Scalable PageRank via Virtual Memory (MMap), Random Forest, Weka Solution



Submission Instructions and Important Notes:

It is important that you read the following instructions carefully and also those about the deliverables at the end of each question or you may lose points.

Submit a single zipped file, called “HW4-{YOUR_LAST_NAME}-{YOUR_FIRST_NAME}.zip”, containing all the deliverables including source code/scripts, data files, and readme. Example: ‘’ if your name is John Doe. Only .zip is allowed (no other format will be accepted)

You may collaborate with other students on this assignment, but you must write your own code and give the

explanations in your own words, and also mention the collaborators’ names on T-Square’s submission page. All GT students must observe the honor code. Suspected plagiarism and academic misconduct will be reported to and directly handled by the Office of Student Integrity (OSI). Here are some examples similar to Prof. Jacob Eisenstein’s NLP course page (grading policy):

OK: discuss concepts (e.g., how cross-validation works) and strategies (e.g., use hashmap instead of


Not OK: several students work on one master copy together (e.g., by dividing it up), sharing solutions, or using solution from previous years or from the web.

If you use any slip days”, you must write down the number of days used in the T-square submission page.

For example, “Slip days used: 1”. Each slip day equals 24 hours. E.g., if a submission is late for 30 hours, that counts as 2 slip days.

At the end of this assignment, we have specified a folder structure about how to organize your files in a

single zipped file. 5 points will be deducted for not following this strictly.

We will use auto-grading scripts to grade some of your deliverables (there are hundreds of students), so it is extremely important that you strictly follow our requirements. Marks may be deducted if our grading scripts cannot execute on your deliverables.

Wherever you are asked to write down an explanation for the task you perform, stay within the word limit.

In your final zip file, please do not include any intermediate files you may have generated to work on the task, unless your script is absolutely dependent on it to get the final result (which it ideally should not be).

After all slip days are used up, 5% deduction for every 24 hours of delay. (e.g., 5 points for a 100-point


We will not consider late submission of any missing parts of a homework assignment or project deliverable.

To make sure you have submitted everything, download your submitted files to double check.

Download the HW4 Skeleton before you begin. [100 points]

Note: You must use Python 2.7 for this homework.

Q1 [40 pts] Scalable single-PC PageRank on 70M edge graph

In this question, you will learn how to use your computer’s virtual memory to implement the PageRank algorithm that will scale to graph datasets with as many as billions of edges using a single computer (e.g., your laptop). As discussed in class, a standard way to work with larger datasets has been to use computer clusters (e.g., Spark, Hadoop) which may involve steep learning curves, may be costly (e.g., pay for hardware and personnel), and importantly may be “overkill” for smaller datasets (e.g., a few tens or hundreds of GBs). The virtual memory based approach offers an attractive, simple solution to allow practitioners and researchers to more easily work with such data (visit the NSFfunded MMap project’s homepage to learn more about the research).

The main idea is to place the dataset in your computer’s (unlimited) virtual memory, as it is often too big to fit in the RAM. When running algorithms on the dataset (e.g., PageRank), the operating system will automatically decide when to load the necessary data (subset of whole dataset) into RAM.

This technical approach to put data into your machine’s virtual memory space is called “memory mapping”, which allows the dataset to be treated as if it is an in-memory dataset. In your (PageRank) program, you do not need to know whether the data that you need is stored on the hard disk, or kept in RAM. Note that memory-mapping a file does NOT cause the whole file to be read into memory. Instead, data is loaded and kept in memory only when needed (determined by strategies like least recently used paging and anticipatory paging).

You will use the Python modules mmap and struct to map a large graph dataset into your computer’s virtual memory. The mmap() function does the “memory mapping”, establishing a mapping between a program’s (virtual) memory address space and a file stored on your hard drive — we call this file a “memory-mapped” file. Since memory-mapped files are viewed as a sequence of

bytes (i.e., a binary file), your program needs to know how to convert bytes to and from numbers (e.g., integers). struct supports such conversions via “packing” and “unpacking”, using format specifiers that represent the desired endianness and data type to convert to/from.

Q1.1 Set up Pypy

Install PyPy, which is a Just-In-Time compilation runtime for python, which supports fast packing and unpacking. (As mentioned in class, C++ and Java are generally faster than Python. However, several projects aim to boost Python speed. PyPy is one of them.)


sudo apt-get install pypy


Install Homebrew

Run brew install pypy


Download the package and then install it.

Run the following code in the Q1 directory to learn more about the helper utility that we have provided

to you for this question.

$ pypy –help

Q1.2 Warm Up (15 pts)

Get started with memory mapping concepts using the code-based tutorial in

You should study the code and modify parts of it as instructed in the file. You can run the tutorial code as-is (without any modifications) to test how it works (run python on the terminal to do this). The warmup code is setup to pack the integers from 0 to 63 into a binary file, and unpack it back into a memory map object. You will need to modify this code to do the same thing for all odd integers in the range of 1 to 42. The lines that need to be updated are clearly marked. Note: You must not modify any other parts of the code. When you are done, you can run the following command to

test whether it works as expected:

$ python test_warmup out_warmup.bin

It prints True if the binary file created after running contains the expected output.

