The model structure is the use of parametric representation of probability model is used to present the statistical characteristics of random process, belong to the double random process, the main content is divided into two parts: on the one hand, refers to the markov chain, on the other hand refers to the general stochastic process, of which the former is mainly used to state transfer, transfer probability can be utilized to performance; The latter can present the relationship between observation sequence and state, which can be represented by observation numerical probability. Because the transformation process of HMM cannot be observed, it is also called hidden Markov model, and its specific structure is shown in Figure 1 below^{[1]}
:

When choosing HMM to conduct research on face recognition authentication, it is necessary to make clear the problems contained therein, which are embodied in the following points: The first is to assess the problem. Under the condition of definite model parameters, the output sequence O=O1, O2... For the probability P (O | λ) of Or, forward-backward algorithm is generally used.

Q=q1, q2... In the case of QR, the forward variable is clear, as shown below:

In other words, under the condition of definite model, the output observation sequence O=O1, O2... Or, the probability that the state at time t belongs to Si. The derivation process as shown below is used for calculation and analysis:

Initialization processing^{[2]}
:

Derivation and analysis:

Termination:

Secondly, it refers to the decoding problem. Viterbi algorithm needs to be analyzed according to the principle of dynamic programming. Define
_{t}(^{[3]}
:

Initialization processing:

Derivation and analysis:

Termination:

Calculate S sequence:

Finally, it refers to learning problems. Nowadays, baum-Welch estimation algorithm is the most common method for HMM parameter selection and optimization. This algorithm is an iterative algorithm, which needs to be estimated according to the user’s accumulated parameter experience at the initial stage, and then ensures that each parameter gradually tends to rationalize in continuous iteration, and finally obtains the optimized value. Specific operation steps are as follows^{[4]}
:

Initialization processing:

Iterative calculation:

Assuming that _{t}

If

Termination:

Nowadays, a lot of face recognition algorithm can get high recognition probability, the reason is that the quality of the captured image is higher, and with the facial expression, posture, the change of the information such as light, application performance of the system will continue to fall, and the lens, the influence of such factors as noise in the image contains also affect the effect of face recognition, Therefore, the pre-processing operation of image information acquisition should be done well before face verification. In this paper, a fixed window face detection method is proposed based on Adaboost algorithm^{[5]}
.

As the most effective content of the current mode classification problem, boost algorithm needs to obtain a strong separator on the basis of merging a large number of weak classifiers. The classification results of strong classifier are obtained by weighted voting of weak classifier. For the binary classification problem, the encoding of the output variable is. For variable X, the classifier belongs to the prediction data and meets this condition. Then the error formula of the corresponding training sample is shown as follows:

From the perspective of practical application, the training process of Adaboost algorithm is shown in Figure 2 below:

In this study, the cascade classifier is selected, which can not only control the detection time, but also accurately detect the contained face samples based on the organization of simple and efficient separator, so as to ensure the error rejection rate is zero. The specific structure is shown in Figure 3 below. Because the included classifier is very simple and the actual calculation speed is very fast, only human faces and regions similar to human faces will be left in the final study. Complex classifiers are used in the subsequent research and analysis. Although it takes more time than the previous classifiers, they can distinguish faces more accurately. At the same time, most of the areas have been excluded in the initial analysis, so sophisticated classifiers can be used to complete accurate calculations. The overall decision-making process is a degenerate decision tree, which can also be called cascade^{[6]}
.

On the basis of defining the traditional HMM observation vector acquisition methods, a variety of feature extraction methods are selected to optimize and improve the OBSERVATION vector of HMM. Among them, wavelet analysis, as the main content of engineering discipline and applied mathematics research at the present stage, has formed a relatively perfect mathematical formal system in the practice of inquiry, and the relevant theoretical basis is very solid. By using effect analysis reasonably in image processing, image enhancement, decomposition, fusion, compression and other problems can be effectively dealt with. The function form of wavelet is as follows^{[7]}
:

In the above formula, A represents the scale parameter and B represents the positioning parameter. Assuming that a is greater than 1,Then the _{a,b}_{a,b}_{a,b}

