COMP9312代做、Java/c++编程设计代写
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Analytics for Graphs
Assignment 2
Distributed Graph Processing, Feature Engineering,
and Graph Neural Networks
Important updates:
Update @ 25 Jul 2024
Fix the error or the weight matrix W and make the GAT layer
formulation clearer in Q2.1.
Summary
Submission Submit an electronic copy of all answers on Moodle
(Only the last submission will be used).
Required
Files
A .pdf file is accepted. The file name should be
ass2_zid.pdf
Deadline 9 pm Friday 2 August (Sydney Time)
Marks 20 marks (10% toward your total marks for this
course)
Late penalty. 5% of max assessment marks will be deducted for each
additional day (24 hours) after the specified submission time and date.
No submission is accepted 5 days (120 hours) after the deadline.
START OF QUESTIONS
Q1 (3 marks)
2024/7/25 11:34 COMP9312 24T2 Assignment 2
https://cgi.cse.unsw.edu.au/~cs9312/24T2/assignment/ass2/ 1/5
Figure 1
Figure 2 Figure 3
1.1 Are the graphs in Figure 1 and Figure 2 homomorphic? If so,
demonstrate a matching instance. (1 mark)
1.2 Present all unique subgraphs in Figure 1 that are isomorphic to the
graph in Figure 3. For example, { }, {
}, and { } are all considered as
the same subgraph 123. (2 marks)
Marking for Q1.1: 1 mark is given for the correct answer. 0 mark is
given for all other cases.
Marking for Q1.2: 2 marks are given if the result subgraphs are
correct, complete, and not redundant. Extra subgraphs and missing
subgraphs will result in a loss of marks.
Q2 (5 marks)
2.1 Given an undirected graph as shown in Figure 4,
Figure 4
we aim to compute the output of the first graph convolutional layer
with self-loops using the Graph Attention Network (GAT) model. The
goal is to transform the initial node embeddings from a dimension of 4
to a dimension of 5 through this layer. The equation can be written as:
v1 : 1, v2 : 2, v3 : 3
v1 : 2, v2 : 1, v3 : 3 v1 : 3, v2 : 1, v3 : 2
H 1
2024/7/25 11:34 COMP9312 24T2 Assignment 2
https://cgi.cse.unsw.edu.au/~cs9312/24T2/assignment/ass2/ 2/5
where indicates the -dimensional embedding of node in layer ,
and . is the
weighting factor of node 's message to node .
denotes the weight matrix for the neighbours of in layer , denotes
the dimension of the node embedding in layer . denotes the
non-linear function. The initial embedding for all nodes is
stacked in . is the weight matrices. Self-loops are included in
the calculation to ensure that the node's information is retained.
Therefore, the term is added to its set of neighbors, which can be
expressed as . Round the values to 2 decimal places (for
example, 3.333 will be rounded to 3.33 and 3.7571 will be rounded to
3.76). (3 marks)
2.2 Please determine whether the following statements are TRUE or
FALSE. (2 marks)
a. Skip-connections is a good technique used to alleviate over-
smoothing.
b. To design a model for predicting dropout on a course website, we
represent it as a bipartite graph where nodes indicate students or
courses. The task here is considered as node classification.
c. Graph Attention Network (GAT) has less expressive power
compared to GCN, as it computes the attention score between
each pair of neighbors, which introduces extra computational
complexity.
d. The main difference between GraphSAGE and GCN is that
GraphSAGE needs an activation function to add nonlinearity.
Marking for Q2.1: 3 marks are given for the correct result. Incorrect
values will result in a deduction of marks. Providing a detailed and
correct description of the calculation will earn marks for a valid
attempt, even if there are major mistakes in the result.
Marking for Q2.2: 0.5 mark is given for each correct TRUE/FALSE
answer.
Q3 (8 marks)
h(l)v =
u N(v) {v}
vuW (l)h
(l?1)
hlv dl v l
H l = [hlv1, h
l
v2, h
l
v3, h
l
v4, h
l
v5, h
l
v6]
T avu = 1|N(v) {v}|
u v W (l) Rdl?dl?1
v l dl
l (?)
ReLU
H 0 W 1
v
{v} N(v)
H 0 =
2024/7/25 11:34 COMP9312 24T2 Assignment 2
https://cgi.cse.unsw.edu.au/~cs9312/24T2/assignment/ass2/ 3/5
Figure 5
Suppose we aim to count the number of shortest paths from a source
vertex to all other vertices in an undirected unweighted graph shown
using Pregel.
