Research on the Improvement of Link Prediction Algorithm and Its

Application in Industrial Structure Adjustment

Junhua Rao

Shandong Institute of Commerce and Technology, Jinan, China

Keywords: Complex Network, Link Prediction, Industrial Network, Path Optimization.

Abstract: The adjustment and establishment of a rational industrial structure is aimed at promoting economic

development and improving the people's material and cultural living standards. The main indicator of the

rationality of the industrial structure is the rational use of resources, so that various industrial sectors can

coordinate the provision of products and services needed by society; provide opportunities for full

employment of workers; promote the application of advanced industrial technology; get the best economic

benefits, etc. The link prediction similarity algorithm is improved, and a new link prediction algorithm is

proposed, which is applied to the industrial structure adjustment strategy of China's new normal economy,

taking the input-output relationship between departments as the research object, and adjusting and optimizing

the network structure based on the link prediction method. In the research of industrial network, this paper

first analyzes the economic development of China from a horizontal static perspective by combining

geographic information and statistical theory, constructs an interregional industrial network structure model

based on the input and output data of the selected main functional area, and finally applies the newly proposed

link prediction algorithm to the industrial network model, and obtains the optimization direction of the

network structure.

1 INTRODUCTION

In recent years, due to the continuous in-depth

development of Internet technology, networking is

reflected in all aspects of people's lives. The

prominent networking characteristics have prompted

people to start studying and analyzing entities from

the perspective of networks. The network analysis

method provides a methodological and theoretical

basis for studying complex network relationships in

the real world (Chen, Z. 2021). The economic input-

output system can be constructed into an industrial

network structure, with nodes representing various

industrial sectors in the system, and edges

representing the input-output relationship between

departments. The network analysis method can

predict the demand relationship between

departments, propose future development strategies,

coordinate and unify the development of industrial

networks, promote regional economic restructuring,

and enable each region to continuously realize the

optimal allocation of resources on the basis of its own

resource endowments, so as to continuously improve

the overall economic benefits of the region (Jiang, Z.

Y. 2021). Under the influence of the new normal

economy, industrial structure adjustment is a major

strategic direction in China today, the most critical is

to form a new engine of innovation-driven economic

growth, that is, to explore an effective industrial

transfer path, this process shows strong dynamics and

complexity (Li, Z 2019).

Link prediction is one of the important tasks in

network analysis methods, which can be used for

mining and predicting network relationships, and it

has important application value in various fields (Ma,

Y. X. 2023). For example, biological networks,

economic networks, social networks, e-commerce

networks, and so on. In biological metabolic

networks, link prediction algorithms can predict the

interaction between proteins (4). In the economic

network, input-output data can be used to construct a

complex network of regional industries, reflect the

influence and vulnerability of industrial sectors in the

industrial chain through network feature values, and

analyze industrial transfer according to link

prediction theory, so as to provide new ideas for

industrial transfer research (Park, J. H.- Sun, W.). The

link prediction algorithm can predict the evolution

characteristics of different network structures, grasp

the dynamic trend of the network, and predict the

Rao, J.

Research on the Improvement of Link Prediction Algorithm and Its Application in Industrial Structure Adjustment.

DOI: 10.5220/0012273600003807

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 2nd International Seminar on Artiﬁcial Intelligence, Networking and Information Technology (ANIT 2023), pages 46-50

ISBN: 978-989-758-677-4

similarity between nodes. There are many similarity

measures for link prediction, but they all have

different application scenarios (Wu, J. H. 2017). In

the process of industrial adjustment, how to

determine the optimal industrial transfer path requires

the analysis of the overall structural characteristics of

the input-output network from the macro and micro

perspectives, so as to determine the expression of its

optimal similarity measurement (Xu, Z. Q. 2017).

Therefore, link prediction can provide a clear reform

direction for the adjustment of industrial structure,

coordinated development between departments and

optimization of industrial path in different regions,

and has a scientific role in promoting the

implementation of economic policies (Yoon, B.-Yu,

Y.).