E-hmm represents a pseudo-two-dimensional HMM. All e-Hmm contain a master state, and all master states contain one-dimensional HMM, which means that a group of one-dimensional HMM will be integrated into another group of HMM, so it can be called embedded HMM. The e-HMM model is used to model and analyze the system user’s face, and the face is mainly divided into five super states as shown in Figure 4 below, including several sub-states. It should be noted that the hyperstate model is analyzed according to the vertical direction of the image, while the substate is studied according to the horizontal state of the model. At the same time, multiple feature extraction methods proposed in the above study are used to improve the acquired observation vector, and the overall authentication is completed in combination with the input E-HMM. The specific operation flow chart is shown in Figure 5 below^{[8]}
:

E-hmm training is studied by maximum likelihood criterion. All people have e-HMM face model and can be trained according to lighting conditions, posture, hairstyle and other content. The specific steps are as follows: First, the observation vector of all people should be obtained; Secondly, the model parameters should be initialized, including the probability distribution and the number of states involved. Again, the parameters after initialization should be adjusted, in other words, the division of various super states and substates on feature vectors should be scientifically optimized. Pay attention to the use of double nested Viterbi algorithm, if in multiple iteration analysis, Viterbi algorithm results are lower than the expected set range, then end the iteration operation, thus completing the initialization process; Finally, the pre-term and post-term algorithm is used to re-estimate the budget of the model parameters, so as to ensure the maximization of the observation vector probability under the condition of a given model, thus ending the training. The specific operation is shown in Figure 6 below^{[7.8]}
:

After the training, the E-HMM training model can perform face recognition. Combined with the flow chart analysis shown in Figure 7 below, specific operations can be divided into the following points: First, the face image feature vector of the visitor is obtained first; Secondly, Viterbi algorithm is used to calculate the probability of observation vector accurately according to the training model. Third, according to the literature to set conditions to accurately judge whether the visitors meet the certification identity. Under the condition of too many users, the authentication threshold should be optimized to ensure that each user has the best threshold as the authentication condition, and then improve the probability of actual face recognition authentication.

Empirical analysis is made on the face recognition authentication technology of generative adverstive network based on wavelet transform hidden Markov model. The CPU of the selected experimental platform is Intel Core Duo T83002.40ghz, the actual memory is DDR 22G, and the operating system is Windows XP. The programming environment is Microsoft Visual Studio6.0. The selected face database is a series of face images taken by The Cambridge Laboratory in the early 1990s, which contains 40 objects of different genders, ages and races. Each object contains 10 images with a size of 92×112, and the image size reaches 48×48 after normalized processing. The total number of images is 400. In addition, the facial expression and posture of the face changed greatly, and the size of the face also changed by 10 percent. At present, ORL database is the most widely used standard database. In practical exploration, the database is divided into two sets with the same number of samples, and the set composed of the first five images of the user belongs to the training set, while the set composed of the remaining five images is the test set. The specific test scheme is shown in Figure 8 below^{[9.10]}:

In the experimental analysis, performance indicators need to be judged from two aspects: on the one hand, the error rejection rate (FRR) and on the other hand, the error acceptance rate (FAR). According to the experimental scheme proposed above, the curve of FRR-FAR can be obtained by using diversified observation vector optimization methods. The specific authentication probability is shown in Table 1 below:

Distribution results of frR-FAR of authentication rate

The threshold value | K - L transformation | DCT | Level of wavelet | Gabor feature | ||||
---|---|---|---|---|---|---|---|---|

