An Evaluation Model of Comprehensive Human Resources Quality of Financial Enterprises Based on Deep Neural Network

In modern times, financial enterprises are in need of talents with strong business capabilities and high comprehensive quality. The traditional model of extensive management can no longer satisfy the development needs of enterprises [1-3]. To enhance competitive advantage, a financial enterprise must implement refined management of talents, and ensure the matching between personnel and posts through scientific planning of human resources (HR) [4-8].

In practice, the evaluation of the comprehensive HR quality has become an important aspect of financial enterprise management, exerting a promoting effect on the economic efficiency of the enterprise. Multiple correlated interactive factors should be considered to evaluate the comprehensive HR quality. In the traditional evaluation systems, the weights of the evaluation indices are highly subjective, and changeable with space and time [9-12]. Moreover, a largescale evaluation will face the problem of over-complex calculations. To overcome these problems, it is very meaningful to develop a robust evaluation model for comprehensive HR quality.

There are four weaknesses in the previous attempts to evaluate the comprehensive HR quality in financial enterprises: the lack of diverse evaluators, the qualitative nature of evaluation method, the fuzziness of evaluation indices, and the looseness of evaluation results [13-15]. The relevant studies at home and aboard generally focus on three aspects: strategic HR management, talent quality evaluation theory, and the relevance between strategic HR management and talent quality evaluation [16-18].

On strategic HR management, O'Donohue and Torugsa [19] elaborated and demonstrated the development of a corporate HR quality model in practice, and highlighted the unique features of comprehensive HR quality: skill, motivation, and self-awareness. Rekalde et al. [20] explained the connotations of corporate HR quality model, introduced the framework and features of corporate management system, and described the construction process of corporate HR quality evaluation system.

On talent quality evaluation theory, Singh et al. [21] summarized that talent quality is both affected by explicit factors like behavior, knowledge, and skill and by implicit factors like motivation and values, and constructed the iceberg model for talent evaluation. Based on the iceberg model, Kelliher and Johnson [22] built up the onion model with implicit factors in the inner layer and explicit factors in the outer layer. According to the dynamic changes of HR advantages and disadvantages, Stone et al. [23] mapped the indices of the iceberg model to different layers, and set up differentiated selection rules to realize efficient and reasonable person-post matching.

On the relevance between strategic HR management and talent quality evaluation, Burke et al. [24] emphasized that strategic HR management directly mirrors the matching between organizational strategy and HR management, and clarified the ultimate goal of HR management as the realization of organizational competitive strategy. Lu et al. [25] measured the values of the self-adaptation of internal HR management and the horizontal matching of HR management, and stressed that the work ability and work motivation of talents on different layers can be unified based on job satisfaction by embedding a high-performance work system into the corporate HR management system.

During the management of financial enterprises, the indices of financial talent potential can be fully mined by optimizing the current HR management model, thereby improving the HR efficiency. To satisfy the strategic HR development of financial enterprises, the top priority is to develop a scientific and innovative management model, and dynamically recognize the HR quality for posts on different layers.

Capable of big data analysis, the deep neural network (DNN) has the advantages of high fault tolerance, dynamic self-organization adaptability, and autonomous learning. Compared with traditional methods like analytic hierarchy process (AHP) and multiple linear regression (MLR), the DNN adapts well to the complex and dynamic needs of financial enterprise management.

Through the above analysis, this paper proposes a comprehensive evaluation model of the HR quality in financial enterprises based on the DNN. Firstly, reasonable evaluation indices were identified for the comprehensive evaluation of the HR quality in financial enterprises, creating an evaluation index system (EIS) of five primary indices and 21 secondary indices. The complex evaluation problem was decomposed into multiple layers and factors through the AHP. On this basis, an N-index convolutional neural network (CNN), i.e. the N-evaluation model, was established based on the N-evaluation model, which takes the improvement of the comprehensive HR quality into consideration. The proposed model was proved effective through experiments.

