROM X GROUP BY g; /*Inserting into Q */ SELECT g, /* Q */,sum(power(X1,2)) AS Q_X1,sum(power(X2,2)) AS Q_X2,sum(power(X3,2)) AS Q_X3 FROM X GROUP BY g; 32/60 /*Lower triangular for PCA and LR*/ SELECT sum(X1*X1), null,...,null,sum(X2*X1), sum(X2*X2),...,null...,sum(Xd*X1), sum(Xd*X2),...,sum(Xd*Xd) FROM X

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Naïve Bayes Aggregate UDF (1 pass) 33/60 public void Init() { nbnlq = new NBNLQ(); int h; nbnlq.N = 0; for (h = 1; h <= nbnlq.d; h++) { nbnlq.L[h] = 0; nbnlq.Q[h] = 0; } public void Merge(udf_nb_train_d3 thread) { int i, h; nbnlq.d = thread.nbnlq.d; nbnlq.N += thread.nbnlq.N; for (h = 1; h <= nbnlq.d; h++) { nbnlq.L[h] += thread.nbnlq.L[h]; nbnlq.Q[h] += thread.nbnlq.Q[h]; } public void Accumulate(Xd3 X) { int h; if (!X.IsNull) { nbnlq.d = X.getD(); nbnlq.N += 1.0; for (h = 1; h <= nbnlq.d; h++) // L,Q { nbnlq.L[h] += X.getColumn(h); nbnlq.Q[h] += X.getColumn(h) * X.getColumn(h); } public SqlString Terminate() { for (h = 1; h <= nbnlq.d; h++) { result.Append("C" + h + "="); result.Append(nbnlq.L[h] / nbnlq.N); result.Append(","); } for (h = 1; h <= nbnlq.d; h++) { result.Append("R" + h + "="); result.Append(nbnlq.Q[h] / nbnlq.N - Math.Pow( nbnlq.L[h] /nbnlq.N, 2)); result.Append(","); }

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Naïve Bayes MapReduce (text file, unoptimized) public void map() { _key.set("n"); context.write(_key, new Text("1")); splitStr = lineWithoutTerminator.split(","); int d = splitStr.length-1; for(h=1;h<=d;h++){ _key.set("g"+splitStr[splitStr.length-1] + "_" + "h" + (h)); _val.set(splitStr[h-1].toString()); context.write(_key, _val); } public void reduce() { if(key.toString().contains("h")){ n=0;L=0;Q=0; for (Text val : values) { attr = Double.parseDouble(val.toString()); n += 1; L += attr; Q += attr*attr; } mean = L/n; var = Q/n -Math.pow(mean, 2); each_row = "N=" + n + ";L=" + L + ";Q=" + Q + ";mean=" + mean + ";var=" + var; _val.set(new Text(each_row)); context.write(new Text(key.toString()), _val); } else { n=0; for (Text val : values) { attr = Double.parseDouble(val.toString()); n+=attr; } _val.set(new Text(Double.toString(n))); context.write(new Text(key.toString()), _val); } 34/60

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3. Storage and Optimizations Storage layouts: –horizontal –vertical Optimizations: –algorithmic: general –systems-oriented: SQL and MapReduce 35/60

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Horizontal Layout DBMS Data Set X(i,X1,…,Xd,G/Y) Most common format in DM Join/Aggregations/arithmetic expressions, pivot iX1X2X3G /60

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Horizontal Layout DBMS [DM2006,SIGMOD] Physical operator (most common): –Table scan (default in SQL query or UDF) External Sort or hash table: –SQL Group By query –UDF Group By Join algorithm : –SQL queries –Not required in UDF 37/60

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Horizontal Layout DBMS Size of table: n rows Limited DDL control in SQL –limited number of columns –requires assigning point id i (Primary index) Clustered storage by block on i allows processing several rows at the same time 38/60

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Horizontal Layout DBMS: X1+X2+X3 No arrays. Access to dimensions through SQL generation (Java/ C++) Example: double X[4], SUM=0.0; int i = 1,h=0, d=3; while( fscanf(fp,"%lf%lf%lf%d",&X[1],&X[2],&X[3]) != EOF ) { SUM = 0.0; for( h = 1; h <= d; h++ ) { SUM += X[h]; } printf("%d\t%g\r\n",i,SUM); i++; } String query = ‘SELECT i’; String sum =‘’; for( int h = 1 ; h <= d; h++ ) { query += ‘, X’+h; sum += ‘X’+h+’+’; } query += ‘,‘ +sum.substring(0,sum.length()-1) +’ FROM X’; SELECT i, x1, x2, x3, X1+X2+X3 FROM X iX1X2X3X1+X2+X /60 C++ JAVA