Link prediction is to use the characteristics of

nodes and network structure to predict the similarity

between nodes, and then predict the unknown

relationship between nodes or the relationship that

may occur in the future (Yuan, W. W. 2019). Through

literature combing, it is found that the research of link

prediction algorithm mainly focuses on algorithm

improvement, structure evolution inference and

recommendation system application. In the direction

of algorithm improvement, predicting unknown

edges between nodes and possible future edges based

on node similarity has always occupied an important

position with low complexity and high accuracy.

Node-based similarity is initially studied only based

on the similarity of node attributes, that is, if two

nodes are close in multiple feature dimensions, the

more similar the two nodes are. An important premise

of this approach is that the greater the similarity

between two nodes, the more likely it is that there will

be a link between them (Chen, Z. Y. 2021). Therefore,

how to define the similarity of nodes has become a

core problem of the method. Although this

framework is very simple, the definition of similarity

itself is rich in meaning, from a very simple number

of common neighbors to a complex mathematical

physics such as the average communication time of

random walks, or a matrix forest method based on

graph theory. So this simple framework offers in fact

endless possibilities. Since the local path index only

considers the local information of the network, its

calculation amount is much smaller than the index

based on global information, especially in the case of

large and sparse network scale, the advantages of

local path index in computational complexity are

more obvious, so its application prospect is

considerable.

On the one hand, hindered by the difficulty of

obtaining the external attributes of network nodes,

and on the other hand, benefiting from the rapid

development of complex network research, the main

research focus of link prediction problems has

gradually shifted from the method of relying on node

attributes to the method of only using network

structure information (Jiang, Z. Y. 2021). Obviously,

the latter is also more beautiful and concise in theory.

However, research in this area mainly focuses on

social networks, and the systematic analysis of the

predictive power of a large number of algorithms in

various networks is not yet summarized. In addition,

there is no in-depth study of the relationship between

algorithm performance and network structure

features. Discussions of more complex networks,

such as rights-based, directed and multipart networks,

are rare and unsystematic. Relevant research should

be the mainstream in this direction in recent years (Li,

Z. 2019).

Network ensemble theory and the associated

concept of network entropy and the maximum

likelihood estimation method are expected to promote

the formation of the theoretical basis of statistical

mechanics for complex networks. One problem with

this research is that the exact computational

complexity of entropy is very large, and it is often not

possible for large-scale networks. Some recent link

prediction algorithms have applied the concepts of

network ensemble and maximum likelihood, but

these algorithms are computationally complex and

not very accurate, and currently can only process

networks with thousands of nodes, and their

prediction effect is not good for networks without

clear hierarchies. At present, the relevant

international research groups are concerned about:

first, how to establish a theoretical framework for

network link prediction based on network ensemble

theory, and produce theoretical conclusions that have

a guiding effect on actual prediction, such as

estimating the predictable limit through statistical

analysis of network structure, guiding the selection of

different prediction methods, etc.; The second is how

to design efficient algorithms to deal with link

prediction problems in large-scale networks.

2 LINK PREDICTION

ALGORITHM

Link prediction is one of the important bridges

linking complex networks with information science,

and it deals with the most basic problem in

information science, the restoration and prediction of

missing information. The research on link prediction

Research on the Improvement of Link Prediction Algorithm and Its Application in Industrial Structure Adjustment

can not only promote the theoretical development of

network science and information science, but also has

great practical application value, such as knowing

protein interaction experiments, conducting online

social recommendations, and finding out the

connections that play a particularly important role in

transportation transmission networks.

