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LECTURE 2 Map-Reduce for large scale similarity computation

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…from last lecture How to convert entities into high-dimensional numerical vectors How to compute similarity between two vectors. For example, is x and y are two vectors then

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..from last lecture Example: X = (1,2,3) ; Y= (3,2,1) ||X|| = (1+4+9) = = 3.74 ||Y|| = ||X|| Sim(X,Y) = ( )/( ) = 10/14 = 5/7 We also learnt that for large data sets computing pair-wise similarity can be very time consuming.

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Map-Reduce Map-Reduce has become a popular framework for speeding up computations like pair-wise similarity Map-Reduce was popularized by Google and then Yahoo! (through the Hadoop open-source implementation) Map-Reduce is a programming model built on top of “cluster computing”

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Cluster Computing Put simple (commodity) machines together, each with their own CPU, RAM and DISK, for parallel computing CPURAMDISK CPURAMDISK CPURAMDISK CPURAMDISK CPURAMDISK CPURAMDISK Switch rack

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Map-Reduce Map-Reduce consists of two distinct entities Distributed File System (DFS) Library to implement Mapper and Reducer functions A DFS seamlessly manages files on the “cluster computer.” A file is broken into “chunks” and these chunks are replicated across the nodes of a cluster. If a node which contains chunk A fails, the system will re-start the computation on a node which contains a copy of the chunk.

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Distributed File System A DFS will “chunk” files and replicated them across several nodes and then keep track of the chunks. Only practical when data is mostly read only (e.g., historical data; not for live data –like airline reservation system). File Chunk Node 3,2,18 Node 2,6,7

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Node failure When several nodes are in play the chances that a single node goes down at any time goes up significantly... Suppose they are n nodes and let p be the probability that a single node will fail.. (1-p) that single node will not fail (1-p) n that none of the nodes will fail 1 – (1-p) n that at least one will fail.

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Node failure The probability that at least one node failing is: f= 1 – (1-p) n When n =1; then f =p Suppose p= but n=10000, then: f = 1 – ( ) = 0.63 [why/how ?] This is one of the most important formulas to know (in general).

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Example: “Hello World” of MR DocidContent 1Silent mind, holy mind 2road kill in Java 3Java programming is fun 4My mind in Java 5Where the fun rolls 6Silent road to Cairns Task: Produce an output which, for each word in the file, counts the number of times it appears in the file. Answer: (Java, 3); (Silent, 2), (mind,3)……

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Example For example {doc1, doc2} machine 1 {doc3,doc4} machine 2 {doc5,doc6} machine 3 Each chunk is also duplicated to other machines.

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Example Now apply the MAP operation to each node and emit the pair (key, 1). Thus doc1 emits: (silent,1); (mind,1); (holy, 1); (mind,1) Similarly doc6 emits: (silent,1);(road,1); (to,1); (Cairns,1)

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Example Note in the first chunk which contains (doc1, doc2)..each doc emits (key,value) pairs. We can think that each computer node emits a list of (key, value) pairs. Now this list is “grouped” so that the REDUCE function can be applied.

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Example Note now that the (key,value) pairs have no connection with the docs… (silent,1),(mind,1), (holy, 1), (mind,1), (road,1),(to,1),(Cairns,1); (Java,1),(programming,1),(is,1),(fun,1),……. Now we have a hash function h:{a..z} {0,1} Basically two REDUCE nodes And (key,value) effectively become (key, list)

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Example For example suppose the hash functions maps {to, Java, road} to one node. Then (to,1) remains (to,1) (Java,1);(Java,1);(Java,1) (Java, [1,1,1]) (road,1);(road,1) (road,[1,1]); Now REDUCE function converts (Java,[1,1,1]) (Java,3) etc. Remember this is a very simple example…the challenge is to take complex tasks and express them as Map and Reduce!

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Schema of Map-Reduce Tasks [MMDS] chunks Map Task (key,value) pairs Group By Keys (k,v) [k,(v,u,w,x,z)] Reduce Task Output

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The similarity join problem Last time we discussed about computing the pair- wise similarity of all articles/documents in Wikipedia. As we discussed it was time consuming problem because if N is the number of documents, and d is the length of each vector, then the running time proportional to O(N 2 d). How can this problem be attacked using the Map Reduce framework.

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Similarity Join Assume we are given two documents (vectors) d1 and d2. Then (ignoring the denominator) Example: d1 = {silent mind to holy mind}; d2 = {silent road to cairns} sim(d1,d2) = 1 silent,d1 1 silent,d2 + 1 to,d11 1 to,d2 = 2 Exploit the fact that a term (word) only contributes if it belongs to at least two documents.

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Similarity Example [2] Notice, it requires some ingenuity to come up with key-value pairs. This is key to suing map-reduce effectively

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Amazon Map Reduce For this class we have received an educational grant from Amazon to run exercises on their Map Reduce servers. Terminology EC2 – is the name of Amazon’s cluster S3 – is the name of their storage machines Elastic Map Reduce – is the name Amazon’s Hadoop implementation of Map-Reduce Lets watch this video.this

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References 1. Massive Mining of Data Sets (Rajaram, Leskovec, Ullman) 2. Computing Pairwise Similarity in Large Document Collection: A Map Reduce Perspective (El Sayed, Lin, Oard)

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