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Vertical Layout DBMS-X(i,h,v,g) When d exceeds the DBMS limits;d>n Index by point i and dimension h Clustered row storage by i (correctness in UDF, efficiency in SQL query) Queries require: joins & aggregations Columns as subscripts Size <= dn rows (sparse) Two tables with n rows with same PK can be joined in time O(n) using hash join 40/60 ihvG

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Vertical Layout DBMS: X1+X2+X3 Requires using UDF functions SQL statements using [index] joins are required double X, SUM = 0.0; int h, old_i = 0, i; while( fscanf(fp,"%d%d%lf",&i,&h,&X) != EOF ) { if ( old_i != i ) { if ( old_i != 0 ) printf("%d\t%g\r\n",old_i,SUM); old_i = i; SUM = X; } else { SUM += X; } printf("%d\t%g\r\n",i,SUM); String query = ‘SELECT i, SUM(v) FROM X’; query += ‘GROUP BY i’ SELECT i, SUM(v) FROM X GROUP BY i iX1+X2+X /60 C++ JAVA

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Horizontal Layout MapReduce Line number represents the point ID (implicit) No indexes in general Flat file 42/60 X.csv x1,x2,x3,G 1.7,8.2,4.3,1 3.4,10.5,1.0,0 9.3,12.2,2.5,0 5.7,7.3,8.8,0 2.5,13.3,3.2,1

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Horizontal vs Vertical HorizontalVertical Limitation with high d (max columns).No problems with high d. Default layout for most algorithms.Requires clustered index. SQL arithmetic expressions and UDFs.SQL aggregations, joins, UDFs. Easy to interpret.Difficult to interpret. Suitable for dense matrices.Suitable for sparse matrices. Complete record processingUDF: detect point boundaries n rows, d columns dn rows, few (3 or 4) columns Fast n I/OsSlow dn I/Os (n I/Os clustered) 43/60

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3.2 Optimizations Algorithmic & Systems Algorithmic –90% research, many efficient algorithms –accelerate/reduce computations or convergence –database systems focus: reduce I/O –approximate solutions Systems (SQL, MapReduce) –Platform: parallel DBMS server vs cluster of computers –Programming: SQL/C++ versus Java 44/60

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Algorithmic [ZRL1996,SIGMOD] Implementation: data set available as flat file, binary file required for random access May require data structures working in main memory and disk Programming not in SQL: C/C++ are preferred languages, although Java becoming common MapReduce is becoming popular Assumption d<

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Algorithmic Optimizations [STA1998,SIGMOD] [ZRL1996,SIGMOD][O2007,SIGMOD] Exact model computation: –summaries: sufficient statistics (Gaussian pdf), histograms, discretization –accelerate convergence, reduce iterations –faster matrix operations: * + Approximate model computation: –Sampling: efficient in time O(s) –Incremental: math: escape local optima (EM), reseed database systems: favor table scan 46/60

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Systems Optimizations DBMS [O2006,TKDE], [ORD2010,TKDE] SQL query optimization –mathematical equations as queries –Turing-complete: SQL code generation and programming language UDFs as optimization –substitute key mathematical operations –push processing into RAM memory 47/60

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Systems Optimizations DBMS SQL query [O2004,DMKD] Denormalization Issue: Query rewriting (optimizer falls short) Index depends on layout Horizontal layout: –indexed by i –d may be an issue, thus vertical partition Vertical layout: –storage: clustered by point –indexing by subscript –Use specific join algorithm 48/60

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Systems Optimizations DBMS SQL query [O2006,TKDE] [OP2010,TKDE],[OP2010,DKE],[MC2002,ICDM] Join: –denormalized storage: model, intermediate tables –favor hash joins over mrg-srt: both tables PI on i –secondary indexing for join: sort-merge join Aggregation (compression): –push group-by before join: watch out nulls and high cardinality columns like point i synchronized table scans: several SELECTs on same table; examples: unpivoting; 2+ models Sampling: O(s), random access, truly random; error 49/60

