# A Generative Adversarial Network for Financial Advisor Recruitment in Smart Crowdsourcing Platforms
## 3 Proposed Recruitment Framework
### Advisor to Investor (AIM) Matching Phase  
The proposed framework aims not only to find the ideal financial advisor that matches an investor profile but also to determine closest profiles existing in the database to this ideal virtual profile. Moreover, our framework aims to maximize the overall gain for a group of investors seeking services from a group of financial advisors. Indeed, some financial advisors might match the profiles of multiple investors; however, they cannot serve them simultaneously. On the other hand, some investors may require a portfolio management service from multiple financial advisors to diversify their investment and maximize their gains. Therefore, in this phase, we propose to design a dedicated many-to-many investor-to-advisor assignment to enhance the overall matching output while overcoming these challenges. In this paper, in order to optimize the execution time of the proposed framework and to facilitate the matching process, we cluster the financial advisors using an unsupervised machine learning clustering algorithm, namely \(K\)-Means++. The algorithm is used to the data of financial advisors in order to arrange them into \(K\) groups  
Figure 4: Standalone model stacking and training cycle of the proposed GAN for generating ideal financial advisors profiles. with a high level of similarity based on their characteristics, such as assets of competence, qualifications, and diplomas. The investigated method is a better variant of the classic \(K\)-Means algorithm. The key benefit of \(K\)-Means++ is that it ensures that the centroids are correctly initialized, resulting in improved clustering outcome that is independent of the initialization points. On the other hand, the number of clusters is a crucial factor when attempting to strike a balance between reducing execution time and retaining good matching results. To improve the provided strategy, we use the elbow method to solve the problem of conveniently clustering financial advisors while taking into account the distortion score that represents the sum of squared distances of the advisors to their closest centroids. Hence, we determine an optimized number of clusters by detecting elbows. We suppose that each investor \(i\in\mathcal{I}\) is only able to recruit \(n_{i}\) financial advisors given his/her budget. On the other hand, each financial advisor \(f\in\mathcal{F}\) is only able to work with \(m_{i}\) investors simultaneously. The matching problem can be then formulated using an ILP as follows:  
\[\max_{x_{i,f}\in\{0,1\}}\sum_{i}\sum_{j}w_{i,f}\times x_{i,f} \tag{4}\] \[\text{s.t. }\quad\left\{ \begin{array}{l}\sum_{i}x_{i,f}\leq n_{ f},\quad\forall f\in\{1,\ldots,\mathcal{F}\},\\ \sum_{f}x_{i,f}\leq m_{i},\quad\forall i\in\{1,\ldots,\mathcal{I}\},\\ \sum_{j}x_{i,f}\geq 1,\quad\forall i\in\{1,\ldots,\mathcal{I}\},\end{array} \right.\]  
where \(x_{if}\) is a binary decision variable indicating whether a financial advisor \(f\) is assigned to investor \(i\). The parameter \(w_{if}\) denotes the similarity between the ideal signature generated by the GAN for the profile of investor \(i\), obtained from the FASG phase, and the signature of financial advisor \(f\) existing in the database. The value of \(w_{i,f}\) is defined as the Structural Similarity Index (SSIM) [59; 60] and can be computed as follow:  
\[w_{i,f}=\frac{(2\mu_{i}\mu_{f}+\alpha_{1})\times(2\sigma_{i,f}+\alpha_{2})}{( \mu_{i}^{2}+\mu_{f}^{2}++\alpha_{1})\times(\sigma_{i}^{2}+\sigma_{f}^{2}+ \alpha_{2})}, \tag{5}\]  
where \(\mu_{i}\), \(\mu_{f}\), \(\sigma_{i}^{2}\), \(\sigma_{f}^{2}\), and \(\sigma_{if}\) are the average, variance, and co-variance of signatures associated to \"ideal\" financial advisor of investor \(i\) and existing financial advisor \(f\), respectively. Moreover, \(\alpha_{1}\) and \(\alpha_{2}\) are two stabilization variables to stabilize the division with weak denominator and are defined as \((k_{1}Q)^{2}\) and \((k_{2}Q)^{2}\), respectively.