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Location category (LC). The location categories are arcade, sidewalk, bike lane, and car lane ... convertible street locations for the decreasing stages are the occupied locations. ... mine the initial places where the illegal street vendors aggregate. .... Stevens D, Dragicevic S and Rothley K. iCity: a GIS–CA modelling tool for ...
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A stochastic artificial neural network model for investigating street vendor behavior in a night market

International Journal of Distributed Sensor Networks 2016, Vol. 12(10) Ó The Author(s) 2016 DOI: 10.1177/1550147716673371 ijdsn.sagepub.com

Pao-Kuan Wu1, Tsung-Chih Hsiao2 and Ming Xiao1

Abstract This article offers a hybrid computational approach that combines an artificial neural network with Bayesian probability to improve on the conventional artificial neural network model. The artificial neural network model, which is renowned for its pattern classification abilities, is a type of deterministic algorithm. However, combining artificial neural network with Bayesian probability can convert the deterministic artificial neural network model into a stochastic artificial neural network model that is useful for conducting dynamic simulations. In this study, an experiment is performed to demonstrate this hybrid computational approach. The objective of this experiment is to analyze the behavior of illegal street vendors in a night market. By applying the hybrid computational approach, we can perform a series of dynamic simulations to investigate the development process of the illegal street vendors. The results of the dynamic simulation have high similarity with the real observations. Furthermore, we can use the simulation results to evaluate the commercial values of different parts of streets and to determine which streets will be unstable due to the impacts of economic fluctuations. Keywords Artificial neural network, Bayesian probability, geographic information system, dynamic simulation

Date received: 16 May 2016; accepted: 16 September 2016 Academic Editor: Gang Wang

Introduction The application of computational modeling is an important subject for urban-related research fields. Comparisons between reality and computational models can help researchers understand the objective phenomenon.1–3 The application of computational modeling has two purposes: first, to establish expert knowledge to investigate and describe the objective phenomenon and second, to predict the future based on the established models.4–6 The development of geographic information systems (GIS) has greatly improved computational modeling by allowing the management of both graphic and numerical data. Thus, applications that combine computational modeling with GIS have become a surging trend of the decade.7–12

The artificial neural network (ANN) and Bayesian probability are the two computational techniques applied in this article. An ANN is an artificial 1

Department of Urban Planning, College of Architecture, Huaqiao University, Xiamen, China 2 College of Computer Science and Technology, Huaqiao University, Quanzhou, China Corresponding author: Pao-Kuan Wu, Department of Urban Planning, College of Architecture, Huaqiao University, Xiamen, Fujian Province 361021, China. Email: [email protected] Tsung-Chih Hsiao, College of Computer Science and Technology, Huaqiao University, Quanzhou, Fujian Province 362021, China. Email: [email protected]

Creative Commons CC-BY: This article is distributed under the terms of the Creative Commons Attribution 3.0 License (http://www.creativecommons.org/licenses/by/3.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (http://www.uk.sagepub.com/aboutus/ openaccess.htm).

2 intelligence (AI) algorithm that originated from mimicking the cognitive processes of neural and brain systems. ANNs have been proven effective through both mathematical and statistical theories.13,14 ANNs are renowned for their pattern classification abilities and for their many other advantages such as optimization and approximation capabilities, robustness against noise in the input data, and high prediction abilities.15 The most important feature of an ANN is that it establishes expert knowledge based on pattern recognition logic to simulate the objective phenomenon. Since Fisher4 and Openshaw5 first applied ANNs for spatial analyses, many subsequent studies have successfully applied ANNs to investigate various urban issues such as land use changes,7,16,17 urban growth research,1,8,18 regional labor markets,19 traffic management,20 management of building energy usage,21 and regional economic activities.22,23 An ANN is a type of deterministic algorithm and is usually used to perform static simulations for pattern classifications;15 however, various urban phenomena are complex and dynamic and often depend on the probabilities with which certain events may be triggered. Because of the inherent limitations of ANNs, it is rare to see them applied to conduct dynamic simulations. Therefore, determining how to extend the conventional ANN to perform dynamic simulations for the purpose of investigating a spatial–temporal urban phenomenon is the main purpose of this article. Bayesian probability is the other technique used to fulfill our research goal. Bayesian probability is a statistical probability tool that can infer the probability of one hypothesis from a prior probability derived from observations of prior events.24,25 Bayesian probability can be applied to infer whether a certain urban phenomenon occurs based on the record of other previously observed events,26,27 but it is hard to clarify the causality of the target event based on the potential factors, as ANN does. However, the most important feature of Bayesian probability is its stochastic mechanism, which can covert the record of observed events into probability data.25 Therefore, adding this feature could change the performance of a conventional ANN model from static to dynamic. Dynamic simulations, more so than static modeling, can embody lively urban phenomena and reveal the information that emerges from a development process. Thus, this article offers the combination of ANN and Bayesian probability as a hybrid computational approach to establish a dynamic simulation model for the purpose of investigating a type of urban commercial phenomenon. Our strategy is as follows: if the original ANN results are considered as prior events (the observations of the target pattern), then the original ANN results can further be converted into the probability data of the target pattern by calculating the

