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CISC 271, Winter 2021

Assignment #1: Binary Clustering of Graph Vertices

Due by 11:30AM on Friday, January 22, 2021

Please read the details and instructions carefully before you begin to work on the problem.

The question in this assignment is relatively straightforward because it is intended to be a practical

introduction to MATLAB and to writing a report in this course. There must be a single results section

and a single discussion section on your report. The results section of the report must contain one

table and one figure; more of either, or fewer tables, will produce deductions from your grade on

this assignment.

Statement of Academic Integrity

This assignment is copyrighted by the instructor, so unauthorized dissemination of this assign-

ment may be a violation of copyright law and may constitute a departure from academic integrity.

Sharing of all or part of a solution to this assignment, whether as code or as a report, will be

interpreted as a departure from academic integrity. This includes sharing of the assignment after

the due date and after completion of this course.

Learning Outcomes

On completion, a successful student will be able to:

• Use for loops in MATLAB

• Transform an edge list to an adjacency matrix and a Laplacian matrix

• Use the Fiedler vector to assign vertices in a graph to one of two clusters

Question 1: Graph Clustering 4% of Final Grade

As described in the course notes, the Fiedler vector of a Laplacian matrix of a graph can be

used to cluster the vertices of a graph into two sets. Set 1 contains the indices of vertices that have

a negative Fiedler entry and Set 2 contains the indices of vertices that have a positive Fiedler entry.

The problem is: given an edge list, use a for loop to create a Laplacian matrix for the graph

and then cluster the vertices of the graph. The input is an array in which each row is a pair of

integers that index the list of vertices. The output is a vector that indicates the clustering of the

vertices, in which each entry is -1 for Set 1 and +1 for Set 2.

For this problem, you will need to modify the instructor’s “starter” code that is in the accompa-

nying ZIP file. The starter code will return a constant clustering vector, intended to act as a guide

for you in learning how a MATLAB function can return values.

For testing, a randomly generated graph has been provided. Diagrams of the test graph are

shown in Figure 1. There are two files that you can use to test your code:testedge.txt contains

edges of the graph, and testsets.txt contains the correct set vector. You can check your

results, replacing xxxxxxxx with your student number, using the MATLAB commands

load(’testedge.txt’);

a1 xxxxxxxx(testedge)

Figure 1: Diagrams of the test graph. The upper part shows the graph in a rectilinear grid. The

lower part shows the graph when plotted according to a computed clustering of the vertices.

The clustering vector has entries ±1, which is useful for checking your code but which is less

useful for a human reader. The clusters of the vertices for the test graph are shown in Table 1.

Table 1: Clusters of vertices for the test graph. Each row contains the vertices of the cluster.

Set Vertices

1 1 2 6 8 9 13 14 15 18 19

2 3 4 5 7 10 11 12 16 17 20

Grading Guide:

We will test your code on your individual, randomly generated edge list. The edges for ev-

eryone are in the file a1files.zip; your data file is coded as your Queen’s netid as indicated

in onQ. A correct clustering of “your” graph will be part of your grade for this assignment. This

means that your single figure should be the diagram produced for your individual edge list, and

your single table should be the clustering of vertices for your individual edge list.

The TA’s have been instructed to use this guide when they mark your assignment. Your grade

will be based on the numerical results and on the report. The distribution of points for the assign-

ment grade are:

4/16 points: numerical values that are produced by the code and that are presented in the results

4/16 points: quality of the code in the modified “starter” functions, and any other changes in

the submission file that was used to generate values and plots for the report

8/16 points: quality of the report, especially including the figures and descriptions; clarity may

be assessed, in part, by the written discussion of results

2

CISC271: 2021

Grading Considerations

• The quality of your report will be considered. You need, at minimum, to conform to the

“student version” of the report style in the onQwebsite; you maywish to consider the “grader

version” that we will use for assessing your report.

• The quality of your MATLAB code will be considered. Your code should be appropriately

indented, sufficiently commented, and otherwise be appropriate software.

• The output of your code will be considered.

• Your code can use functions provided by MATLAB, but the code that you submit must be your

original work. You may not use any builtin functions that perform optimization or clustering

such as k-means, although you may wish to use such functions as you develop and test your

software.

• Code that causes MATLAB to produce an error or warning will result in a failing grade.

What to turn in:

• You will submit your answers electronically as two files. The code will be tested by one

or more graders. The PDF report will be read by one or more graders and will be checked,

using electronic methods, to ensure that it meets professional standards for originality.

• The code must be in one MATLAB file (a1 xxxxxxxx.m). This file will contain all of

the code needed to verify that the values and tables in the report can be reproduced. The

functions must produce the values for your table and for each figure.

• Your functions must take one argument, return one value, and require no user input or ac-

tion such as using the “enter” key. Running this function should produce, on the console,

every value that is in the report; the function should also produce every plot that is in your

report, each plot in a separate figure. The function should produce no other values or figures.

The graders will compare your computed values to the values in the report and may deduct

marks from the report for differences between any reported value/plot and the corresponding

computed value/plot.

• The report must be in a single PDF file (a1 xxxxxxxx.pdf). The PDF file must include

a description of how you tested your code. You can also include notes, comments on the

problems, and assumptions you have made, as appropriate.

• The assignment must be submitted using the Queen’s “onQ” software.

Policies:

• You must complete these questions individually.

• Although you are allowed to discuss the questions with other students, you must write your

own answers and MATLAB code.

• The syllabus standards apply to this assignment.

• Lateness policy applies starting the minute after the submission deadline, at a rate of 20%

off the assignment value per calendar day. Please note: the time in the onQ system is beyond

your control, so submitting within an hour of the deadline is inherently a risky process for

which you assume full responsibility.

