An Innovative Thinking-Based Intelligent Information Fusion Algorithm

This study proposes an intelligent algorithm that can realize information fusion in reference to the relative research achievements in brain cognitive theory and innovative computation. This algorithm treats knowledge as core and information fusion as a knowledge-based innovative thinking process. Furthermore, the five key parts of this algorithm including information sense and perception, memory storage, divergent thinking, convergent thinking, and evaluation system are simulated and modeled. This algorithm fully develops innovative thinking skills of knowledge in information fusion and is a try to converse the abstract conception of brain cognitive science to specific and operable research routes and strategies. Furthermore, the influences of each parameter of this algorithm on algorithm performance are analyzed and compared with those of classical intelligent algorithms trough test. Test results suggest that the algorithm proposed in this study can obtain the optimum problem solution by less target evaluation times, improve optimization effectiveness, and achieve the effective fusion of information.


Introduction
Information fusion [1] refers to the process in which relevant information is searched and extracted from multiple distributed heterogeneous network resources and then converted into a unified knowledge mode. It aims at constructing effective knowledge resources for solving the problems in certain field or generating new integrative knowledge object by conversing, integrating, combining, and so forth various information coming from distributed information resources.
Common information fusion algorithms can be divided into two main categories, which are probability statistics method and artificial intelligence method. Probability statistics method includes Bayes, the transformation of Bays [2], and D-S evidence reasoning [3]. It has axiomatic basis and low computational complexity and is intuitive and easy to be understood, but it needs more prior information and its applicable condition is harsher; while in artificial intelligence method, information fusion is similarly regarded as that human brain comprehensively treats information. In this method, artificial neural network [4], support vector machine [5], and genetic algorithm (GA) [6] account for approximately 85% of the whole information fusion algorithm. And the machine learning methods, that is, swarm intelligence, artificial immune, quantum genetic algorithm, and so forth, have been applied in information fusion. This method shows fewer requirements to the prior information of object and stronger self-fitness. Moreover, the fusion of the subjective and objective information in system can be realized using this method. Most of existing intelligent algorithms are proposed based on natural evolution rule, animal collective intelligence, and life system mechanism. However, they fail to make good use of the background factors of problems and the knowledge produced in the process of solving problems. This situation limits the natural combination of intelligent algorithm and knowledge to some extent and the full play of the role of knowledge.
The researches on information fusion currently show a developing trend of further combining with the cognitive system-based human natural intelligence. The cognitive behaviors of humans, such as learning and reasoning, handle various information by widely simulating human intelligence from each link of information carrier to fusion based on knowledge [7]. Innovative thinking is the advanced stage of  thinking activities. It is a thinking process of discovering new things, creating new methods, and solving new problems on the basis of personal experiences. Moreover, it is the source of wisdom [8,9]. Through modeling and simulating innovative thinking by computer, the innovative ability on human level can be obtained and produced. By simulating human thinking mechanism, it is expected to reach a higher solving efficiency than that obtained by the natural selection mechanism-based intelligent algorithm [10]. Therefore, in references to the relevant research achievements of brain cognitive theory and creativity computation, this study puts forward an intelligent algorithm which can realize information fusion-innovative thinking-based intelligent information fusion algorithm (ITIIF algorithm) by the algorithmization to cognitive process and behavior of innovative thinking.