The classic triadic closure principle in social network

analysis states that if A and B have a common friend

C, then the two people are likely to become friends in

the future, so that the three nodes form a closed

triangle ABC. For general networks, we can

generalize this principle as follows: the more

neighbors two nodes have, the more similar the two

nodes are, and thus the more inclined they are to

connect to each other. The simplest node similarity

metric based on Common neighbors is defined as

follows:

𝑠







𝛤



𝑥

|

∩

𝛤



𝑦

|

(1)

The advantage of the similarity index based on

common neighbor is that the computational

complexity is low, but due to the very limited

information used, the prediction accuracy is limited,

so there are three path-based similarity indicators,

which are local path, Katz index and LHN-II index.

A. Local Path Indicators

Consider the factors of the third-order path on the

basis of common neighbors, based on the similarity

index of the local path, which is defined as：

𝑆𝐴



𝛼𝐴



(2)

where α are tunable parameters, A represents the

adjacency matrix of the network, and α 𝐴







represents the number of paths with length 3 between

nodes Vx and Vy. When α = 0, the LP indicator

degenerates into a CN indicator. The CN indicator

can also be considered path-based in nature, except

that it only takes into account the number of second-

order paths. The local path indicator can be extended

to higher-order cases, i.e. when considering n-order

paths:

𝑆



𝐴



𝛼⋅𝐴



𝛼



⋅𝐴



⋯𝛼



⋅𝐴



(3)

As n increases, the computational complexity of

the local path indicator increases. In general, consider

the computational complexity of nth-order paths

O(N<k>^n). However, when n tends to infinity, the

local path indicator is equivalent to the Katz indicator

considering all the paths of the network, and the

amount of computation may decrease, because it can

be converted into the inverse of the calculation matrix.

B. Katz Indicator

The Katz indicator takes into account the paths of

all networks, so it is defined as:

𝑆





∑





𝛼



⋅|𝑝𝑎𝑡ℎ𝑠

,



|𝛼𝐴



𝛼



⋅𝐴







𝛼



⋅𝐴







⋯ (4)

where α>0 is a tunable parameter that controls the

path weight, and |𝑝𝑎𝑡ℎ𝑠

,



| represents the number

of paths of length I in the path connecting nodes Vx

and Vy. For the above series to converge, the

parameter α should be less than the reciprocal of the

maximum eigenvalue of the adjacency matrix, and

this definition can also be expressed as:

𝑆𝐼𝛼⋅𝐴



𝐼 (5)

Obviously, when the parameter α is small, the

contribution of higher-order paths is also small, so

that the prediction results of the Katz indicator are

close to those of the local path indicator.

C. LHN-II Indicator

The LHN-II indicator is another similarity

calculation method proposed by Leicht, Holme and

Newman, whose basic idea is based on the general

equivalence Regular equivalence. Unlike structural

equivalence, general equivalence is defined more

broadly. Under the definition of general equivalence,

if two nodes are connected to similar nodes, then the

two nodes are also similar, even if they do not have a

common neighbor node between them.

Most of the similarity indicators in the existing

link prediction algorithms are single indicators and

are only suitable for specific network structures. In

this paper, it is proposed to predict the similarity

index by mixing links, and the weight in the mixed

similarity index is optimized and adjusted by the

experimental design method, so as to propose a link

prediction algorithm based on the optimal mixed

similarity index based on experimental design.

3 OPTIMIZATION OF

INDUSTRIAL STRUCTURE

With the deepening of China's economic new normal

policy, industrial transfer is a major proposition in

China. Adjusting the industrial structure through

industrial transfer and eliminating the imbalance in

economic development between regions are urgent

problems to be solved by China's new economic

policy. Therefore, the link prediction method is used

to analyze the industrial transfer path, and an

industrial transfer path suitable for different regional

industrial networks is given, so as to optimize the

industrial structure.

The simulation results of different link prediction

similarity indicators of the industrial network models

in regions A and B are shown in the following table:

ANIT 2023 - The International Seminar on Artiﬁcial Intelligence, Networking and Information Technology

Table 1. Simulation table of different link prediction

similarity indicators of two industrial network models.