3.1 N-evaluation model

Due to the high mobility of financial talents, the financial enterprises need to adjust their HR management model and measures as per the real-time evaluation result on the comprehensive HR quality. Therefore, it is important to include the improvement of comprehensive HR quality into the evaluation process. For this purpose, an N-evaluation model was built up for the comprehensive HR quality of financial enterprises. The algorithm of the model can be divided into the following steps:

Step 1. Replace the original index score with the standard index score

The standard score Z_ij of expert i in evaluation j can be calculated by:

${{Z}_{ij}}={{\alpha }_{i}}+{{\beta }_{i}}\cdot j+{{\varepsilon }_{ij}}$     (8)

where, α_i and β_i are two unknown parameters; ε_ij is the accidental evaluation error. Suppose n experts make k evaluations in one cycle. Let a_ij be the score of expert i in evaluation j. Then, the scores of n experts in k evaluations can be expressed as an n×k matrix:

$A={{\left( {{a}_{ij}} \right)}_{n\times k}}$     (9)

Replacing a_ij into standard score Z_ij, the standard score matrix of n experts in k evaluations can be defined as:

$Z=\left( {{Z}_{ij}} \right)_{n\times k}^{{}}=\left( \frac{{{a}_{ij}}\text{-}{{{\bar{a}}}_{j}}}{{{\eta }_{j}}} \right)_{n\times k}^{{}}=\left( \frac{{{a}_{ij}}\text{-}{{{\bar{a}}}_{j}}}{\sqrt{\frac{1}{n}\sum\limits_{i=1}^{n}{{{\left( {{a}_{ij}}-{{{\bar{a}}}_{j}} \right)}^{2}}}}} \right)_{n\times k}^{{}}$     (10)

where, $\bar{a}_{j}$ is the mean score of n experts in evaluation j; η_j is the standard deviation of a_j.

Step 2. Estimate the increment of expert score.

The regressed line can be established as:

${{\hat{Z}}_{ij}}={{\alpha }_{i}}+{{\beta }_{i}}j$     (11)

The error between the regressed line and the actual line (7) can be expressed as:

$\varepsilon _{ij}^{*}={{Z}_{ij}}-{{\hat{Z}}_{ij}}$      (12)

The e_ij values could be positive or negative and vary in size. The total error of M evaluations can be obtained by calculating its sum of squares:

${{\varepsilon }_{total}}={{\sum\limits_{j=1}^{M}{{{\varepsilon }_{ij}}^{2}=\sum\limits_{j=1}^{M}{\left( {{Z}_{ij}}-{{\alpha }_{i}}-{{\beta }_{i}}\cdot j \right)}}}^{2}}$     (13)

To minimize the sum of squares of the error, i.e. the total error, the principle of seeking extreme values can be adopted to make a_i and b_i satisfy:

$\left\{ \begin{align}  & \frac{\partial {{\varepsilon }_{total}}}{\partial {{\alpha }_{i}}}=-2\sum\limits_{j=1}^{M}{\left( {{Z}_{ij}}-{{\alpha }_{i}}-{{\beta }_{i}}\cdot j \right)}=0 \\ & \frac{\partial {{\varepsilon }_{total}}}{\partial {{\beta }_{i}}}=-2\sum\limits_{j=1}^{M}{\left( {{Z}_{ij}}-{{\alpha }_{i}}-{{\beta }_{i}}\cdot j \right)}=0 \\\end{align} \right.$     (14)

The above formula can be converted into:

$\left\{ \begin{align}  & \sum\limits_{j=1}^{M}{{{Z}_{ij}}-M{{\alpha }_{i}}-{{\beta }_{i}}\sum\limits_{j=1}^{M}{j}}=0 \\ & \sum\limits_{j=1}^{M}{j{{Z}_{ij}}-{{\alpha }_{i}}\sum\limits_{j=1}^{M}{j}}-{{\beta }_{i}}\sum\limits_{j=1}^{M}{{{j}^{2}}}=0 \\\end{align} \right.$     (15)

Solving the above formula:

$\left\{ \begin{matrix}   {{\alpha }_{i}}=\frac{1}{M}\sum\limits_{j=1}^{M}{{{Z}_{ij}}-{{\beta }_{i}}\frac{1}{M}}\sum\limits_{j=1}^{M}{j}  \\   {{\beta }_{i}}=\frac{\sum\limits_{j=1}^{M}{j{{Z}_{ij}}-\frac{1}{M}\left( \sum\limits_{j=1}^{M}{j} \right)\left( \sum\limits_{j=1}^{M}{{{Z}_{ij}}} \right)}}{\sum\limits_{j=1}^{M}{{{j}^{2}}-\frac{1}{M}{{\left( \sum\limits_{j=1}^{M}{j} \right)}^{2}}}}  \\\end{matrix} \right.$     (16)

where, β_i is the estimated increment of the score given by expert i on comprehensive HR quality of financial enterprises. Then, the estimated increments of n experts can be expressed as an n-dimensional vector:

$B=\left( {{\beta }_{1}},{{\beta }_{2}},...,{{\beta }_{n}} \right)$     (17)

Step 3. Solve the number b_i^* of indices with score increment.