3.1 Write the pseudocode for the compute implementation in Pregel. (3
marks)
3.2 Assume we run your algorithm with the source node 1 for the graph
in Figure 5 on three workers. Vertices 1 and 5 are in worker X. Vertices
2 and 4 are in worker Y. Vertices 3, 6 and 7 are in worker Z. Please
indicate the set of active vertices and how many messages are sent in
each iteration. (3 marks)
3.3 Can the combiner optimization be used in this case? If yes, write
the pseudocode for a combiner implementation. Calculate how many
messages are sent in each iteration if the combiner is used in 3.2. If no,
briefly discuss why a combiner cannot be used. (2 marks)
Marking for Q3.1: 3 marks are given for the correct answer. 0 mark is
given for all other cases.
Marking for Q3.2: 2 marks are given for the correct answer. 0 mark is
given for all other cases.
Marking for Q3.3: 3 marks are given for the correct answer. 0 mark is
given for all other cases.
Q4 (4 marks)
Consider the graph in Figure 6,
2024/7/25 11:34 COMP9312 24T2 Assignment 2
https://cgi.cse.unsw.edu.au/~cs9312/24T2/assignment/ass2/ 4/5
Figure 6
Figure 7
4.1 Compute the betweenness centrality and closeness centrality of
nodes C and H in Figure 6. Round the values to 2 decimal places (for
example, 3.333 will be rounded to 3.33 and 3.7571 will be rounded to
3.76). (2 marks)
4.2 Given the graphlets in Figure 7, derive the graphlet degree vector
(GDV) for nodes A and G. Note that only the induced matching
instances are considered in GDV. (2 marks)
Marking for Q4.1: 1 mark is given for correct betweenness centrality
values. 1 mark is given for correct closeness centrality values.
Marking for Q4.2: 1 mark is given for each correct vector. Incorrect
values in each vector will result in a deduction of marks.
END OF QUESTIONS
2024/7/25 11:34 COMP9312 24T2 Assignment 2
https://cgi.cse.unsw.edu.au/~cs9312/24T2/assignment/ass2/ 5/5
Analytics for Graphs
Assignment 2
Distributed Graph Processing, Feature Engineering,
and Graph Neural Networks
Important updates:
Update @ 25 Jul 2024
Fix the error or the weight matrix W and make the GAT layer
formulation clearer in Q2.1.
Summary
Submission Submit an electronic copy of all answers on Moodle
(Only the last submission will be used).
Required
Files
A .pdf file is accepted. The file name should be
ass2_zid.pdf
Deadline 9 pm Friday 2 August (Sydney Time)
Marks 20 marks (10% toward your total marks for this
course)
Late penalty. 5% of max assessment marks will be deducted for each
additional day (24 hours) after the specified submission time and date.
No submission is accepted 5 days (120 hours) after the deadline.
START OF QUESTIONS
Q1 (3 marks)
2024/7/25 11:34 COMP9312 24T2 Assignment 2
https://cgi.cse.unsw.edu.au/~cs9312/24T2/assignment/ass2/ 1/5
Figure 1
Figure 2 Figure 3
1.1 Are the graphs in Figure 1 and Figure 2 homomorphic? If so,
demonstrate a matching instance. (1 mark)
1.2 Present all unique subgraphs in Figure 1 that are isomorphic to the
graph in Figure 3. For example, { }, {
}, and { } are all considered as
the same subgraph 123. (2 marks)
Marking for Q1.1: 1 mark is given for the correct answer. 0 mark is
given for all other cases.
Marking for Q1.2: 2 marks are given if the result subgraphs are
correct, complete, and not redundant. Extra subgraphs and missing
subgraphs will result in a loss of marks.
Q2 (5 marks)
2.1 Given an undirected graph as shown in Figure 4,
Figure 4
we aim to compute the output of the first graph convolutional layer
with self-loops using the Graph Attention Network (GAT) model. The
goal is to transform the initial node embeddings from a dimension of 4
to a dimension of 5 through this layer. The equation can be written as:
v1 : 1, v2 : 2, v3 : 3
v1 : 2, v2 : 1, v3 : 3 v1 : 3, v2 : 1, v3 : 2
H 1
2024/7/25 11:34 COMP9312 24T2 Assignment 2
https://cgi.cse.unsw.edu.au/~cs9312/24T2/assignment/ass2/ 2/5
where indicates the -dimensional embedding of node in layer ,
and . is the
weighting factor of node 's message to node .
denotes the weight matrix for the neighbours of in layer , denotes
the dimension of the node embedding in layer . denotes the
non-linear function. The initial embedding for all nodes is
stacked in . is the weight matrices. Self-loops are included in
the calculation to ensure that the node's information is retained.
