Palm print image recognition method based on complex value convolutional neural network

Abstract

The invention provides a palmprint image recognition method based on a complex value convolutional neural network, and relates to the technical field of biological feature recognition. An obtained initial palmprint image is converted into an HSV image, and a complex-valued palmprint image in an iHSV format is generated through a complex-valued image conversion model; constructing a palmprint image recognition network of full complex value operation, and optimizing network parameters of the palmprint image recognition network by adopting a complex value dynamic activation function and a complex value dynamic loss function; inputting the complex value palmprint image into an optimized palmprint image recognition network, and obtaining an output result; and matching the output result with palmprint data in a database, and outputting an identification result. The problems existing in small sample palmprint recognition are solved, and the accuracy of palmprint recognition is improved.

Description

Technical Field

[0001] The present application relates to the field of biometric recognition technology, and in particular, to a palmprint image recognition method based on a complex-valued convolutional neural network. Background Art

[0002] Palmprint recognition is a human recognition technology that uses the right or left palm to work in the same way as fingerprints. Compared with common biometrics such as face and fingerprint, palmprint has the advantages of large collection area, rich texture information, low requirements for collection equipment, and high security, especially the data matching process that can be performed using low-resolution images. Therefore, it has attracted wide attention in the field of biometric recognition. In addition, users have greater initiative during the palmprint collection process, can decide whether to present their palmprint, and are also more difficult to be secretly captured by surveillance cameras, thus having a lower risk of privacy infringement. Therefore, palmprint shows great potential in recognition applications. Early palmprint recognition mainly relied on manually annotating unique feature points of palmprints, such as main palm lines, wrinkles, fine textures, ridge endings, and bifurcation points. By calculating the positions of these feature points and the texture information around them, and then comparing them with the palmprint database, the recognition result is obtained. However, this method highly depends on manual intervention and has strong subjectivity. For example, different operators may have inconsistent understandings of the positions of each feature point in the palmprint, and errors are inevitable during the annotation process. Even for the same palmprint, different operators may obtain different annotation results. In addition, this method takes a long time, but the recognition efficiency and accuracy cannot reach the ideal effect.

[0003] Therefore, how to improve the accuracy of palmprint recognition in small-sample scenarios has become an urgent technical problem to be solved. Summary of the Invention

[0004] In order to improve the accuracy of palmprint recognition in small-sample scenarios, the present application provides a palmprint image recognition method based on a complex-valued convolutional neural network.

[0005] A palmprint image recognition method based on a complex-valued convolutional neural network provided by the present application adopts the following technical solutions: A palmprint image recognition method based on a complex-valued convolutional neural network, comprising: Converting the obtained initial palmprint image into an HSV image, and generating a complex-valued palmprint image in iHSV format through a complex-valued image conversion model; Constructing a palmprint image recognition network with all complex-valued operations, the network includes a complex-valued convolutional module, a complex-valued pooling module, a complex-valued normalization module, a complex-valued residual block, and a complex-valued dense block, wherein the complex-valued residual block and the complex-valued dense block are connected through a conversion layer, and the conversion layer is composed of complex-valued convolution and complex-valued pooling; Optimize the network parameters of the palmprint image recognition network by using a complex-valued dynamic activation function and a complex-valued dynamic loss function; Input the complex-valued palmprint image into the optimized palmprint image recognition network and obtain the output result; Match the output result with the palmprint data in the database and output the recognition result.

[0006] Optionally, the step of converting the obtained initial palmprint image into an HSV image and generating a complex-valued palmprint image in iHSV format through a complex-valued image conversion model includes: Obtain the initial palmprint image and convert the palmprint image in RGB format into an HSV format image , where h represents hue, S represents saturation, and V represents value; Convert the HSV format image into an iHSV complex-valued format image , which is achieved through the following channel settings: Hue fixed channel , with saturation S as the real axis and value V as the imaginary axis; Saturation fixed channel , with value V as the real axis and the product of saturation and hue as the imaginary axis; Value fixed channel , which is generated through polar coordinate transformation; Separate and recombine the real and imaginary parts of the three channels to generate a complete complex-valued image.

