Suppose we apply graph convolutional networks (GCNs) on grid-like graphs (e.g., images) without normalizing adjacency matrix (i.e.,
Question:
Suppose we apply graph convolutional networks (GCNs) on grid-like graphs (e.g., images) without normalizing adjacency matrix (i.e., removing Steps 2-3 in Fig. 10.38). Explain why it is essentially a 2 -D convolution with a special type of filters.
Transcribed Image Text:
Input: A, adjacency matrix of the input graph of size n x n; X, the node attribute matrix of size n x d; w (L= 1,..., L), the weight matrix at each layer; L, the number of layers; f, nonlinear activation function (e.g., sigmoid or ReLU function). . Output: The node embedding matrices Z (1 = 1, ..., L). Method: //Preprocessing and Initialization (1) Add a self-edge for each node: A A+ I where I is an identity matrix; (2) Calculate the degree matrix D of A; (3) Normalize = D-1/2AD-1/2, (4) Initialize z0 = X; (5) for (/= 1,..., L){ // for each layer of GCNs //Propagation (6) (7) -AZ-1: // aggregate the neighboring embedding = //Linear Transformation 2 2w; // linear transformation of aggregated embedding //Nonlinear activation z = f(2'); // nonlinear activation of linearly transformed embedding } (8) (9) FIGURE 10.38
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (QA)
Suppose the dimensions of input feature map and output feature map are p q respectively then t...View the full answer
Answered By
Mary Njunu
I posses Vast, diversified knowledge and excellent grammar as a result of working in ACADEMIC WRITING for more than 5 years. I deliver work in various disciplines with assurance of quality work. I purpose at meeting the clients’ expectations precisely. Let’s work together for the best and phenomenal grades.
4.90+
928+ Reviews
2551+ Question Solved
Related Book For
Data Mining Concepts And Techniques
ISBN: 9780128117613
4th Edition
Authors: Jiawei Han, Jian Pei, Hanghang Tong
Question Posted:
Students also viewed these Computer science questions
-
In this exercise, we will derive the graph convolutional networks shown in Sec. 10.5.2 from spectral graph signal processing perspective. The classic convolution on graphs can be computed by y = U g ...
-
In the chapter, we discussed the deadweight loss from taxes on consumption goods when tastes are quasilinear in the taxed good, and we treated deadweight loss when tastes are not quasilinear for the...
-
Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...
-
Mario and Kaitlin are married and file a joint tax return. They have adjusted gross income of $385,000 that includes $4,700 of investment income ($3,000 short-term capital gains and $1,700 of...
-
Determine by direct integration the moment of inertia of the shaded area with respect to the x axis. be
-
1. Do you think the Court would have found the union in violation of the Sherman Antitrust Act if the price of hosiery had been affected by the strike? 2. The dissenting judge felt the Court's...
-
The following MINITAB output presents a multiple regression equation y = b0 + b1x1 + b2x2 + b3x3 + b4x4 + b5x5. It is desired to drop one of the explanatory variables. Which of the following is the...
-
Refer to the preceding facts for Postmans acquisition of 80% of Spartans common stock and the bond transactions. Postman uses the simple equity method to account for its investment in Spartan. On...
-
2. Let S be the portion of the surface x-2x + y + z = 8 for 1z2. Find the area of the surface S. Surface integral formula: 9(x,y,z)d = {f9[x, y, z(x, y)] 2 of 1+ (0) of + 2 dA, for the surface given...
-
In this exercise, we aim to implement and learn the graph convolutional networks (GCNs) shown in Fig. 10.38. Specifically, we apply a two-layer GCN for semisupervised node classification on Cora data...
-
LSTM and GRU Compare LSTM with GRU, and answer the following questions: a. What do they have in common? b. What are the differences between them? c. What are the pros and cons of them?
-
The parallel-plate capacitor in Figure Q26.11 is connected to a battery having potential difference ÎV bat . Without breaking any of the connections, insulating handles are used to increase the...
-
Task 1 Task 2 a = 1, when the exponent on a increases, the power itself increases, provided a is greater than 1. It follows that if the exponent is infinitely small and positive, then the power also...
-
Given an array of 20 elements 10, 21, 0, 41, 24, 9, 29, 0, 90, 85, 77, 56, 62, 17, 0, 33, 23, 44, 50, 52. Complete the program to print the total number of odd numbers in the array and even numbers...
-
Current Attempt in Progress Amy Dyken, controller at Crane Pharmaceutical Industries, a public company, is currently preparing the calculation for basic and diluted earnings per share and the related...
-
(a) Calculate the negative number of 01012 using 2's complement representation. (b) Calculate the negative number of 01012 using sign magnitude representation. (c) 10002 is written in 2's complement...
-
Prepare a formal letter to each of the property owners and issue along with their monthly statements. Prepare an informal letter and a copy of the statements for the principal of the agency.
-
Kays Beauty Supply uses the gross profit method to estimate the cost of ending inventory for in-house interim financial statements. Based on the following information for March, calculate Kays Beauty...
-
On October 1, 2014, the Dow Jones Industrial Average (DJIA) opened at 17,042 points. During that day it lost 237 points. On October 2 it lost 4 points. On October 3 it gained 209 points. Deter-mine...
-
If w is a (k- 1) -form on a compact k-dimensional manifold M, prove that Mdw =0. Give a counter-example if M is not compact.
-
An absolute k-tensor on v is a function Vk R of the form |w| for w Є Ak (V). An absolute k-form on M is a function such that n (x) is an absolute k-tensor on Mx. Show that Mn can be defined,...
-
If M1CRN is an -dimensional manifold-with-boundary and M 2 C M1 - M1 is an -dimensional manifold with boundary, and M1, M2 are compact, prove that
-
Andretti Company has a single product called a Dak. The company normally produces and sells 8 4 , 0 0 0 Daks each year at a selling price of $ 5 8 per unit. The company s unit costs at this level of...
-
This article indicates that the popular 2022 Tesla Y has had above average reliability and quality issues. The article does not recomend consumers purchase that Tesla. The same article suggests that...
-
Stokel-Walker, C. HP wins huge fraud case against autonomy's Mike Lynch. Wired. Retrieved from https://www.wired.com/story/mike-lynch-autonomy-extradition/ This can also be found on the ACFE.com home...
Study smarter with the SolutionInn App