The Basic Framework of ITIIF Algorithm
ITIIF algorithm treats knowledge as core and information fusion as a knowledge-based innovative thinking process. It gives full play to the role of the knowledge-based innovative thinking skills in information fusion. This algorithm is composed by five parts, which are information sense and perception, memory storage, innovative thinking, evaluation system, and execution. Among which, innovative thinking includes two thinking skills, which are divergent thinking and convergent thinking. The basic framework and the relationship of the five parts of this algorithm are shown in Figure 1.
ITIIF algorithm can be expressed by sextuple as where is the perceptual information module, is memory storage module, is divergent thinking module, is convergent thinking module, is evaluation system module, and is execution module. The functions of each module are as follows.
(1) Perceptual information module: it reasons and fuses the information collected from environment and maps this information into knowledge. It includes information sense and information perception.
(2) Memory storage module: it organizes and manages knowledge; it includes long-term memory (LTM) and short-term memory (STM).
(3) Divergent thinking module: it integrates the physical world information world obtained and information world knowledge into a structural knowledge divergent model. This process can be regarded as a selforganizing process of the knowledge in human brain. It assembles the knowledge fragments into a knowledge mode with certain structure (tree or figure).
(4) Convergent thinking module: it transforms the knowledge divergent model produced by divergent thinking into decision by focus, modification, or innovation.
(5) Evaluation system module: it is the assessment standard for the decision satisfaction degree. It is used to evaluate the whole or part of decision plan. In this module, value system will affect thinking modules.
(2) Information perception: it maps a plurality of sense information into knowledge cluster by reasoning and integrating. It is expressed as F-perception: S1 ( , , , . . .) → KC, where F-perception: S1( , , , . . .) is the processing of cognitive information and KC refers to knowledge cluster.
Definition 1 (knowledge cluster (KC)). It refers to the knowledge structure connected by target object (including attribute and behavior) and related objects; it is expressed as where tar o represents target object, ro is related object, O is object set, and Re is the set of the relationships of target object and related objects. For example, in a traffic intersection, the KC formed with an automobile as object is shown in Figure 2.

Memory Storage. Memory storage is divided into LTM and STM; it is denoted as
STM is used to store the knowledge cluster constructed by information perception as well as thinking process data. LTM is used to store the knowledge unit produced by innovative thinking. It can carry out the automatic evolution of knowledge. 3.2.1. STM. STM is a temporary memory space opened in thinking process for the development of thinking activities. STM can be expressed as where kc represents an independent knowledge cluster, kc = ⟨ kc , kc ⟩, kc denotes the stimulation intensity of KC, which suggests the influencing degree of KC on target environment. Bigger kc explains that KC cannot be easily forgotten; kc is the existing time of KC in STM. The greater the kc is, the more easily the knowledge cluster can be forgotten.

LTM. LTM is the container of knowledge units. The knowledge units obtained by innovative thinking are stored in LTM.
Definition 2 (knowledge unit). It refers to the knowledge structure connected by subobjects in sequence to achieve the expected state of system. It can be expressed as 4 The Scientific World Journal where Ω is subtarget space, Re denotes the set of the interaffecting relationship of and to realize the expected effect of system. LTM is expressed as ku is an independent knowledge unit, ku = ⟨ ku , ku ⟩, ku is the fitness of knowledge unit. Larger ku indicates a stronger activeness of knowledge unit, and this knowledge unit can more easily be extracted by thinking module. ku refers to the time that knowledge unit is stored in LTM. Larger ku suggests that the knowledge unit will be more easily forgotten.

Knowledge Evolution. The knowledge units in LTM
continuously evolve under the effect of innovative thinking activities. This evolution contains quality development and quantity growth. The quantity growth of knowledge represents the increase of total knowledge quantity in LTM after a certain period. The quality development of knowledge refers to the improvement of the depth and truth degree of the recently emerged knowledge units produced by innovative thinking comparing with that in certain past historical period. By quality development of knowledge, the knowledge units in LTM can be updated and continuously evolve.
The specific steps of knowledge evolution are as follows.
(3) (ku 1 , ku 2 , ku 3 , . . . , ku ) //select() select the first knowledge units into evolution pool.   ( ∈ ku new ∩ Ω )/| Ω |, where ku new is the sub-target contained in knowledge unit ku new , | ku new | is the cardinal number of ku new , and Ω denotes the subtarget contained in realizing the expected target of system in theory.
(ku new ) is the correctness degree of knowledge unit, (ku new ) = (1 + (( Ω − 1)/ LTM ))/ Ω ; in this formula, Ω indicates the number of knowledge unit in realizing the expected target of system in theory; LTM is the number of knowledge unit in realizing expected target of system contained in LTM.