[0007] Optionally, the complex-valued residual block includes at least two residual structures: Residual structure 1: Make the number of input and output channels consistent through complex-valued convolution and complex-valued normalization, and perform weighted fusion; Residual structure 2: Process the input data through a complex-valued activation function and then perform weighted fusion with the original input.

[0008] Optionally, each layer in the complex-valued dense block receives the outputs of all previous layers as inputs and is processed by a non-linear transformation module, which is composed of complex-valued normalization, a complex-valued activation function, and complex-valued convolution.

[0009] Optionally, the complex-valued dynamic activation function is defined as: ; where the complex number ; ; ; represents the restricted region for dynamically adjusting the phase of the complex number, represents the activation threshold for dynamically adjusting ReLU.

[0010] Optionally, the complex-valued dynamic loss function is composed of a complex-valued cross-entropy loss function and a complex-valued weighted triplet loss function : ; where: ; ; represents the complex output of the model; ; wherein, represents the anchor sample, represents the positive sample, represents the negative sample, and represent the positive and negative sample weights respectively.

[0011] Optionally, the distance metric in the complex-valued weighted triplet loss function is calculated by the following formula: .

[0012] In summary, the present application converts the obtained initial palmprint image into an HSV image, and generates a complex-valued palmprint image in iHSV format through a complex-valued image conversion model; constructs a palmprint image recognition network with all complex-valued operations, and optimizes the network parameters of the palmprint image recognition network by using a complex-valued dynamic activation function and a complex-valued dynamic loss function; inputs the complex-valued palmprint image into the optimized palmprint image recognition network and obtains an output result; matches the output result with the palmprint data in the database, and outputs a recognition result. This solves the problems existing in small-sample palmprint recognition and improves the accuracy of palmprint recognition. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 is a schematic flowchart of the first embodiment of the palmprint image recognition method based on a complex-valued convolutional neural network according to the present application; Figure 2 is a flowchart of the complex-valued conversion model according to the present application; Figure 3 is an overall recognition model diagram of the present application; Figure 4 is a structural diagram of four complex-valued residual blocks in the complex-valued convolutional neural network model of the present application, where Figure 4 (a) is the complex-valued residual block 1; Figure 4 (b) is the complex-valued residual block 2; Figure 4 (c) is the complex-valued residual block 3; Figure 4(d) is the complex-valued residual block 4; Figure 5 are two major residual structure diagrams of this application, where Figure 5 (a) represents the residual structure 1, Figure 5 (b) is the residual structure 2; Figure 6 is the complex-valued dense block diagram of this application. Detailed implementation manners

[0014] In order to make the objectives, technical solutions and advantages of this application clearer, the following further details this application through the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not used to limit this application.

[0015] The embodiment of this application provides a palmprint image recognition method based on a complex-valued convolutional neural network. Referring to Figure 1 , Figure 1 is the flow diagram of the first embodiment of the palmprint image recognition method based on the complex-valued convolutional neural network of this application.

[0016] In this embodiment, the palmprint image recognition method based on the complex-valued convolutional neural network includes the following steps: Step S10: Convert the obtained initial palmprint image into an HSV image, and generate a complex-valued palmprint image in iHSV format through a complex-valued image conversion model.

[0017] The step of converting the obtained initial palmprint image into an HSV image and generating a complex-valued palmprint image in iHSV format through a complex-valued image conversion model includes: Obtain the initial palmprint image and convert the palmprint image in RGB format into an HSV format image , where h represents hue, S represents saturation, and V represents value; Convert the HSV format image into an iHSV complex-valued format image , which is achieved through the following channel settings: Hue fixed channel , with saturation S as the real axis and value V as the imaginary axis; Saturation fixed channel , with value V as the real axis and the product of saturation and hue as the imaginary axis; Value fixed channel , which is generated through polar coordinate conversion; Separate and recombine the real and imaginary parts of the three channels to generate a complete complex-valued image.