3

CISC271: 2021

Assignment #1: Binary Clustering of Graph Vertices

Due by 11:30AM on Friday, January 22, 2021

Please read the details and instructions carefully before you begin to work on the problem.

The question in this assignment is relatively straightforward because it is intended to be a practical

introduction to MATLAB and to writing a report in this course. There must be a single results section

and a single discussion section on your report. The results section of the report must contain one

table and one figure; more of either, or fewer tables, will produce deductions from your grade on

this assignment.

Statement of Academic Integrity

This assignment is copyrighted by the instructor, so unauthorized dissemination of this assign-

ment may be a violation of copyright law and may constitute a departure from academic integrity.

Sharing of all or part of a solution to this assignment, whether as code or as a report, will be

interpreted as a departure from academic integrity. This includes sharing of the assignment after

the due date and after completion of this course.

Learning Outcomes

On completion, a successful student will be able to:

• Use for loops in MATLAB

• Transform an edge list to an adjacency matrix and a Laplacian matrix

• Use the Fiedler vector to assign vertices in a graph to one of two clusters

Question 1: Graph Clustering 4% of Final Grade

As described in the course notes, the Fiedler vector of a Laplacian matrix of a graph can be

used to cluster the vertices of a graph into two sets. Set 1 contains the indices of vertices that have

a negative Fiedler entry and Set 2 contains the indices of vertices that have a positive Fiedler entry.

The problem is: given an edge list, use a for loop to create a Laplacian matrix for the graph

and then cluster the vertices of the graph. The input is an array in which each row is a pair of

integers that index the list of vertices. The output is a vector that indicates the clustering of the

vertices, in which each entry is -1 for Set 1 and +1 for Set 2.

For this problem, you will need to modify the instructor’s “starter” code that is in the accompa-

nying ZIP file. The starter code will return a constant clustering vector, intended to act as a guide

for you in learning how a MATLAB function can return values.

For testing, a randomly generated graph has been provided. Diagrams of the test graph are

shown in Figure 1. There are two files that you can use to test your code:testedge.txt contains

edges of the graph, and testsets.txt contains the correct set vector. You can check your

results, replacing xxxxxxxx with your student number, using the MATLAB commands

load(’testedge.txt’);

a1 xxxxxxxx(testedge)

Figure 1: Diagrams of the test graph. The upper part shows the graph in a rectilinear grid. The

lower part shows the graph when plotted according to a computed clustering of the vertices.

The clustering vector has entries ±1, which is useful for checking your code but which is less

useful for a human reader. The clusters of the vertices for the test graph are shown in Table 1.

Table 1: Clusters of vertices for the test graph. Each row contains the vertices of the cluster.

Set Vertices

1 1 2 6 8 9 13 14 15 18 19

2 3 4 5 7 10 11 12 16 17 20

Grading Guide:

We will test your code on your individual, randomly generated edge list. The edges for ev-

eryone are in the file a1files.zip; your data file is coded as your Queen’s netid as indicated

in onQ. A correct clustering of “your” graph will be part of your grade for this assignment. This

means that your single figure should be the diagram produced for your individual edge list, and

your single table should be the clustering of vertices for your individual edge list.

The TA’s have been instructed to use this guide when they mark your assignment. Your grade

will be based on the numerical results and on the report. The distribution of points for the assign-

ment grade are:

4/16 points: numerical values that are produced by the code and that are presented in the results

4/16 points: quality of the code in the modified “starter” functions, and any other changes in

the submission file that was used to generate values and plots for the report

8/16 points: quality of the report, especially including the figures and descriptions; clarity may

be assessed, in part, by the written discussion of results

2

CISC271: 2021

Grading Considerations

• The quality of your report will be considered. You need, at minimum, to conform to the

“student version” of the report style in the onQwebsite; you maywish to consider the “grader

version” that we will use for assessing your report.

• The quality of your MATLAB code will be considered. Your code should be appropriately

indented, sufficiently commented, and otherwise be appropriate software.

• The output of your code will be considered.

• Your code can use functions provided by MATLAB, but the code that you submit must be your

original work. You may not use any builtin functions that perform optimization or clustering

such as k-means, although you may wish to use such functions as you develop and test your

software.

• Code that causes MATLAB to produce an error or warning will result in a failing grade.

What to turn in:

• You will submit your answers electronically as two files. The code will be tested by one

or more graders. The PDF report will be read by one or more graders and will be checked,

using electronic methods, to ensure that it meets professional standards for originality.

• The code must be in one MATLAB file (a1 xxxxxxxx.m). This file will contain all of

the code needed to verify that the values and tables in the report can be reproduced. The

functions must produce the values for your table and for each figure.

• Your functions must take one argument, return one value, and require no user input or ac-

tion such as using the “enter” key. Running this function should produce, on the console,

every value that is in the report; the function should also produce every plot that is in your

report, each plot in a separate figure. The function should produce no other values or figures.

The graders will compare your computed values to the values in the report and may deduct

marks from the report for differences between any reported value/plot and the corresponding

computed value/plot.

• The report must be in a single PDF file (a1 xxxxxxxx.pdf). The PDF file must include

a description of how you tested your code. You can also include notes, comments on the

problems, and assumptions you have made, as appropriate.

• The assignment must be submitted using the Queen’s “onQ” software.

Policies:

• You must complete these questions individually.

• Although you are allowed to discuss the questions with other students, you must write your

own answers and MATLAB code.

• The syllabus standards apply to this assignment.

• Lateness policy applies starting the minute after the submission deadline, at a rate of 20%

off the assignment value per calendar day. Please note: the time in the onQ system is beyond

your control, so submitting within an hour of the deadline is inherently a risky process for

which you assume full responsibility.

3

CISC271: 2021