Indicator A B

LHN-I 0.470713 0.500014

HDI 0.622898 0.644432

Sorenson 0.679876 0.688796

Jaccard 0.653559 0.754876

Salton 0.699932 0.767789

HPI 0.706543 0.699802

LP 0.712122 0.708758

PA 0.770007 0.711724

CN 0.755432 0.700542

Katz 0.799643 0.699652

RA 0.723117 0.778782

By comparing the accuracy measurement results

of the two industrial network models, it can be seen

that the AUC accuracy of the RA index considered

from the perspective of network resource allocation,

considering the number of all paths, the Katz

indicator with a large weight for short paths, the CN

indicator based on neighbor nodes, and the PA

indicator based on the size of the degree value are

higher. Among them, the Katz indicator and the RA

indicator have a similar idea, and as the path is longer,

the lower its weight.

The rules for network optimization according to

PA indicators are: priority nodes with large

connectivity are reflected in whether the two

industrial sectors have greater influence in the same

industrial chain. Therefore, the essence of path

optimization based on PA indicators is industry chain

collaboration. Specifically, according to the industrial

chain where the industrial sector is located, priority is

given to establishing links between each department

and the most influential department, enhancing the

inter-departmental connectivity on the network

industry chain, and optimizing the allocation of

industrial facilities and resource endowments to

improve the system cooperation ability of the entire

region and promote the closeness of the main

functional areas.

The rules for network optimization according to

RA metrics are: from the perspective of path, from the

x node to the y node to pass part of the resources, their

common neighbor becomes the medium of

transmission. Assuming that each medium has one

unit of resources and distributes them equally to its

neighbors, you can get the number of resources that y

can receive. The number of resources that can be

received is the RA similarity between nodes x,y. In

industrial networks, direct input-output relationships

are more likely to form between sectors with less

influence and those with strong industrial ties.

Reflected in the input-output relationship, it also

shows that the sectors with less influence in the

industrial chain should be the focus of transfer. For

example, sectors with less influence should be

prioritized as key targets for supply-side reform

because of their overcapacity or insufficient technical

capabilities. Coordinate the relationship with other

departments to form an industrial division of labor,

learn from each other's strengths, and promote the

productivity of the department.

The path connection tendency of the CN indicator

is: there are more neighbor nodes between the two

nodes, which is likely to be related. In the industrial

network, if two industrial sectors are related to other

similar sectors at the same time, they are more likely

to have a direct relationship. This idea is embodied in

the integration and development of more similar

industrial sectors, so that the entire industrial network

forms a coordinated whole. For example, two

industrial sectors with the same business will produce

input-output relationships with the same departments

at the same time, and the two departments are more

substitutable with each other, and priority should be

given to integrating the two departments to develop

and grow, strengthen control, achieve capital

conservation and technological growth, and make the

entire industrial network achieve intensive economic

growth.

4 CONCLUSION

With the advancement of science and technology,

more and more complex systems have emerged. Data

derived from complex networks have increased

straightly as well, which have in turn promoted the

research process of complex networks. Link

prediction is an important research direction of

complex networks. It mainly utilizes the known data

and their interactions to predict the data that already

exists but has not been observed, the data that may

appear in the future, and some of the false data.

The hybrid link prediction similarity index can

grasp the overall structural characteristics of the

industrial network better than the other indicators.

The structural adjustment of industrial network

through the idea of hybrid link prediction similarity

index has the role of coordinated development and

overall consideration. The industrial hybrid transfer

path is embodied in the convergence of capacity

elimination path based on RA indicators, industrial

convergence path based on CN indicators, and

optimal configuration path based on PA indicators.

The three will be mixed in an appropriate proportion,

with the production capacity elimination path as the

Research on the Improvement of Link Prediction Algorithm and Its Application in Industrial Structure Adjustment

main transfer direction, supplemented by the

industrial integration path and the optimal allocation

path. This combines the advantages of the three paths

to make the migrated network more coordinated.

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