International Journal of Distributed Sensor Networks Bayesian probability, and the dynamic simulations of pattern classification can be made possible. This is a novel notion in the field of urban computational modeling that can directly convert the static performance of ANN pattern classification into a stochastic performance. We perform an experiment to demonstrate the application of the hybrid computational approach that involves a commercial phenomenon: street vendor behavior in a night market. The features of urban commercial behavior are complex, vivid, and dynamic.23,28,29 By applying the hybrid computational approach, we can dynamically simulate street vendor behavior and perform some analyses related to spatial– temporal issues. The following section is a discussion of the computational techniques related to the hybrid computational approach.

Computational techniques ANNs ANNs, renowned for their perceptron logic, are a type of pattern classification technique. The mechanism behind ANN was derived by imitating human perception, which receives outside incentives through neurons and can recognize situations from experience.13,14 In research applications, the observed factors are analogous to the recipient parts of neurons. Then, through a series of neural computations, the algorithm can produce the ANN outcomes or pattern classification results. An ANN normally consists of three components. As Figure 1 shows, these components are an input layer, one or more hidden layers, and an output layer. Nonlinear ANNs contain at least one hidden layer (multi-layer ANNs), while linear ANNs contain no hidden layer (single-layer ANNs). Nonlinear ANNs can easily achieve better pattern classification performances than linear ANNs, but they lose the direct correlations between the target pattern and the observed factors. Therefore, the hidden layer is an awkward part of an ANN application because of the notorious ‘‘black box’’ issue.4,5,30 The main purpose of this article is to improve on the conventional ANN architecture to perform dynamic pattern classification. Thus, we applied a linear ANN for our experiment to simplify the experimental operation. ANNs perform pattern classification tasks using a supervised learning process that modifies weight values according to real observations of the target pattern. Making real observations of the target pattern is standard for the ANN training step. The goal of the ANN training step is to minimize the deviation between the ANN output and the target pattern. After the ANN training step is complete, the trained ANN can generate

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Figure 1. A typical ANN consists of an input layer, one or more hidden layers, and an output layer.

a trained ANN is a judgment as to whether a given sample belongs to the target pattern. Generally, there is an ANN decision threshold for judging the target pattern; if a sample’s ANN outcome is higher than the ANN decision threshold, the sample is classified as the target pattern. Thus, a trained ANN can actually generate two results: one is the ANN outcomes of all the samples generated by equation (1) and the other is the pattern classification results denoted by a categorical variable. The application of Bayesian probability with these two ANN results can convert the deterministic and static ANN performance into a stochastic performance. Figure 2. The process for generating the ANN outcome.

The combination of ANN and Bayesian probability an ANN outcome of one objective sample using equation (1).14,15 Figure 2 illustrates the process for generating the ANN outcome Yj = d

n X

! Wij Xi + b

ð1Þ

i=1

where Yj is the ANN outcome of the jth sample generated from the trained ANN, Xi is the ith factor, Wij is the ANN weight value, s is the transfer function, and b is a bias value. The ANN outcome can be considered as an indicator of the tendency of the target pattern. The output of

Bayesian probability is one of the statistical probability skills derived from conditional probability.24,25 Bayesian probability can be used to infer the occurrence probability of a particular event or the probability of a specific hypothesis according to one given event and prior observed evidence.26,27 In the following discussion, we use our research problem to directly explain the application of Bayesian probability. As stated in the ANN discussion above, there are two ANN results: the ANN outcomes and the pattern classification results. Our problem is to determine how to convert the ANN outcomes into the occurrence probability of the target pattern to conduct dynamic simulation instead of static simulation. We can use the ANN

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Figure 3. The combination of ANN and Bayesian probability; the original ANN outcome can be converted into stochastic data by Bayesian probability.