Since financial enterprises continue to optimize their comprehensive HR quality, the expert scores on most indices will increase. To maintain the score increments realistic, the number of indices with score increment was adjusted as:

$\beta_{i}^{*}=\left\{\begin{array}{l}12 M \cdot \hat{\beta}(\hat{\beta} \geq 0) \\ 6 M \cdot \hat{\beta}(\hat{\beta} \geq 0)\end{array}=\left\{\begin{array}{l}12 M \cdot\left[\beta_{i}+\frac{1}{3} \gamma \cdot \max \left(\beta_{i}\right)\right](\hat{\beta} \geq 0) \\ 6 M \cdot\left[\beta_{i}+\frac{1}{3} \gamma \cdot \max \left(\beta_{i}\right)\right](\hat{\beta} \geq 0)\end{array}\right.\right.$     (18)

The number of experts with γ>0 and β₁>0 can reach or exceed 4/5 of the total number of experts. Then, the number of indices with score increment by n experts can be described as a vector:

${{B}^{*}}=\left( {{\beta }_{1}}^{*},{{\beta }_{2}}^{*},...,{{\beta }_{n}}^{*} \right)$     (19)

Step 4. Obtain the total number of indices

The total number of indices evaluated by experts is the N-index value. The N-index can be calculated by adding the mean or weighted mean of the scores in multiple evaluations with the number of indices with score increment:

${{N}_{i}}={{\bar{a}}_{i}}+\beta _{i}^{*}$     (20)

The N-index provides a panorama of the multiple evaluations by experts, because it not only considers the number of indices evaluated each time, but also takes account of the score increment induced by the optimization of comprehensive HR quality.

3.2 CNN construction

Among deep learning (DL) algorithms, the CNN is a feedforward neural network good at learning multi-dimensional matrix inputs. The CNN structure can be diversified by changing the combination between convolution and pooling layers. The structure of the traditional CNN is illustrated in Figure 1.

1.png

Figure 1. The structure of the traditional CNN

2.png

Figure 2. The connections between different layers of the CNN

Figure 2 shows the connections between different layers of the CNN. The traditional neural network (NN) cannot effectively handle the index data of our EIS, for most data are non-Euclidean space data with irregular and nonuniform dimensions and structures. If the traditional NN is directly applied to such data, the output results cannot accurately reflect the memberships, correlations, or relative importance between indices.

3.png

Figure 3. The parameter values of the proposed CNN

To solve the problem, this paper designs a CNN specifically for the evaluation of comprehensive HR quality of financial enterprises. The designed network can effectively classify the evaluation results based on the structure of the EIS. Figure 3 presents the parameter values of the proposed network.

Then, the convolution layers in Figure 3 were optimized in details. The index data C_ij and N-index convolution can be calculated by:

${{C}_{ij}}{{*}_{G }}CON={{U}_{C{{K}_{\phi }}}}{{H}^{T}}{{C}_{ij}}$     (21)

where, CK_φ is the convolution kernel of the CNN:

$C{{K}_{\phi }}=\sum\limits_{p=0}^{P}{{{\phi }_{p}}{{\Psi }^{p}}}$     (22)

where, ψ^p is the diagonal matrix composed of eigenvalues; φ_p is the kernel coefficient. After N-index convolution, the index data C_ij can be expressed as:

$u=H\left( \sum\limits_{p=0}^{P}{{{\phi }_{p}}{{\Psi }^{p}}} \right){{H}^{T}}{{C}_{ij}}$     (23)

where, φ_p is the parameter matrix to be learned by the CNN. To minimize the computing load and complexity of the kernel, the kernel can be approximated by P-order Chebyshev polynomial:

$C{{K}_{\phi }}=\sum\limits_{p=0}^{P}{{{\phi }_{p}}{{Q}_{p}}\left( \frac{2\Psi }{{{\tau }_{max}}}-{{I}_{N}} \right)}$     (24)

where, φ_p is the coefficient of the P-order Chebyshev polynomial. The recursive expansion of the polynomial can be expressed as:

${{Q}_{p}}\left( {{C}_{ij}} \right)=2{{C}_{ij}}\cdot {{Q}_{p-1}}\left( {{C}_{ij}} \right)-{{Q}_{p-2}}\left( {{C}_{ij}} \right)$     (25)

Taking the initial term Q₀(C_ij) as1, then Q₁(C_ij)=C_ij. Formula (25) can be redescribed by the recursively expanded polynomial as:

$\begin{align}  & u=H\left( \sum\limits_{p=0}^{P}{{{\phi }_{p}}{{Q}_{p}}\left( \frac{2\Psi }{{{\tau }_{max}}}-{{I}_{N}} \right)} \right){{H}^{T}}{{C}_{ij}} \\ & =\sum\limits_{p=0}^{P}{{{\phi }_{p}}{{Q}_{p}}\left( {\hat{\Gamma }} \right)}{{C}_{ij}}=\sum\limits_{p=0}^{P}{{{\phi }_{p}}{{Q}_{p}}\left( \frac{2\Gamma }{{{\tau }_{max}}}-{{I}_{N}} \right)}{{C}_{ij}} \\\end{align}$     (26)

The above formula eliminates the multiplication with matrix H, thereby simplifying the calculation. Let the values of P and τ_max be 2. Formula (27) can be simplified as:

$u={{\phi }_{0}}{{C}_{ij}}+{{\phi }_{1}}\left( \Gamma -{{I}_{N}} \right){{C}_{ij}}$      (27)

Then, the Laplace matrix can be normalized by:

${{\Gamma }^{*}}={{U}^{-{1}/{2}\;}}\Gamma {{U}^{-{1}/{2}\;}}={{I}_{N}}-{{U}^{-{1}/{2}\;}}L{{U}^{-{1}/{2}\;}}$     (28)

Substituting formula (28) to formula (27):

$u={{\phi }_{0}}{{C}_{ij}}+{{\phi }_{1}}\left( {{U}^{-{1}/{2}\;}}L{{U}^{-{1}/{2}\;}} \right){{C}_{ij}}$     (29)

If φ₀ equals -φ₁=θ, the above formula can be further simplified as:

$u=\left( {{I}_{N}}+{{U}^{-{1}/{2}\;}}A{{U}^{-{1}/{2}\;}} \right){{C}_{ij}}$     (30)

Then, the N-index convolution can be computed by:

$C_{ij}^{p+1}=\Phi \left( LC_{ij}^{p}{{\phi }^{p}} \right)$     (31)

where, L=I_N+U^-1/2AU^-1/2; C_ij^p is the N×M-dimensional input of layer p (i.e. the input of each layer has N nodes, each has M-dimensional features); φ_p is the M×W-dimensional parameter matrix of layer p. M and W are the feature dimensions of input and output nodes in convolution layer, respectively. Hence, the output dimension of layer p+1 equals N×W. The workflow of N-index convolution is explained in Figure 4.

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Figure 4. The workflow of N-index convolution

Under the cumulative effect of multiple convolutions, the eigenvalues generated in the two nearest matrices will be relatively large, resulting in vanishing gradients. To ensure the credibility of the evaluation results, L was renormalized by:

$\hat{L}={{\hat{U}}^{-{1}/{2}\;}}{{A}^{*}}{{\hat{U}}^{-{1}/{2}\;}}$      (32)

where, A^*=λI_N+W (I_N is a self-connected identity matrix). Each node l can be calculated by:

$C_{ij}^{p+1}=\Phi \left( \sum\limits_{k\in {{N}_{l}}}{\frac{1}{{{\sigma }_{lk}}}C_{ij}^{p+1}}{{\phi }^{p}} \right)$     (33)

where, N_l is the set of neighboring nodes of node l; σ_ij is the connection weight between nodes l and k. Figure 5 shows the update method of node l.

5.png

Figure 5. The update method of node l