Divergent
Thinking. Divergent thinking is a process of assembling the sub-targets in different knowledge units to produce new target path according to the characteristics of problem and the process required in assembling knowledge units [11]. It extracts and assembles certain knowledge units in memory storage to achieve the reflection from LTM to knowledge tree. It is represented as where KST refers to the knowledge structure tree assembled; divergent composes two processes, which are memory extraction and knowledge assembling.
where (ku ) is the extraction intensity of the knowledge unit. Larger (ku ) suggests that knowledge unit can more possibly be extracted at divergent thinking stage. Divergent thinking will extract LTM knowledge units with larger (ku ) value from LTM. LTM is the extraction capacity of knowledge unit; it determines the number of the maximum knowledge units that can be extracted from LTM.

Knowledge Assembling.
Knowledge assembling combines the knowledge units extracted by memory into knowledge structure tree (KST). Several definitions that are related to KST are shown in the following.
Definition 3 (knowledge structure tree). It refers to the data structure produced by combining the knowledge units in certain order according to the characteristics of problem. It is presented as where is target node; it reflects the purposiveness of divergent thinking. There is only one target node in KST; is sub-target node set; it refers to all subtargets that are related to problem solution; DB is directed border set; is the relationship parameter maintained by each node. The knowledge structure tree constructed with D as target node The knowledge units extracted by memory A Figure 3: The assembling process of knowledge structure tree.
(node , node ) refers to that node is the parent node of node .

Definition 5 (knowledge radius). If there is a knowledge path
(node , node ) between node and node in KST, the node conversion times on this path are called the distance between node and node . And the shortest distance is the knowledge radius of node and node . Figure 3 presents the assembling process from knowledge unit to KST.
Each knowledge path from source node to target node represents one problem solving plan. Source node is the subtarget node containing no subnodes. Divergent thinking is, namely, a process of listing all problem solving plans according to existing knowledge level and cognitive conditions. Every knowledge path can be regarded as a special kind of knowledge unit. But there is no one-to-one corresponding relationship between knowledge path and knowledge unit. All knowledge units can find their corresponding knowledge paths in KST, but not all knowledge paths in KST can find their corresponding knowledge units. This phenomenon suggests that divergent thinking has combining and innovating capacity. For example, the knowledge unit extracted by the knowledge path → → in KST from memory does not exist, it is generated by the combination of knowledge units → and → → . That is, the combination of → and → → creates a problem solution plan → → .
Knowledge assembling constructs KST based on the method of knowledge radius and with knowledge target as center. The specific KST construction algorithm is as follows (see Algorithm 2).

Convergent Thinking.
Multiple problem solving plans have been produced through assembling and innovating knowledge units by divergent thinking, while there is a focus process when human's thinking proceeds to certain stage. After focusing, usually several limited objects are retained. This is the process of convergent thinking. Convergent thinking refers to the process that the divergent knowledge model formed by divergent thinking is transformed into new problem solving plans by focusing, modifying, and innovating. It realizes the reflection from KST to the optimum problem solving plan. It is indicated as convergent: KST → CS. (12)

Convergent Operation Focus().
Focus() can select several paths with higher values form multiple knowledge paths of KST. Its convergent rule is where (kp ) is focus function, kp ∈ KST represents all knowledge paths included in KST, con is convergent dimension, namely, the number of the knowledge paths focused.
where is the sub-target modified; is the expected target achieved by implementing modified operation; is the environment of modified operation, namely, the affecting relationship of and the integrity degree of the subtargets except in focused knowledge path. is resource restriction. It refers to the usable resources in the premise of ensuring the resource demand of other sub-targets.

Innovation Operation: Innovate().
When the problem solving value achieved by the focused knowledge path shows a larger difference with expected target value, innovate() is conducted. It is expressed as where new ∈ Ω is the new target after innovation. FKP is the sub-target on focused knowledge path. Aiming at different problems and different problem solving stages, human thinking will choose different innovation styles (modified operation or innovation operation) according to environment changes: 6 The Scientific World Journal (1) Set = 1 ( is the variable of knowledge radius) and 000 ← ( is goal) (2) while ( ≤ ) do (3) for (i = 0; i < | |; i++) do (4) for (j = 0; j < | |; j++) do (5) for ∀ ∈ ( is knowledge unit) do (6) for ∀ ∈ ( is the sub-target of knowledge unit ) do (7) if is a parent node then (8) ← (9) end (10) end (11) end (12) end (13) r = r + 1; (14) end where kp is the knowledge path produced by focus operation, cre style ∈ {0, 1} is creative style. cre style = 1 refers to dynamic creative style parameter; cre style = 0 is static creative style parameter; V is target expected value; ∈ [0, 1] is modified operation coefficient; = 1 − is innovation operation coefficient. If cre style = 1, the style is dynamic creative style; its parameter is defined as where V refers to the value that can be achieved by current knowledge path. It can be known that, with the increase of V, the probability of implementing modified innovation is gradually enhanced, while the probability of implementing innovative innovation is gradually weakened.