outcomes and the pattern classification results as two pieces of observed prior evidence, and then, the occurrence probability of the target pattern can be calculated by Bayesian probability given the ANN outcomes. Figure 3 illustrates the process of converting one sample’s ANN outcome into the occurrence probability of the target pattern. Equation (2) originates from the formula in Bayesian probability theory for calculating the occurrence probability of the target pattern conditioned on one ANN outcome; the result is denoted as P(Tp|Yj)     P Yj jTp    P Tp P Tp jYj = P Yj 



ð2Þ

where Yj is the ANN outcome of the jth sample derived from equation (1), Tp is the categorical variable of the target pattern, and P(Tp) is the prior probability of the target pattern, which can be calculated from the real observation record of the target pattern distribution. After the ANN training step finishes and generates the ANN outcomes for all the samples from the trained ANN, P(Yj) can then be calculated. P(Yj) is the other prior probability of the ANN outcome. P(Tp) and P(Yj) are the marginal likelihoods of the prior events. After all the marginal likelihoods of the prior events are obtained, we can further calculate P(Yj|Tp), which is the occurrence probability of Yj conditioned on Tp, which is given by the matrix calculation. The term P(Yj|Tp)/P(Yj) represents the standardized likelihood, which is the strength of the evidence that the observational value Yj provides for P(Tp). After obtaining all the terms mentioned above, we can finally generate the inferential probability of P(Tp|Yj). The hybrid computational approach consisting of ANN and Bayesian probability can generate the occurrence probability of the target pattern according to the original ANN outcomes to drive dynamic simulations. The following section explains the experimental

objective for the application of the hybrid computational approach.

Experimental objective: street vendor behavior in a night market The experimental objective is to understand street vendor behavior in the Feng-Chia Night Market, Taichung, Taiwan. The Feng-Chia Night Market is a typical Taiwanese night market; it sprawls along the streets around Feng-Chia University. This type of urban commercial phenomenon is uncertain, complex, organic, flexible, and dynamic.31 Because of these features, understanding street vendor behavior in the Feng-Chia Night Market is an appropriate research objective to apply the hybrid computational approach. The goal of the experiment is to establish a dynamic simulation model to investigate the behavior of illegal street vendors in the Feng-Chia Night Market. Illegal street vendor behavior means that the commercial vendors occupy various street locations such as the arcades, sidewalks, and pedestrian or bike lanes shown in Figure 4. Trade is not allowed in these locations according to local regulations; therefore, the vendor phenomenon is criticized as being ‘‘out of place.’’28 The streets of the Feng-Chia Night Market are the experimental area in which we perform the dynamic simulations. The target pattern is the phenomenon of the street locations being occupied by the illegal street vendors, as mentioned above. To precisely depict and record the experimental area, the experimental area was analyzed by GIS using a grid formation as the GIS data platform, as shown in Figure 5. Each grid represents one street location and contains information on the environmental factors and the target pattern based on the geographic configuration. There were 10,940 street locations that included 1717 occupied street locations (the target pattern) and 9223 unoccupied street locations, according to the field

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Figure 4. Various commercial vendors often occupy two sides of the streets as the illegal street vendor behavior, and that is the main feature of Taiwanese night markets.

Figure 5. The distribution of the target pattern, as recorded from real observations; the darkest grids are the locations occupied by the illegal street vendors that form the target pattern.

survey. Each street location is described by seven environmental factors that were derived from the related literature.28,32–34 These environmental factors may attract the illegal street vendors who aggregate and occupy the streets. The environmental factors and descriptions are listed in Table 1. All environmental factors were normalized to values between 0 and 1. The following section describes the experimental methodology and the results of the hybrid computational approach. All the computational work of ANN and Bayesian probability was conducted in MATLAB.

Experimental methodology and results The application of the hybrid computational approach The first step in the experiment is to conduct the conventional ANN procedure. Here, a linear ANN was implemented to simplify the experimental operation. We selected 5000 street locations with their accompanying environmental factor information and target patterns to train the ANN and an additional 1000 street locations to use as validation. Moreover, the logistic

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Table 1. The environmental factors. Environmental factor

Description

Location category (LC) Intersection (Int) Street width (SW) Background building width (BBW) Core zone 1 (C1)

The location categories are arcade, sidewalk, bike lane, and car lane The measured distance from a target location to the nearest street intersection The street width for a target location The width of the building behind a target location The distance measured from a target location to core zone 1. Core zone 1 is the main gate of Feng-Chia University The distance measured from a target location to core zone 2. Core zone 2 is the location of the first busy street intersection The distance measured from a target location to core zone 3. Core zone 3 is the location of the second busy street intersection

