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 NSF-funded 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.)
Ubuntu sudo apt-get install pypy
MacOS Install Homebrew
Run brew install pypy
Windows 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 q1_utils.py –help
Q1.2 Warm Up (15 pts)
Get started with memory mapping concepts using the code-based tutorial in warmup.py.
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 warmup.py” 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 q1_utils.py test_warmup out_warmup.bin
It prints True if the binary file created after running warmup.py 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 q1_utils.py convert Example: Consider the following toy-graph.txt, which contains 7 edges:
To convert the graph to its binary format, you will type:
$ python q1_utils.py 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,
0000 0000 0100 0000 # 0 1 (in little-endian “int” C type)
0100 0000 0000 0000 # 1 0
0100 0000 0200 0000 # 1 2
0200 0000 0100 0000 # 2 1
0300 0000 0400 0000 # 3 4
0400 0000 0500 0000 # 4 5
0500 0000 0200 0000 # 5 2
ffff ffff ffff ffff
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 pagerank.py 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 q1_utils.py pagerank This will output the 10 nodes with the highest PageRank scores.
For example: $ pypy q1_utils.py 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 q1_utils.py 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. warmup.py [10pt]: your modified implementation.
2. out_warmup.bin [4pt]: the binary file, automatically generated by your modified warmup.py.
3. out_warmup_bytes.txt [2pt]: the text file with the number of bytes, automatically generated
by your modified warmup.py.
4. pagerank.py [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 q1_utils.py.
○ 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:
● util.py: A file containing utility functions that will help you build a decision tree.
● decision_tree.py: A file containing a decision tree class that you will use to build your random
● random_forest.py: A file containing a random forest class and a main to test your random
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 util.py, decision_tree.py, and random_forest.py. The
functions in util.py 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
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. util.py: The utility functions you need to implement.
3. decision_tree.py: The source code for your decision tree implementation.
4. random_forest.py: The source code of your random forest implementation with detailed
comments for your code.
● Specific the implementation steps of the random forest and why you choose the
specific approach (<75 words) ● Report the OOB estimate. 8 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
J48 -C 0.25 -M 2
Time taken to build model: 3.73 seconds
Overall accuracy: 86.0675 %
a b <– classified as
33273 2079 | a = no
4401 6757 | b = yes
1. The result of Weka is 86.1% compared to my result because…
2. I choose which is …
Submit the deliverables as a single zip file named hw4-LastName-FirstName.zip (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):
You must follow the naming convention specified above.