Evaluation System.
Evaluation system aims at evaluating the satisfaction degree to problem solving plan, which is, evaluating the values of the knowledge paths contained in KST. The satisfaction degree of the knowledge path is denoted as where is expected values of target; it is decided by decision makers; (KST kp ) is the values of the knowledge path in KST. The specific calculation formula is as follows: is weight; (kp ( )) is the contribution value provided by the sub-target in the knowledge path in achieving the total target; (kp ( ) = ( , , ), ( , , ) are the evaluation functions related to the memory time, the layer number in KST, and the subnodes number of sub-target .
(kp ( )) is closely connected with knowledge expression form. Therefore, the calculation mode of ( , , ) should be instantiated when facing specific problem.

ITIIF Algorithm Realization
According to the analysis on each module of ITIIF algorithm, the specific realization of ITIIF algorithm is explained in Algorithm 3.

Experiment and Analysis on the Parameters of ITIIF
Algorithm. The experimental data employ the data in "The Famous Knowledge Base for OpenCyc". By sorting, test data set is formed. It includes 37,310 knowledge units and 6, 531 correlations between knowledge units. This test aims at analyzing the parameters ( LTM , con , cre style) in ITIIF algorithm using knowledge navigation path optimization problem. First, we define two indexes-thinking set degree and information quantity.
Definition 6 (thinking set degree). It refers to the aggregation degree of the solutions obtained by convergent thinking. It is expressed as where is evolution generation number, SE( ) is the thinking set degree of the generation. ( ) is the total focused times of the solution that has been focused up to the generation. IQ( ) refers to the information quantity obtained after evolution of generations. It is expressed as where ( ) refers to the different knowledge unit number in current LTM. is the knowledge unit number in corpus. The influences of parameter LTM , con , cre style on the performance of ITIIF algorithm are shown in Figures 4, 5, and 6, respectively.
As shown in Figure 4, LTM shows great influences on the optimization effect of navigation path. In view of the whole The Scientific World Journal 7 (1) Parameter initialization: memory extraction capacity LTM , convergent dimension con , creative style (2) Generate sense information set and conduct sense information treatment to : − ( ) ⇒ 1 (3) Perform mode reorganization and KS construction to 1 : (S1) ⇒ STM. (4) Construct knowledge units by learning: ku = (TSM) ⇒ LTM (5) Proceed divergent thinking to the knowledge units in LTM (divergent(LTM)) according to specific problem, and assemble KST (6) Evaluate all the knowledge paths in KST(SAT(KST kp )) and operate convergent thinking; (i) Conduct focus operation (focus(KST kp )) to obtain the optimum problem solving plan.  process, problem solving effect experiences a process that first increases then decreases with the increase of LTM ; on one hand, with the increase of LTM , thinking set degree SE( ) first increases and then decreases. SE( ) increase indicates that convergent thinking is easy to "focus" on certain solution with a relatively small number; on the other hand, with the increase of LTM , information quantity IQ( ) firstly increases then decreases and increases again. Information quantity increase suggests that the information required in solving the problem is perceived more completely and deeply. Meanwhile, there is a law that the target value of optimum solution is proportional to SE( ) * IQ( ).
In Figure 5, with the increase of convergence dimension con , optimization effect of problem solving first reaches a certain value and then decreases. This phenomenon suggests  that, with the increase of information quantity, the divergent degree of thinking will increase. But when the divergent degree is too high, problem solving effect will be influenced.
As shown in Figure 6, as for dynamic creative style cre style = 1, better optimization effect can be obtained when the V selected is close to the optimum value. When the V selected is deviated from the optimum value, the performance of ITIIF algorithm reduces greatly; while as for the static creative style cre style = 0, the optimizing capacity of ITIIF algorithm is continuously improved with the increase of . In general, the SE( ) * IQ( ) value obtained when dynamic creative style parameter is applied is lower than that when static creative style parameter is applied. So it can be concluded that if the probable range of the optimum value of target can be predicted, it is proper to select dynamic creative 8 The Scientific World Journal  style; if the range of target value cannot be confirmed, static creative style is more proper. At the same time, the global optimization capacity of ITIIF algorithm can be improved by increasing value. Commonly, is set in 0.6 to 0.9.