Core zone 2 (C2) Core zone 3 (C3)

Figure 6. The conventional ANN result of pattern classification; the darkest grids are the target pattern as judged by the trained ANN.

sigmoid transfer function was employed as the ANN transfer function to restrict all the ANN outcomes to a range from 0 to 1. After the ANN training step, we obtained the ANN outcomes of all street locations by equation (1) to generate the pattern classifications (the conventional ANN result) shown in Figure 6. The ANN pattern classification accuracy was 84.1%, of which the accuracy for the target pattern was 94.3%. We can compare Figure 6 with Figure 5 to see the similarity between the target pattern distributions. The pattern classification result can help us learn the street locations chosen by the illegal street vendors that are correlated with the environmental factors. In other words, the conventional ANN model can establish expert knowledge on the objective phenomenon and its

potential factors. However, because our experimental objective is to understand the dynamic development of this night market, we need to extend the conventional ANN result to allow it to perform dynamic simulations, so that we can not only simulate the development process of the night market but also observe the information that emerges to conduct spatial–temporal analyses. Based on the previous ANN results, we can calculate the occurrence probability of the target pattern using equation (2). The GIS demonstration can help us easily observe the distribution of the occurrence probability. The occurrence probability of the target pattern is classified into four levels: P \ 25%, 25%  P\50%, 50%  P\75%, and 75%  P. Table 2 lists detailed information concerning the occurrence probability

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Table 2. The occurrence probability of the target pattern classified into four levels. The probability level

P\25%

25%  P\50%

50%  P\75%

75%  P

The number of locations The average probability

7981 3.21%

1159 36.35%

1681 63.67%

119 75.42%

Figure 7. The distribution of the occurrence probability classified into four levels.

levels, and Figure 7 depicts a demonstration of the GIS data platform. The highest occurrence probability of the target pattern is 75.68%. The darker street locations have higher occurrence probabilities of the target pattern as shown in Figure 7; in other words, these locations are more likely to attract the illegal street vendors. At the same time, these locations also carry higher rental costs for commercial reasons. Thus, the distribution of the occurrence probability can help us evaluate the commercial values for different areas of the streets. The following section further describes the experimental procedure for dynamically simulating the development process of the night market.

Dynamic simulations and analyses The crucial part of this experimental phase is the setting of transitional rules to drive the iterative simulation model. Each iterative loop consists of two stages: an increasing stage followed by a decreasing stage. The total number of iterative loops is 500, which includes 500 increasing stages and 500 decreasing stages. The convertible street locations for the increasing stages are the vacant locations, which can be converted from a vacant state into an occupied state. In contrast, the

convertible street locations for the decreasing stages are the occupied locations. During the increasing stages, the number of vacant locations that can be selected as candidates for conversion into occupied locations is randomly determined according to their occurrence probabilities with respect to the target pattern (P(Tp|Yj)). Moreover, the total number of final converted locations for one increasing stage has a limit of 300. If the number is less than or equal to 300, all are counted; otherwise, the candidate locations to be counted are selected randomly. The limited number of final converted locations represents the increasing momentum for the increasing stages. During the decreasing stages, the number of occupied locations to be selected as candidates for conversion into vacant locations is randomly determined according to their non-occurrence probabilities with respect to the target pattern (1 2 P(Tp|Yj)). Moreover, the total number of final converted locations for one decreasing stage is limited to 20. If the number is less than or equal to 20, all are counted; otherwise, the candidate locations to be counted are selected randomly. The limited number of final converted locations represents the decreasing momentum for the decreasing stages.

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Figure 8. The dynamic simulation results for 1000 stages.

Through the occurrence probability and the transitional rules, a series of dynamic simulations can be performed. Figure 8 displays the results of the dynamic simulation for 1000 stages (500 iterative loops). Stable fluctuations appear after approximately the 40th stage. Thus, the stages before the 40th stage correspond to the development phase of the illegal street vendors, while after the 40th stage, the average number of occupied locations is 1719.3; this number is close to the real value of 1717 occupied locations. There is an experimental issue: the stage number at which the stable fluctuations begin to occur and the average number of occupied locations can be modified by changing the increasing and decreasing momenta. We engaged in a period of trial-and-error work to adjust these two momenta to imitate the real development process of the illegal street vendors. The crucial strategy was to make sure that the average number of occupied locations was close to the real value, so that we could have sufficient confidence to conduct the following analyses. Figure 9 depicts the results of a series of dynamic simulations that demonstrate the development process of the illegal street vendors before the stable fluctuations appear (at approximately the 40th–46th stage). This demonstration can help us observe the sprawling behavior of the illegal street vendors and further determine the initial places where the illegal street vendors aggregate. Figure 10 illustrates the sixth stage. The two areas marked by dotted circles are the initial places where the illegal street vendors tend to aggregate. The Feng-Chia Night Market originated from this

