Shared Memory Parallelization of Decision Tree Construction Using a General Middleware Ruoming Jin Gagan Agrawal Department of Computer and Information Sciences Ohio State University

Motivation Can the algorithms for a variety of mining tasks be parallelized using a common parallelization structure ? If so, we can Have a common set of parallelization techniques Develop general runtime / middleware support Parallelize starting from a high-level interface

Context Part of the FREERIDE (Framework for Rapid Implementation of Datamining Engines) system Support parallelization on shared-nothing configurations Support parallelization on shared memory configurations Support processing of large datasets Previously reported our work for Distributed memory parallelization and processing of disk- resident datasets (SDM 01, IPDPS 01 workshop) Shared memory parallelization applied to association mining and clustering (SDM 02, IPDPS 02 workshop, SIGMETRICS 02)

Decision Tree Construction One of the key mining problems Previous parallel algorithms have had a significantly different structure than parallel algorithms for association mining, clustering, etc. Frequently require sorting of data (SPRINT, SLIQ etc.) Require attributes to be written back Difficult to obtain very high speedups Can we perform shared memory parallelization of decision tree construction using the same techniques that were used for association mining and clustering ?

Outline Previous work on shared memory parallelization Observation from major mining algorithms Parallelization Techniques Decision tree construction problem and algorithms RainForest Based Approach Parallelization methods Experimental Results

Common Processing Structure Structure of Common Data Mining Algorithms {* Outer Sequential Loop *} While () { { * Reduction Loop* } Foreach (element e) { (i,val) = process(e); Reduc(i) = Reduc(i) op val; } Applies to major association mining, clustering and decision tree construction algorithms How to parallelize it on a shared memory machine?

Challenges in Parallelization Statically partitioning the reduction object to avoid race conditions is generally impossible. Runtime preprocessing or scheduling also cannot be applied Can’t tell what you need to update w/o processing the element The size of reduction object means significant memory overheads for replication Locking and synchronization costs could be significant because of the fine-grained updates to the reduction object.

Parallelization Techniques Full Replication: create a copy of the reduction object for each thread Full Locking: associate a lock with each element Optimized Full Locking: put the element and corresponding lock on the same cache block Fixed Locking: use a fixed number of locks Cache Sensitive Locking: one lock for all elements in a cache block

Memory Layout for Various Locking Schemes Full Locking Fixed Locking Optimized Full LockingCache-Sensitive Locking LockReduction Element

Trade-offs between Techniques Memory requirements: high memory requirements can cause memory thrashing Contention: if the number of reduction elements is small, contention for locks can be a significant factor Coherence cache misses and false sharing: more likely with a small number of reduction elements

Summary of Results on Association Mining and Clustering  Applied techniques on apriori association mining and k-means clustering  Each of full replication, optimized full locking, and cache-sensitive locking can outperform each other, depending upon the size of the reduction object  Near-linear speedups obtained in all our experiments

Decision Tree Construction Problem Input: a set of training records, each with several attributes One attribute is special, called the class label, others are predictor attributes The goal is to construct a prediction model, which predicts the class model for a new record, using values of its predictor attributes A tree is constructed in a top-down fashion

Existing Algorithms Initial algorithms: required training records to fit in memory SLIQ: scalable, but Requires sorting of numerical attributes Separation of attribute lists A data-structure called class list to be maintained in main memory (size proportional to the number of training records) SPRINT: scalable and parallelizable, but Requires sorting of numerical attributes Separation of attribute lists Partitioning of attribute lists while splitting a node

RainForest Based Decision Tree Construction A general approach to scaling decision tree construction Key idea: AVC-set (Attribute Value, Classlabel) Sufficient information for deciding on split condition For an attribute and node, size is proportional to the number of distinct values and class labels Easily constructed by taking one pass on data A number of different algorithms: RF-read, RF-Write, RF-hybrid RF-read has a structure that fits in very well with canonical loop presented earlier

RF-read Algorithm High-level structure of the algorithm While the stop condition is not satisfied read the data build the AVC-group for nodes choose the splitting attributes to split nodes select a new set of node to process as long as the main memory could hold it Never need to write-back any data to disks May require multiple passes to process one levels of the tree

Overall Parallelization Approach Training records can be processed independently by processors AVC-sets of nodes are reduction objects : race conditions can arise in updating the values Use the different parallelization techniques we have for avoiding race conditions Higher memory requirements can mean more passes to process one level of the tree

Parallelization Strategies Pure approach: only apply one of full replication, optimized full locking and cache-sensitive locking Vertical approach: use replication at top levels, locking at lower Horizontal: use replication for attributes with a small number of distinct values, locking otherwise Mixed approach: combine the above two

Experimental Setup SMP Machine SunFire MHz processors (only up to 8 for our experiments) 64 KB L1 cache, 8 MG L2 cache, 24 GB memory Dataset 1.3 GB dataset with 32 million records Synthetic data, using a tool available from IBM almaden 9 attributes, 3 categorical, 6 numerical Used functions 1 and 7 (1 in paper)

Results Performance of pure versions, 1.3GB dataset with 32 million records in the training set, function 7, the depth of decision tree = 16.

Results Combining full replication and optimized full locking

Results Combining full replication and cache-sensitive locking

Summary A set of common techniques can be used for shared memory parallelization of different mining algorithms Combination of parallelization techniques gives the best performance for decision tree construction Best speedup of 5.9 on 8 processors – comparable with other results on shared memory and distributed memory parallelization