[0018] It should be noted that since the HSV model describes colors through hue, saturation, and value, which is more in line with the intuitive perception of colors by humans. In the HSV model, color comparison and matching are usually more intuitive and accurate than in the RGB model because the changes in hue, saturation, and value are independent and linear. Since it can more easily distinguish and isolate objects with similar colors, converting the original palmprint image into the HSV format is more conducive to subsequent recognition. HSV is used to express the three main attributes of colors: hue, saturation, and value. Hue, saturation, and value represent the angular axis, radial axis, and vertical axis of the cylindrical HSV color model.

[0019] In specific implementation, the image conversion process is carried out around three channels, namely the hue-fixed channel , the saturation-fixed channel , and the value-fixed hue .

[0020] Hue-fixed channel : Fix the hue element to form a rectangular plane. Take saturation and value as the axes to establish a coordinate system, with saturation as the real axis and value as the imaginary axis, and then derive its position in the coordinate system as shown in the following formula: ; Saturation-fixed channel : Fix the saturation element to form a hollow cylinder, which is unfolded to form a rectangular plane. The plane takes value as the real axis and the product of saturation and hue as the imaginary axis, and then derive its position in the coordinate system as shown in the following formula: ; Value-fixed hue : Fix the saturation element to form a circular plane. Therefore, polar coordinates are established on this plane, with the central angle in units of , and its position in the coordinate system is derived as shown in the following formula: ; Recombine the real and imaginary parts of the above three channels to form the real and imaginary parts corresponding to the complex-valued image respectively. The flow of the entire complex-valued conversion model is as Figure 2 shown.

[0021] Step S20: Construct a palmprint image recognition network for full complex-valued operations. The network includes a complex-valued convolution module, a complex-valued pooling module, a complex-valued normalization module, a complex-valued residual block, and a complex-valued dense block. Among them, the complex-valued residual block and the complex-valued dense block are connected through a conversion layer, and the conversion layer is composed of complex-valued convolution and complex-valued pooling.

[0022] The complex-valued residual block contains at least two types of residual structures: Residual structure 1: The number of input and output channels is made consistent through complex-valued convolution and complex-valued normalization, and weighted fusion is performed. Residual structure 2: The input data is processed through a complex-valued activation function and then weighted and fused with the original input.

[0023] Each layer in the complex-valued dense block receives the outputs of all previous layers as inputs and is processed through a non-linear transformation module, which consists of complex-valued normalization, a complex-valued activation function, and complex-valued convolution.

[0024] In a specific implementation, the main body of the overall recognition model is composed of a complex-valued residual block and a complex-valued dense block. The combination of the two modules can better extract the corresponding features of the image, and at the same time solve problems such as gradient vanishing and gradient explosion. A conversion layer is used to connect the two major modules. The conversion layer is composed of complex-valued convolution and complex-valued pooling, and the conversion layer can effectively reduce the size of the feature map to make the feature map data consistent during the transmission process. The introduced designed complex-valued activation function and complex-valued loss function further improve the efficiency of the model. The overall recognition model is as Figure 3 shown. Each complex-valued residual block is composed of two residual structures, but different residual blocks have different numbers of residual structures. The structures of four complex-valued residual blocks are as Figure 4 shown. Figure 4 Represents the structures of four complex-valued residual blocks in the complex-valued convolutional neural network model, Figure 4 (a) is the complex-valued residual block 1, which is composed of one residual structure 1 and two residual structures 2. Figure 4 (b) is the complex-valued residual block 2, which is composed of one residual block structure 1 and three residual structures 2. Figure 4 (c) is the complex-valued residual block 3, which is composed of one residual block structure 1 and five residual structures 2. Figure 4 (d) is the complex-valued residual block 4, which is composed of one residual block structure 1 and two residual structures 2.