−43.4 | FRR | FAR | FRR | FAR | FRR | FAR | FRR | FAR |

−43.6 | 56.52% | 0.75% | 39.75% | 0.75% | 37.25% | 0.75% | 59.25% | 0.25% |

−43.8 | 42.75% | 1.00% | 32.00% | 1.50% | 31.75% | 1.00% | 49.75% | 0.75% |

−44.0 | 33.25% | 1.25% | 23.75% | 3.25% | 25.50% | 2.25% | 42.25% | 1.25% |

−44.2 | 25.5% | 3.25% | 16.00% | 4.00% | 20.50% | 4.25% | 33.50% | 3.25% |

−44.4 | 20.75% | 5.25% | 11.25% | 7.50% | 14.75% | 7.25% | 24.75% | 5.50% |

−44.6 | 15.50% | 8.75% | 8.50% | 12.50% | 10.50% | 9.75% | 16.00% | 6.25% |

−44.8 | 11.75% | 12.50% | 7.00% | 16.75% | 8.75% | 13.50% | 9.75% | 8.25% |

−45.0 | 10.00% | 17.25% | 5.25% | 21.00% | 6.75% | 18.25% | 7.50% | 11.75% |

−45.2 | 7.75% | 23.25% | 4.50% | 25.00% | 5.25% | 23.25% | 4.75% | 15.00% |

−45.4 | 4.25% | 29.75% | 2.75% | 29.25% | 3.25% | 26.75% | 3.00% | 19.25% |

−45.6 | 2.75% | 36.00% | 1.75% | 33.75% | 1.75% | 31.00% | 2.00% | 25.50% |

−45.8 | 1.25% | 42.50% | 1.25% | 37.75% | 1.25% | 35.50% | 1.00% | 32.75% |

−43.4 | 1.00% | 49.25% | 0.50% | 42.50% | 0.75% | 40.25% | 1.00% | 38.75% |

Combined with the above results, it can be seen that the authentication error rate obtained by the four observation vector optimization methods can reach 10% on average, among which the wavelet transform method proposed in this paper is more effective. Training at the same time, in order to get more reasonable results, on the basis of the integration of the above research, but also in the experiment was carried out on the training set and testing set scientific adjustment, such as accurate eliminate tilted too serious samples in the training set, etc., and then to adjust after the sample data to experimental analysis, the obtained results are shown in table 2 below:

Comparison results of authentication rate before and after adjustment

Original authentication rate | Adjust the certification rate after training set | |
---|---|---|

K - L transformation | 12.10% | 7.20% |

DCT | 9.80% | 6.05% |

Level of wavelet | 10.05% | 6.20% |

Gabor feature | 8.90% | 4.95% |

The authentication performance of the model is improved and meets the requirements of practical application. Therefore, it can be seen that by analyzing the error samples with examples, summarizing the main causes of authentication errors, scientifically adjusting some users’ collection samples according to the conclusion, and removing the imperfect sample data in time, it can not only improve the efficiency of actual authentication, but also ensure the effectiveness of sample authentication. Because different users are affected by light conditions, sample characteristics and other factors, the distribution of actual similarity varies greatly. Different users of the similarity of the overall average value and variance are different, and the use of dynamic threshold adjustment constantly optimize the threshold of all users, scientific construction of authentication experiments, can obtain effective information on the basis of improving the hidden Markov model as the core of the face authentication model performance.

At present, face authentication technology is not mature, the actual system design directly affects the efficiency of algorithm application, therefore, on the basis of clear application algorithm and model composition, to ensure the perfection and effectiveness of system design, only in this way, to fully show the application value of the core algorithm. Combined with the analysis of the working principle shown in Figure 9 below, it can be seen that the system should first build the image information database, and put forward the storage and training of standard face information. At the same time, the system should be connected with the camera, so as to obtain the face information of entering a specific place, and on the basis of accurate authentication, put forward an alarm to illegal visitors.

To sum up, in the innovation and development of social economy and scientific and technological concepts, whether information security or public security, most fields have raised the application requirements of identity authentication technology, and began to build new research models based on the integration of previous development experience and advanced technological concepts. Hidden markov model as the core, on the basis of integration optimization of observation vector, put forward modeling of two-dimensional face image analysis, and on the basis of the model training, using high quality hidden markov models to face verification, preferable dynamic threshold adjustment way, strengthen the authentication model of adaptive level, not only can improve model certification application performance, It also demonstrates the unique value of the applied algorithm. Therefore, in the continuous exploration of identity authentication system and related technologies, we should pay attention to the hidden Markov model, strengthen the strength of practical exploration, define the direction of future scientific research, so as to solve the problems of traditional models, put forward a more effective authentication system.