Therefore, the term is added to its set of neighbors, which can be
expressed as . Round the values to 2 decimal places (for
example, 3.333 will be rounded to 3.33 and 3.7571 will be rounded to
3.76). (3 marks)
2.2 Please determine whether the following statements are TRUE or
FALSE. (2 marks)
a. Skip-connections is a good technique used to alleviate over-
smoothing.
b. To design a model for predicting dropout on a course website, we
represent it as a bipartite graph where nodes indicate students or
courses. The task here is considered as node classification.
c. Graph Attention Network (GAT) has less expressive power
compared to GCN, as it computes the attention score between
each pair of neighbors, which introduces extra computational
complexity.
d. The main difference between GraphSAGE and GCN is that
GraphSAGE needs an activation function to add nonlinearity.
Marking for Q2.1: 3 marks are given for the correct result. Incorrect
values will result in a deduction of marks. Providing a detailed and
correct description of the calculation will earn marks for a valid
attempt, even if there are major mistakes in the result.
Marking for Q2.2: 0.5 mark is given for each correct TRUE/FALSE
answer.
Q3 (8 marks)
h(l)v =
u N(v) {v}
vuW (l)h
(l?1)
hlv dl v l
H l = [hlv1, h
l
v2, h
l
v3, h
l
v4, h
l
v5, h
l
v6]
T avu = 1|N(v) {v}|
u v W (l) Rdl?dl?1
v l dl
l (?)
ReLU
H 0 W 1
v
{v} N(v)
H 0 =
2024/7/25 11:34 COMP9312 24T2 Assignment 2
https://cgi.cse.unsw.edu.au/~cs9312/24T2/assignment/ass2/ 3/5
Figure 5
Suppose we aim to count the number of shortest paths from a source
vertex to all other vertices in an undirected unweighted graph shown
using Pregel.
3.1 Write the pseudocode for the compute implementation in Pregel. (3
marks)
3.2 Assume we run your algorithm with the source node 1 for the graph
in Figure 5 on three workers. Vertices 1 and 5 are in worker X. Vertices
2 and 4 are in worker Y. Vertices 3, 6 and 7 are in worker Z. Please
indicate the set of active vertices and how many messages are sent in
each iteration. (3 marks)
3.3 Can the combiner optimization be used in this case? If yes, write
the pseudocode for a combiner implementation. Calculate how many
messages are sent in each iteration if the combiner is used in 3.2. If no,
briefly discuss why a combiner cannot be used. (2 marks)
Marking for Q3.1: 3 marks are given for the correct answer. 0 mark is
given for all other cases.
Marking for Q3.2: 2 marks are given for the correct answer. 0 mark is
given for all other cases.
Marking for Q3.3: 3 marks are given for the correct answer. 0 mark is
given for all other cases.
Q4 (4 marks)
Consider the graph in Figure 6,
2024/7/25 11:34 COMP9312 24T2 Assignment 2
https://cgi.cse.unsw.edu.au/~cs9312/24T2/assignment/ass2/ 4/5
Figure 6
Figure 7
4.1 Compute the betweenness centrality and closeness centrality of
nodes C and H in Figure 6. Round the values to 2 decimal places (for
example, 3.333 will be rounded to 3.33 and 3.7571 will be rounded to
3.76). (2 marks)
4.2 Given the graphlets in Figure 7, derive the graphlet degree vector
(GDV) for nodes A and G. Note that only the induced matching
instances are considered in GDV. (2 marks)
Marking for Q4.1: 1 mark is given for correct betweenness centrality
values. 1 mark is given for correct closeness centrality values.
Marking for Q4.2: 1 mark is given for each correct vector. Incorrect
values in each vector will result in a deduction of marks.
END OF QUESTIONS
2024/7/25 11:34 COMP9312 24T2 Assignment 2
https://cgi.cse.unsw.edu.au/~cs9312/24T2/assignment/ass2/ 5/5