[0025] Residual structure 1 makes the number of output channels at both ends consistent by adding a complex-valued convolution and a complex-valued regularization process, and then performs a weighted sum. Residual structure 2 directly performs a weighted sum of the input data and the processed score data through a complex-valued activation function. The two major residual structures are as Figure 5 shown. Figure 5 Represents the two residual structures in the complex-valued residual block, where Figure 5 (a) represents residual structure 1. Residual structure 1 makes the number of output channels at both ends consistent by adding a complex-valued convolution and a complex-valued regularization process, and then performs a weighted sum. Among them, Figure 5 (b) is residual structure 2. Residual structure 2 directly performs a weighted sum of the input data and the processed score data through a complex-valued activation function.

[0026] The complex-valued dense block is as Figure 6 shown. Each layer Xi in the block receives all the previous layers as inputs. Where C represents the non-linear transformation process, which consists of complex-valued normalization, complex-valued activation function, and complex-valued convolution.

[0027] Step S30: Optimize the network parameters of the palmprint image recognition network by using a complex-valued dynamic activation function and a complex-valued dynamic loss function.

[0028] It can be understood that the activation function can introduce non-linearity into the model, enabling the neural network to learn complex patterns. However, traditional activation functions can only handle real values and cannot handle complex values. Therefore, for a fully complex-valued network, a complex-valued activation function that can efficiently process complex values needs to be set. Existing complex-valued activation functions all have some defects. For example, the ZReLU activation function only retains the case when both the real part and the imaginary part are positive, and the CReLU activation function processes the real part and the imaginary part of the complex number separately through the ReLU activation function. Such complex-valued activation functions will have problems such as information fragmentation, destroying the internal correlation of complex numbers. Therefore, a dynamic complex-valued activation function DCZReLU is set to solve the deficiencies of existing activation functions by introducing dynamic adjustment parameters.

[0029] It should be noted that the complex-valued dynamic activation function is defined as: ; where the complex number ; ; ; represents the restricted region for dynamically adjusting the phase of the complex number, represents the activation threshold for dynamically adjusting ReLU.

[0030] In specific implementation, the loss function is used to quantify the difference between the model prediction value and the true value, reflecting the performance of the model. By minimizing the loss function, the model can gradually adjust the parameters to improve the prediction accuracy. The loss function can also provide a direction for optimization algorithms (such as gradient descent) to help the model continuously improve during training. The cross-entropy loss function focuses on optimizing the probability distribution of classification tasks to ensure that the model output is consistent with the true labels. The triplet loss function enhances the feature discrimination ability through contrastive learning, making similar samples closer and dissimilar samples farther apart. In this embodiment, a complex-valued dynamic triplet loss function and a complex-valued cross-entropy loss function are dynamically combined. By combining the advantages of both, the model can not only optimize the classification probability but also learn more discriminative features. At the same time, it can balance the classification task and feature learning, reduce the risk of overfitting, and improve the generalization performance of the model. The dynamic combination can further optimize the feature learning and classification performance of complex-valued data.

[0031] It is understandable that the complex-valued dynamic loss function is composed of a complex-valued cross-entropy loss function and a complex-valued weighted triplet loss function as follows: ; where: ; ; represents the complex output of the model; ; wherein, represents the anchor sample, represents the positive sample, represents the negative sample, and respectively represent the positive and negative sample weights.

[0032] In a specific implementation, the distance metric in the complex-valued weighted triplet loss function is calculated by the following formula: .

[0033] Step S40: Input the complex-valued palmprint image into the optimized palmprint image recognition network and obtain the output result.

[0034] Step S50: Match the output result with the palmprint data in the database and output the recognition result.