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Naïve Bayes SQL (optimized) /*Inserting into NLQ */ INSERT INTO NLQ SELECT g,sum(1.0) AS Ng /* N */,sum(X1) AS L_X1 /* L */,sum(X2) AS L_X2,sum(X3) AS L_X3,sum(power(X1,2)) AS Q_X1 /* Q */,sum(power(X2,2)) AS Q_X2,sum(power(X3,2)) AS Q_X3 FROM X GROUP BY g; /*Inserting into NB */ INSERT INTO NB SELECT g,Ng/T.Nglobal /* pi */,L_X1/Ng /* C */,L_X2/Ng,L_X3/Ng,Q_X1/Ng-power(L_X1/Ng,2) /* R */,Q_X2/Ng-power(L_X2/Ng,2),Q_X3/Ng-power(L_X3/Ng,2) FROM NLQ,( SELECT SUM(Ng) AS Nglobal FROM NLQ)T; 50/60

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Systems Optimization DBMS UDF [HLS2005,TODS] [O2007,TKDE] UDFs can substitute SQL code –UDFs can express complex math computations –Scalar UDFs: vector operations Aggregate UDFs: compute data set summaries in parallel Table UDFs: stream model; external temporary file 51/60

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Naïve Bayes Aggregate UDF (optimized, 1 pass, same as before) public void Init() { nbnlq = new NBNLQ(); int h; nbnlq.N = 0; for (h = 1; h <= nbnlq.d; h++) { nbnlq.L[h] = 0; nbnlq.Q[h] = 0; } public void Merge(udf_nb_train_d3 thread) { int i, h; nbnlq.d = thread.nbnlq.d; nbnlq.N += thread.nbnlq.N; for (h = 1; h <= nbnlq.d; h++) { nbnlq.L[h] += thread.nbnlq.L[h]; nbnlq.Q[h] += thread.nbnlq.Q[h]; } public void Accumulate(Xd3 X) { int h; if (!X.IsNull) { nbnlq.d = X.getD(); nbnlq.N += 1.0; for (h = 1; h <= nbnlq.d; h++) // L,Q { nbnlq.L[h] += X.getColumn(h); nbnlq.Q[h] += X.getColumn(h) * X.getColumn(h); } public SqlString Terminate() { for (h = 1; h <= nbnlq.d; h++) { result.Append("C" + h + "="); result.Append(nbnlq.L[h] / nbnlq.N); result.Append(","); } for (h = 1; h <= nbnlq.d; h++) { result.Append("R" + h + "="); result.Append(nbnlq.Q[h] / nbnlq.N - Math.Pow( nbnlq.L[h] /nbnlq.N, 2)); result.Append(","); } 52/60

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MapReduce [ABASR2009,VLDB] [CDDHW2009,VLDB] [SADMPPR2010,CACM] Data set –keys as input, partition data set –text versus sequential file –loading into file system may be required Parallel processing –high cardinality keys: i –handle skewed distributions –reduce row redistribution in Map( ) Main memory processing 53/60

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MapReduce Processing [DG2008,CACM] [FPC2009,PVLDB] [PHBB2009,PVLDB] Modify Block Size Disable Block Replication Delay reduce() Tune M and R (memory allocation and number) Several M use the same R Avoid full table scans by using subfiles (requires naming convention) combine() in map() to shrink intermediate files SequenceFiles as input with custom data types. 54/60

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MapReduce Issues Loading, converting to binary may be necessary Input key generally OK if high cardinality Skewed map key distribution Key redistribution (lot of message passing) 55/60

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MapReduce Optimized public static class NBHMapper() { context.write(key,val); } public static class NBHCombiner() { for (DoubleArrayWritable val : values) { n++; x = (DoubleWritable[]) val.toArray(); for (int h = 1; h <= d; h++) { attr = x[h - 1].get(); L[h] += attr; Q[h] += attr * attr; } _val_array[1].set(n); for (int h = 1; h <= d; h++) { _val_array[1+h].set(L[h]);} for (int h = 1; h <= d; h++) { _val_array[1+d+h].set(Q[h]);} } public static class NBHReducer(){ for (DoubleArrayWritable val : values) { x = (DoubleWritable[]) val.toArray(); n += x[1].get(); for (int h = 1; h <= d; h++) { L[h] += x[1+ h].get();} for (int h = 1; h <= d; h++) { Q[h] += x[1+d+h].get();} } each_row = "N=" + n; each_row += ";C="; for (int h = 1; h <= d; h++) { each_row += L[h]/n + ",";} each_row += ";R="; for (int h = 1; h <= d; h++) { each_row += Q[h] / n - Math.pow((L[h] / n), 2) + ",";} } 56/60