#### Distribution results of frR-FAR of authentication rate

The threshold value | K - L transformation | DCT | Level of wavelet | Gabor feature | ||||
---|---|---|---|---|---|---|---|---|

−43.4 | FRR | FAR | FRR | FAR | FRR | FAR | FRR | FAR |

−43.6 | 56.52% | 0.75% | 39.75% | 0.75% | 37.25% | 0.75% | 59.25% | 0.25% |

−43.8 | 42.75% | 1.00% | 32.00% | 1.50% | 31.75% | 1.00% | 49.75% | 0.75% |

−44.0 | 33.25% | 1.25% | 23.75% | 3.25% | 25.50% | 2.25% | 42.25% | 1.25% |

−44.2 | 25.5% | 3.25% | 16.00% | 4.00% | 20.50% | 4.25% | 33.50% | 3.25% |

−44.4 | 20.75% | 5.25% | 11.25% | 7.50% | 14.75% | 7.25% | 24.75% | 5.50% |

−44.6 | 15.50% | 8.75% | 8.50% | 12.50% | 10.50% | 9.75% | 16.00% | 6.25% |

−44.8 | 11.75% | 12.50% | 7.00% | 16.75% | 8.75% | 13.50% | 9.75% | 8.25% |

−45.0 | 10.00% | 17.25% | 5.25% | 21.00% | 6.75% | 18.25% | 7.50% | 11.75% |

−45.2 | 7.75% | 23.25% | 4.50% | 25.00% | 5.25% | 23.25% | 4.75% | 15.00% |

−45.4 | 4.25% | 29.75% | 2.75% | 29.25% | 3.25% | 26.75% | 3.00% | 19.25% |

−45.6 | 2.75% | 36.00% | 1.75% | 33.75% | 1.75% | 31.00% | 2.00% | 25.50% |

−45.8 | 1.25% | 42.50% | 1.25% | 37.75% | 1.25% | 35.50% | 1.00% | 32.75% |

−43.4 | 1.00% | 49.25% | 0.50% | 42.50% | 0.75% | 40.25% | 1.00% | 38.75% |

#### Comparison results of authentication rate before and after adjustment

Original authentication rate | Adjust the certification rate after training set | |
---|---|---|

K - L transformation | 12.10% | 7.20% |

DCT | 9.80% | 6.05% |

Level of wavelet | 10.05% | 6.20% |

Gabor feature | 8.90% | 4.95% |

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Multiple Effects Analysis of Hangzhou Issuing Digital Consumer Coupons Based on Simultaneous Equations of CDM Model Response Model of Teachers’ Psychological Education in Colleges and Universities Based on Nonlinear Finite Element Equations A Hybrid Computational Intelligence Method of Newton's Method and Genetic Algorithm for Solving Compatible Nonlinear Equations Pressure Image Recognition of Lying Positions Based on Multi-feature value Regularized Extreme Learning Algorithm English Intelligent Question Answering System Based on elliptic fitting equation Precision Machining Technology of Jewelry on CNC Machine Tool Based on Mathematical Modeling Application Research of Mathematica Software in Calculus Teaching Computer Vision Communication Technology in Mathematical Modeling Skills of Music Creation Based on Homogeneous First-Order Linear Partial Differential Equations Mathematical Statistics Technology in the Educational Grading System of Preschool Students Music Recommendation Index Evaluation Based on Logistic Distribution Fitting Transition Probability Function Children's Educational Curriculum Evaluation Management System in Mathematical Equation Model Query Translation Optimization and Mathematical Modeling for English-Chinese Cross-Language Information Retrieval The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization research on prefabricated concrete frame buildings based on the dynamic equation of eccentric structure and horizontal-torsional coupling Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Green building considering image processing technology combined with CFD numerical simulation MCM of Student’s Physical Health Based on Mathematical Cone Sports health quantification method and system implementation based on multiple thermal physiology simulation Research on visual optimization design of machine–machine interface for mechanical industrial equipment based on nonlinear partial equations Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Mathematical function data model analysis and synthesis system based on short-term human movement Human gait modelling and tracking based on motion functionalisation The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate Differential equation model of financial market stability based on Internet big data 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Children’s cognitive function and mental health based on finite element nonlinear mathematical model Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsThe internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Research on threat assessment problems of island air defence system based on the leader-follower model Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks Evaluation of ecosystem health in Futian mangrove wetland based on the PSR-AHP model A study of local smoothness-informed convolutional neural network models for image inpainting Towards more efficient control of the ironmaking blast furnace: modelling gaseous reduction of iron ores in H _{2}-N_{2}atmosphereAlgorithm of overfitting avoidance in CNN based on maximum pooled and weight decay Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model