[0035] It should be noted that the emergence of convolutional neural networks has provided a practical solution for palmprint recognition based on deep learning algorithms. This field has brought a new direction to biometric recognition. Convolutional neural networks usually perform convolution operations by extracting features of the region of interest in an image, and use the extracted texture features for linear classification, significantly reducing the labor cost. Compared with traditional palmprint recognition methods, palmprint recognition based on deep learning reduces human intervention, avoids the influence of subjective factors, and can also extract effective features from low-resolution palmprint images, with advantages such as high recognition accuracy and strong generalization ability. Complex-valued neural networks have also been a research hotspot in recent years. In the fields of speech enhancement, image, and signal processing, complex-valued neural networks have shown better performance than real-valued networks. Currently, the vast majority of building blocks, technologies, and architectures of deep learning are based on real-valued operations and representations. However, recent research on recurrent neural networks and earlier fundamental theoretical analyses have shown that complex numbers may have richer representation capabilities and may also promote anti-noise memory retrieval mechanisms. The current mainstream convolutional neural networks are basically real-valued networks. Although real-valued networks have achieved remarkable results in the field of computer vision, complex-valued networks still have certain advantages in some aspects. For example, complex numbers have a series of good properties that real numbers do not have in expressing vector aggregation, rotation, and exponential operations. Complex numbers can handle both amplitude and phase information simultaneously, making the model more flexible in capturing the complexity of data. This dual information helps to simplify the representation of the model. Complex-valued functions can operate in a higher-dimensional feature space, enabling the model to better separate different classes of data. The higher dimension provides more degrees of freedom for the decision boundary. The orthogonal decision boundary in complex-valued networks can effectively reduce the interference between classes, making the performance of the model more stable on new data, thereby improving the generalization ability. Since complex-valued neural networks can effectively express complex patterns in a higher dimension, they often can achieve the same performance with fewer parameters, which helps to reduce the risk of overfitting. Starting from the actual application scenario, this embodiment reduces the palmprint data acquisition cost and the recognition model training cost, and improves the accuracy of palmprint recognition in small-sample scenarios; in addition, it directly operates on the image in the complex number domain without the need to convert the data into two independent parts of real and imaginary parts, greatly reducing the computational complexity and also improving the anti-interference ability of the model.

[0036] It should be noted that the effects achieved by the method of this embodiment include: Improve the recognition performance in small-sample scenarios: Through the complex-valued convolutional neural network (CV-CNN) architecture, combined with complex-valued image transformation and dynamic loss function, the accuracy and efficiency of small-sample palmprint recognition are significantly improved. Complex-valued networks can make full use of the phase and amplitude information in the complex number domain, reduce the dependence on large-scale training data, and solve the recognition bottleneck problem caused by traditional real-valued networks ignoring phase information.

[0037] Enhanced feature representation ability: The complex-valued image conversion model (iHSV format) combines the intuitive perception advantages of the HSV color model with the multi-dimensional representation ability of complex numbers, mapping the hue, saturation, and brightness of palm prints into complex domain features, effectively retaining the texture details and phase information of palm prints; The combination of complex-valued residual blocks and dense blocks enables the extraction and reuse of multi-level semantic features. Through gradient optimization and feature aggregation mechanisms, the model's sensitivity to subtle differences in palm prints is enhanced.

[0038] Optimized training stability and model depth: The complex-valued residual block alleviates the problems of gradient vanishing and explosion by weighted fusion of input and output features, supporting the training of deeper networks; The complex-valued dense block enhances the model's non-linear expression ability through multi-scale feature reuse while reducing parameter redundancy.

[0039] Dynamic adaptive mechanism to improve generalization ability: The dynamic complex-valued activation function (DCZReLU) avoids information fragmentation of complex-valued features and maintains internal complex-valued correlations by adjusting the phase limit parameter (α) and activation threshold (β); The dynamic combined loss function (cross-entropy + triplet loss) adaptively balances the classification task and feature discriminability through weight parameters (α, β), reducing the risk of overfitting and enhancing the model's robustness to noise and interference.