Q1.3 Implementing and running PageRank (25 pts)

You will implement the PageRank algorithm, using the power iteration method, and run it on the LiveJournal dataset (an online community with millions of users to maintain journals and blogs). You may want to revisit the MMap lecture slides (slide 9, 10) to refresh your memory about the PageRank algorithm and the data structures and files that you may need to memory-map. (For more details, read the MMap paper.) You will perform three steps (subtasks) as described below.

Step 1: Download the LiveJournal graph dataset (an edge list file)

The LiveJournal graph contains almost 70 million edges. It is available on the SNAP website. We are hosting the graph on our course homepage, to avoid high traffic bombarding their site.

Step 2: Convert the graph’s edge list to binary files (you only need to do this once)

Since memory mapping works with binary files, you will convert the graph’s edge list into its binary format by running the following command at the terminal/command prompt:

$ python convert <path-to-edgelist.txt>

Example: Consider the following toy-graph.txt, which contains 7 edges:

0 1

1 0

1 2

2 1

3 4

4 5

5 2

To convert the graph to its binary format, you will type:

$ python convert toy-graph/toy-graph.txt

This generates 3 files:


toy-graph.bin: binary file containing edges (source, target) in little-endian “int” C type toy-graph.idx: binary file containing (node, degree) in little-endian “long long” C type toy-graph.json: metadata about the conversion process (required to run pagerank)

In toy-graph.bin we have,







1 (in little-endian “int” C type)
















































ffff ffff ffff ffff ffff ffff ffff ffff

In toy-graph.idx we have,

0000 0000 0000 0000 0100 0000 0000 0000 # 0 1 (in little-endian “long long” C type )

0100 0000 0000 0000 0200 0000 0000 0000 # 1 2


ffff ffff ffff ffff ffff ffff ffff ffff

Note: there are extra values of -1 (ffff ffff or ffff ffff ffff ffff) added at the end of the binary file as padding to ensure that the code will not break in case you try to read a value greater than the file size. You can ignore these values as they will not affect your code.

Step 3: Implement and run the PageRank algorithm on LiveJournal graph’s binary files

Follow the instructions in to implement the PageRank algorithm.

You will only need to write/modify a few lines of code.

Run the following command to execute your PageRank implementation:

$ pypy pagerank <path to JSON file for LiveJournal>

This will output the 10 nodes with the highest PageRank scores.

For example: $ pypy pagerank toy-graph/toy-graph.json















(Note that only 6 nodes are printed here since the toy graph only has 6 nodes.)

Step 4: Experiment with different number of iterations.

Find the output for the top 10 nodes for the LiveJournal graph for n=10, 25, 50 iterations (try the

–iterations n argument in the command above; the default number of iterations is 10). A file in the format pagerank_nodes_n.txt for “n” number of iterations. For example:

$ pypy pagerank toy-graph/toy-graph.json –iterations 25

You may notice that while the top nodes’ ordering starts to stabilize as you run more iterations, the nodes’ PageRank scores may still change. The speed at which the PageRank scores converge depends on the PageRank vector’s initial values. The closer the initial values are to the actual pagerank scores, the faster the convergence.


1. [10pt]: your modified implementation.

2. out_warmup.bin [4pt]: the binary file, automatically generated by your modified

3. out_warmup_bytes.txt [2pt]: the text file with the number of bytes, automatically generated by your modified

4. [18pt]: your modified implementation.

5. pagerank_nodes_n.txt [6pt]: the 3 files (as given below) containing the top 10 node IDs and their pageranks for n iterations, automatically generated by

pagerank_nodes_10.txt [2pt] for n=10

pagerank_nodes_25.txt [2pt] for n=25

pagerank_nodes_50.txt [2pt] for n=50

Q2 [40 pts] Random Forest Classifier

You will implement a random forest classifier in Python. The performance of the classifier will be evaluated via the out-of-bag (OOB) error estimate, using a provided dataset. To refresh your memory about random forest and OOB, see Chapter 15 in the Elements of Statistical Learning book, lecture slides, and a nice online discussion. (Here is a blog post that introduces random forests in a fun way, in layman’s terms.) Note: You must not use existing machine learning or random forest libraries.

You will use the UCI Breast Cancer Dataset, which is often used for evaluating classification algorithms. You will perform binary classification on the dataset to determine if a tumor is benign or malignant. The data is stored in a comma-separated file (csv) in your Q2 folder as hw4-data.csv. Each line describes an instance using 10 columns: the first 9 describe the tumor’s characteristics, and the last column is the ground truth label for the tumor classification. (0 for benign, 1 for malignant). Note: The last column should not be treated as an attribute.