Comparison of Optimization Results.
To better display the performance of ITIIF algorithm, this paper adopts five testing functions to develop simulation tests. Moreover, the simulation results of ITIIF algorithm are compared with those of the currently used binary particle swarm and binary differential evolution algorithm. Table 1 lists the test functions.
To provide comparability, the evaluation indexes in this test employ mean best fitness (MBF) and standard deviation (SD). MBF reflects the accuracy that algorithm can achieve when iteration times are given. SD reflects the stability and robustness of algorithm. Table 2 shows the solution results of the testing functions by ITIIF algorithm, binary particle swarm algorithm, and binary differential evolution algorithm. The values of MBF and SD are obtained by independently running each algorithm for 20 times, respectively.
It can be seen from Table 2 that the ITIIF algorithm proposed in this study shows better optimization performances to the functions, regardless of unimodal function or multimodal function. Moreover, it achieves more ideal optimization effects in terms of solution accuracy and stability. This result shows that ITIIF algorithm has certain advantages in function optimization.

Performance Comparison.
The ITIIF algorithm proposed in this study is compared with the commonly used genetic algorithms (GA), estimate distribution algorithms (EDAs), and ant colony optimization (ACO) in three aspects, which are average distance, average time, and average assessment value. The parameters settings of each algorithm are shown in Table 3.
The comparison results are presented in Figure 7. It can be obtained that ITIIF and EDAs show better optimization effects, while GA present the poorest optimization effect. The average time of ITIIF is longer than that of the other three algorithms. This is because the evolution of ITIIF algorithm requires learning and innovative thinking. And the longer average time of ITIIF algorithm is just the result of fully used knowledge. With the accumulation of knowledge, the time consumed in solving problem will be decreasing, just as human can improve the problem solving efficiency through continuous accumulations of knowledge and experience by learning. The assessment value of ITIIF is only 4.5% to 8% of other algorithms. This result means that the time required in target evaluation is greatly reduced.
According to above experimental results, it can be concluded that ITIIF algorithm shows better efficiency than  The solution results of the testing functions by ITIIF algorithm, binary particle swarm algorithm, and binary differential evolution algorithm.

Function
Binary particle swarm algorithm Binary differential evolution algorithm ITIIF algorithm proposed in this study MBF SD MBF SD MBF SD some of current intelligent algorithms. This is because ITIIF algorithm replaces evaluation operation with creative thinking process. Thus ITIIF algorithm can make better use of the knowledge generated by target evaluation to further improve efficiency. In addition, the evolution process of ITIIF algorithm can be explained. And ITIIF algorithm directly simulates the cognitive behavior of human and is consistent with the cognitive habits of human. This is what not possessed by other intelligent algorithms.

Conclusions
In references to the research achievements of modern brain science, neurophysiology, and cognitive theories, this study proposes a knowledge-based and value evaluation-oriented information fusion algorithm starting from the viewpoints of biological control theory and macro control system theory. Besides, this algorithm integrates the skills of convergent thinking and divergent thinking and applies the structure analysis methodology of macro system control theory into the simulation and modeling of innovative thinking. The test results show that this algorithm can reduce the number of target evaluation times, improve optimization efficiency, and realize the effective fusion of information. The following work is to strengthen strict theoretical derivation, incorporate innovative thinking into the frame of this algorithm, extensively integrate this algorithm with various traditional evolutionary algorithms, and widen the application area.