gathering of the illegal street vendors.31 Thus, the marked areas can be considered the original locations of the Feng-Chia Night Market development. Furthermore, we can determine which streets will be unstable due to the impacts of economic fluctuations in the future. Table 3 presents a statistical analysis of the average rate of change on each street. The average rate of change on each street is calculated by equation (3) 500 O O P j s(t) s(t1) j

Rs =

t = 20

Ns

500  t

ð3Þ

where Rs is the average rate of change of the target street and t is the iterative loop number at which stable fluctuations appear. In this case, t = 20 (the 40th stage), Ns is the number of street locations on the target street, and Os is the number of occupied locations on the target street. Figure 11 is an illustration of Table 3. The streets with darker colors have higher average rates of change. This means that these streets are less stable in the dynamic simulation process (examples include street 2, street 3, and street 4 in Figure 11). The development of the night market is easily affected by different economic situations. Thus, based on the analysis of their average rates of change, we can determine that these streets will be unstable because of the impacts of economic fluctuations. The aforementioned two analyses in this section can only be performed by observing the dynamic development process. Dynamic simulations can reveal the

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Figure 9. The development process of the illegal street vendors.

Table 3. The average rate of change on each street. Street

The average rate of change (Rs)

The rank of instability

Street 1 Street 2 Street 3 Street 4 Street 5 Street 6 Street 7 Street 8 Street 9

0.3475 0.4169 0.4521 0.3876 0.3421 0.2518 0.2832 0.2361 0.249

4 2 1 3 5 7 6 9 8

information that emerges, which can help us learn more about the development of the illegal street vendors than the conventional ANN results. That is the main contribution of the hybrid computational approach.

Conclusion This article presented an experiment to demonstrate an improvement to the conventional ANN model. The conventional ANN model can help us establish expert

knowledge on objective phenomena and their observed factors. However, more information can be revealed when we extend the conventional ANN model to be able to perform dynamic simulations of pattern classifications. In this article, to investigate a dynamic urban commercial phenomenon, we combined an ANN with Bayesian probability as a hybrid computational approach to convert the original deterministic ANN model into a stochastic ANN model, allowing the realization of a series of dynamic simulations by setting the transitional rules. This is a novel technique in the field of urban computational modeling. The experimental objective was to determine the behavior of illegal street vendors in the Feng-Chia Night Market. Through the application of the hybrid computational approach, we can dynamically simulate the development process of the illegal street vendors and obtain high similarity with the real observations. Three additional analyses can be conducted according to the result of the dynamic simulation. First, the commercial values on different parts of the streets can be represented by the distribution of the occurrence probability of the vendors. Second, the original locations of the Feng-Chia Night Market development can be determined by analyzing the early stages of the

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Figure 10. A demonstration of the original locations of the Feng-Chia Night Market development.

Figure 11. Illustration of the average rate of change on each street.

dynamic simulation. Third, the unstable streets that are affected by economic fluctuations can be determined by analyzing the average rate of change on each street. The latter two analyses depend on observations of the information that emerges from the dynamic simulation

process, which is the main contribution of the hybrid computational approach described here. The hybrid computational approach can not only deal with pattern classification problems but also embody uncertain, complex, organic, flexible, and dynamic features.

Wu et al. The hybrid computational approach can also be applied to research problems outside of urban development phenomena. However, the dynamic simulations demonstrated by this article are driven by the initialization of the trained ANN and the transitional rules; the role of Bayesian probability is to convert the static ANN results into stochastic data. All the observed factors should be considered in the ANN procedure before a dynamic simulation is performed. Thus, the modification and addition of the observed factors in the process of dynamic simulation are the limitations of this research, especially for the factors related to temporal effects. Adding and modifying the observed factors during the process of dynamic simulation allow for complete consideration of the development process of the objective phenomenon and reveal more detailed information. Improving the hybrid computation approach by adding adaptability to the observed factors is the goal of future research. Declaration of conflicting interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was funded by the Fund of Scientific Research Projects for Introduced Talents in Huaqiao University (Z14Y0009 and 13BS412) and the Quanzhou Science and Technology Plan Project of the Education Department of Fujian Province (JA15031).

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