MatrixMap: Programming abstraction and implementation of matrix computation for big data analytics

Yaguang  Huangfu; Guanqing  Liang; Jiannong  Cao

doi:10.3934/bdia.2016015

Article Contents

2016, Volume 1, Issue 4: 349-376. Doi: 10.3934/bdia.2016015

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MatrixMap: Programming abstraction and implementation of matrix computation for big data analytics

Department of Computing, The Hong Kong Polytechnic University, Hong Kong, China

* Corresponding author: Jiannong Cao
* Corresponding author: Jiannong Cao

Revised: March 31, 2017

Published: September 2017

Abstract Full Text(HTML) Figure(13) / Table(10) Related Papers Cited by

Abstract

The computation core of many big data applications can be expressed as general matrix computations, including linear algebra operations and irregular matrix operations. However, existing parallel programming systems such as Spark do not have programming abstraction and efficient implementation for general matrix computations. In this paper, we present MatrixMap, a unified and efficient data-parallel programming framework for general matrix computations. MatrixMap provides powerful yet simple abstraction, consisting of a distributed in-memory data structure called bulk key matrix and a programming interface defined by matrix patterns. Users can easily load data into bulk key matrices and program algorithms into parallel matrix patterns. MatrixMap outperforms current state-of-the-art systems by employing three key techniques: matrix patterns with lambda functions for irregular and linear algebra matrix operations, asynchronous computation pipeline with context-aware data shuffling strategies for specific matrix patterns and in-memory data structure reusing data in iterations. Moreover, it can automatically handle the parallelization and distribute execution of programs on a large cluster. The experiment results show that MatrixMap is 12 times faster than Spark.

Keywords:

Mathematics Subject Classification: Primary:68N15, 68Nxx; Secondary:68Txx.

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Figure 1. MatrixMap Framework

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Figure 2. Matrix Plus Pattern

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Figure 3. Matrix Multiply Pattern

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Figure 4. Matrix Join Pattern

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Figure 5. System Architecture

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Figure 6. Data flowchart of MatrixMap framework

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Figure 7. Asynchronous Computing Process

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Figure 8. CSR Format

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Figure 9. Key-CSR Format

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Figure 10. Breadth-First Search in Matrix Operations

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Figure 11. Runtime comparison between MatrixMap and other programming models in non-iterative algorithms

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Figure 12. Runtime comparison between MatrixMap and other programming models in iterative algorithms

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Figure 13. Scalability in PageRank Run Time

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Table Listing 1. Matrix Interface

class BKM {
// Matrix Patterns
Map(MapLambda);
Reduce(ReduceLambda);
Multiply(MultiplyLambda);
Plus(PlusLambda);
Join(JoinLambda);

// Matrix supporting method
BKM(string file_name);
Load(string file_name);
Cahe();
Save();
};
void map(string, string, Context);
void reduce(string, Iterable < int>, Context);
float multiply(float, float);
float plus(float, float);
bool join(float, float);

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Table Listing 2. WordCount Code

BKM m("wordcount.txt");
m.Map([](string key, string word, Context c){
c.Insert(word, 1);})
.Sort().Reduce([](string key, Iterable < Int> i,
Context c) {
int sum = 0;
for (int e: r) {
sum += e;
}
context.Insert(key, sum);
}
);

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Table Listing 3. Inner Join

BKM matrix1("matrix1.data");
BKM matrix2("matrix2.data");
matrix1.Join(matrix2,
[](float key1, float key2) {
return key1 == key2;
});

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Table Listing 4. Logistic Regression

BKM data("points.data");
BKM weights, label, error;
BKM temp;
int iterations = 100;
for (int i = 0; i < iterations; ++i) {
temp = data.Multiply(weights)
float h = sigmoid(temp);
error = label.Plus(h);
temp = data.Multiply(error);
temp = temp.Multiply(alpha);
weights = temp.Plus(weights);
}

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Table Listing 5. K-Means

BKM centroids;
int iterations = 100;
for (int i = 0; i < iteraions; ++i) {
point.Map([](string key, vector < double> point,
Context c) {
BKM temp = point.Multiply(centroids);
int index = min_index(temp);
c.Insert(index, point);
}).Reduce([](string key, Iterable < double> i,
Contex c){
centroids = c.insert(key, average(point)).Dump();
});
}

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Table Listing 6. Alternating Least Squares

BKM m("r.data");
BKM u, r, error;
int iteration 100;
for (int i = 0; i < iterations; ++i) {
BKM temp = m.Multiply(u);
error = r.Plus(temp);
temp = m.Multiply(error);
temp = temp.Multiply(alpha);
u = temp.Plus(u);
temp = u.Multiply(m);
error = r.Plus(temp);
temp = u.Multiply(error);
temp = temp.Multiply(alpha);
m = temp.Plus(m);
}

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DownLoad: CSV

Table Listing 7. Breadth-first Search

BKM graph("graph.data");
BKM trace;
graph.Multiply(trace);

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Table Listing 8. Graph Merge

BKM A("a.data");
BKM B("b.data");
BKM C = A.Plus(B,
[](float a, float b){
if (a!= 0) return a;
else if(b!= 0)return b;
else return 0;
}
);

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DownLoad: CSV

Table Listing 9. All Pair Shortest Path

BKM W("graph.data");
int iteration = W.GetRows();
for(int i = 0; i < n -1; i = 2*i){
W = W.Multiply(W,
[](float x, float y) {
return min(x+y, x);
}
);
}

| Show Table

DownLoad: CSV

Table Listing 10. PageRank

BKM M("web.data");
BKM r_new, r_old;
int iterations = 100;
for(int i = 0; i < iterations; ++i){
r_new = M.Multiply(r_old);
r_old = r_new;
}

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