A. Implementing Random Forest (25 pt)

The main parameters in a random forest are:

Which attributes of the whole set of attributes do you select to find a split?

When do you stop splitting leaf nodes?

How many trees should the forest contain?

We have prepared starter code written in Python which you will be using. This would help you setup the environment (loading the data and evaluating your model). The following files are provided for you: A file containing utility functions that will help you build a decision tree. A file containing a decision tree class that you will use to build your random forest. A file containing a random forest class and a main to test your random forest.

References for decision tree implementation:

Building Classification Models: ID3 and C4.5

PERT Perfect Random Tree Ensembles

Please implement all the functions and classes in,, and The functions in will help you build your decision tree, but in your final random forest implementation, you may apply any variations that you like (e.g., using entropy, Gini index, random attribute selection, binary split, random split). However, you must explain your approaches and their effects on the classification performance in a text file description.txt (<75 words).

B. Computing and reporting out-of-bag error estimates (15 pt)

In random forests, it is not necessary to perform explicit cross-validation or use a separate test set for performance evaluation (also discussed in class). Out-of-bag (OOB) error estimate has shown to be reasonably accurate and unbiased. Below, we summarize the key points about OOB described in the original article by Breiman and Cutler.

Each tree in the forest is constructed using a different bootstrap sample from the original data (usually, a bootstrap sample has the same size as the original dataset). Statistically, about one-third of the cases are left out of the bootstrap sample and not used in the construction of the kth tree. For each record left out in the construction of the kth tree, it can be assigned a class by the kth tree. As a result, each record will have a “test set” classification by the subset of trees that treat the record as an out-of-bag sample. The majority vote for that record will be its predicted class. The proportion of times that a predicted class is not equal to the true class of a record averaged over all records is the OOB error estimate.

Modify the code template to compute the OOB error estimate. Report the estimate of your implementation in description.txt.


1. hw4-data.csv: The dataset used to develop your program. (unmodified)

2. The utility functions you need to implement.

3. The source code for your decision tree implementation.

4. The source code of your random forest implementation with detailed comments for your code.

5. description.txt:

Specific the implementation steps of the random forest and why you choose the specific approach (<75 words)

Report the OOB estimate.

Q3 [20 points] Using Weka

You will use Weka, a popular machine learning software, to train classifiers for the same dataset used in Q2, and to compare the performance of your random forest implementation with Weka’s.

Download and install Weka. Note that Weka requires Java Runtime Environment (JRE) to run. We suggest that you install the latest JRE, to avoid Java or runtime-related issues.

How to use Weka:

Load data into Weka Explorer : Weka supports file formats such as arff, csv, xls.

Preprocessing: you can view your data, select attributes, and apply filters.

Classify: under Classifier you can select the different classifiers that Weka offers. You can adjust the input parameters of many models by clicking on the text to the right of the Choose button in the Classifier section.

A. Experiment (10 pt)

Run the following experiments. After each experiment, report your parameters, running time, confusion matrix, and prediction accuracy. An example is provided below, under the “Deliverables section. For the Test options, choose 10-fold cross validation.

1. Random Forest. Under classifiers -> trees, select RandomForest. You might have to preprocess the data before using this classifier. (5 pt)

2. Your choice choose any classifier you like from the numerous classifiers Weka provides.

You can use package manager to install the ones you need. (5 pt)

Note: You may not be able to create the confusion matrix initially (it may be grayed out). The reason is that all your features/columns are Numeric. Convert the last column (your label) to Nominal using filters to resolve this issue.

B. Discussion (10 pt)

1. Compare the Random Forest result from A1 to your implementation in Q2 and discuss possible reasons for the difference in performance. (< 50 words, 5 pt)

2. Compare and explain the two approaches’ classification results in Section A, specifically their running times, accuracies, and confusion matrices. If you have changed/tuned any of the parameters, briefly explain what you have done and why they improve the prediction accuracy. (< 100 words, 5 pt)


report.txt A text file containing the Weka result and your discussion for all questions above. For example:

Section A


J48 -C 0.25 -M 2

Time taken to build model: 3.73 seconds

Overall accuracy: 86.0675 % Confusion Matrix:

a b <– classified as

33273 2079 | a = no

4401 6757 | b = yes


Section B

1. The result of Weka is 86.1% compared to my result <accuracy> because…

2. I choose <classifier> which is <algorithm>…

Submission Guidelines

Submit the deliverables as a single zip file named (should start with lowercase hw4). Write down the name(s) of any students you have collaborated with on this assignment, using the text box on the T-Square submission page.

The zip file’s directory structure must exactly be (when unzipped):

hw4-LastName-FirstName/ Q1/ out_warmup.bin out_warmup_bytes.txt pagerank_nodes_10.txt pagerank_nodes_25.txt



hw4-data.csv description.txt



You must follow the naming convention specified above.