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SQL vs MapReduce Processing & I/O Bottleneck (bulk load) [PPRADMS2009,SIGMOD] [O2010,TKDE] n x 1MSQLMR* ImportBuildTotalImportBuildTotal *MR times include conversion into a SequenceFile. Import and Model Computation Times for SQL and MR (times in secs). 57/60

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Systems optimizations SQL vs MR (optimized versions, run same hardware) TaskSQLUDFMR Speed: compute model123 Speed: score data set132 Programming flexibility321 Process non-tabular data321 Loading speed112 Ability to add optimizations213 Manipulating data key distribution123 Immediate processing (push=SQL,pull=MR) /60

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Research Issues Both: SQL and MapReduce [BFR1998,KDD], [CFB1999,ICDE] [SADMPPR2010,CACM] Fast data mining algorithms solved? Yes, but not considering data sets are stored in a DBMS SQL and MR have many similarities: shared-nothing Fast load/unload interfaces between both systems; tighter integration General tradeoffs in speed and programming: horizontal vs vertical layout Incremental algorithms –one pass (streams) versus parallel processing –reduce passes/iterations 59/60

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Research Issues on Each [ABASR2009,VLDB], [CDDHW2009,VLDB [CKLRSS2009,VLDB] DBMS: –C++/Java libraries generating SQL code, pushing processing: Oracle, Teradata, SAS, KXEN –Internal C code: commercial DBMSs, open-source? –Study aggregate UDFs for complex models; extend Table UDF support: I/O bottleneck, streams –Extend SQL with more DM primitives and constructs or forget extending SQL for DM? –Specialized DBMS, middleware: SciDB, RIOT MapReduce: –SQL+MapReduce: Greenplum, Aster, Teradata –MapReduce only: Mahout –MapReduce for query processing and data mining: especially joins, aggregations OK 60/60

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Thank you… Q&A Special thanks: –Carlos Garcia-Alvarado DBMS Group at UH: –Sasi K. Pitchaimalai –Mario Navas –Zhibo Chen

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References [ABASR2009,VLDB] A. Abouzeid, K. Bajda-Pawlikowski, D. Abadi, A. Silberschatz, and A. Rasin. HadoopDB: an architectural hybrid of MapReduce and DBMS technologies for analytical workloads. Proc. VLDB Endow., pages , [BFR1998,KDD] P. Bradley, U. Fayyad, and C. Reina. Scaling clustering algorithms to large databases. In ACM KDD Conference, pages 9-15, [BRKPHK2008,SIGMOD] J.A Blakeley, V. Rao, I. Kunen, A. Prout, M. Henaire, and C. Kleinerman..NET database programmability and extensibility in microsoft SQL server. In ACM SIGMOD, pages [CFB1999,ICDE] S. Chaudhuri, U. Fayyad, and J. Bernhardt. Scalable classification over SQL databases. ICDE, 00:470, [CDHHL1999,KDD] J. Clear, D. Dunn, B. Harvey, M.L. Heytens, and P. Lohman. Non-stop SQL/MX primitives for knowledge discovery. In ACM KDD Conference, pages , [CDDHW2009,VLDB] J. Cohen, B. Dolan, M. Dunlap, J. Hellerstein, and C. Welton. MAD skills: New analysis practices for big data. In VLDB Conference, pages , [CKLRSS2009,VLDB] A demonstration of SciDB: a science-oriented DBMS. In VLDB Conference, pages ,2009. [DG2008,CACM] J. Dean and S. Ghemawat. MapReduce: simplified data processing on large clusters. Commun. ACM, 51(1): ,2008. [DLR1977,RSS] A.P. Dempster, N.M. Laird, and D. Rubin. Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of The Royal Statistical Society, 39(1):1-38, [DM2006,SIGMOD] A. Deshpande and S. Madden. MauveDB: supporting model-based user views in database systems. In SIGMOD Conference, pages 73-84, 2006.

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