[0040] Efficient end-to-end complex-valued processing: The all-complex-valued operation process does not require splitting data into real and imaginary parts for separate processing, reducing computational complexity and information loss; The end-to-end architecture simplifies the palm print recognition process, improves operation efficiency, and is suitable for real-time or resource-constrained scenarios.

[0041] Reduced application costs: Efficient training in small-sample scenarios reduces the need for labeled data volume and computational resources; High-precision recognition ability reduces the dependence on high-resolution acquisition devices, broadening the application prospects of palm print recognition in low-cost terminal devices.

[0042] This embodiment combines complex-valued image conversion, dynamic complex-valued network architecture, and adaptive optimization mechanism, significantly improving the accuracy, efficiency, and robustness of palm print recognition. It has outstanding practical value especially in small-sample and low-resolution scenarios, providing an efficient and low-cost solution for the field of biometric recognition.

[0043] In this embodiment, the obtained initial palmprint image is converted into an HSV image, and a complex-valued palmprint image in iHSV format is generated through a complex-valued image conversion model; a palmprint image recognition network with all complex-valued operations is constructed, and the network parameters of the palmprint image recognition network are optimized by using a complex-valued dynamic activation function and a complex-valued dynamic loss function; the complex-valued palmprint image is input into the optimized palmprint image recognition network to obtain an output result; the output result is matched with the palmprint data in the database to output a recognition result. This solves the problems existing in small-sample palmprint recognition and improves the accuracy of palmprint recognition.

[0044] It should be noted that the above-described work process is only illustrative and does not limit the protection scope of this application. In actual applications, those skilled in the art can select some or all of them according to actual needs to achieve the purpose of the solution of this embodiment, and no limitation is imposed here.

[0045] In addition, for the technical details not described in detail in this embodiment, reference can be made to the method for palmprint image recognition based on a complex-valued convolutional neural network provided in any embodiment of this application, which will not be elaborated here.

[0046] In addition, it should be noted that in this article, the terms "including", "comprising" or any other variant thereof are intended to cover non-exclusive inclusion, so that a process, method, article or system including a series of elements not only includes those elements, but also includes other elements not expressly listed, or further includes elements inherent to such process, method, article or system. Without further limitation, an element defined by the statement "including one..." does not exclude the existence of another identical element in the process, method, article or system including that element.

[0047] The serial numbers of the embodiments of the present application above are only for description and do not represent the advantages and disadvantages of the embodiments.

[0048] Through the description of the above embodiments, those skilled in the art can clearly understand that the above-described example methods can be implemented by means of software plus a necessary general hardware platform. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation. Based on such an understanding, the technical solution of the present application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as a read-only memory (ROM) / RAM, magnetic disk, optical disk), and includes several instructions for causing a terminal device (which can be a mobile phone, computer, server, or network device, etc.) to execute the methods of the various embodiments of the present application. The above is only the preferred embodiment of the present application, and does not limit the patent scope of the present application. Any equivalent structure or equivalent process transformation made by using the content of the specification and drawings of the present application, or directly or indirectly applied in other related technical fields, shall be equally included in the patent protection scope of the present application.

Claims

1. A palmprint image recognition method based on a complex-valued convolutional neural network, characterized in that, Including: Converting the obtained initial palmprint image into an HSV image, and generating a complex-valued palmprint image in iHSV format through a complex-valued image conversion model; Constructing a palmprint image recognition network with all complex-valued operations, the network including a complex-valued convolution module, a complex-valued pooling module, a complex-valued normalization module, a complex-valued residual block, and a complex-valued dense block, wherein the complex-valued residual block and the complex-valued dense block are connected by a conversion layer, and the conversion layer is composed of complex-valued convolution and complex-valued pooling; Optimizing the network parameters of the palmprint image recognition network by using a complex-valued dynamic activation function and a complex-valued dynamic loss function; Inputting the complex-valued palmprint image into the optimized palmprint image recognition network and obtaining an output result; Matching the output result with the palmprint data in the database and outputting a recognition result.

2. The method according to claim 1, wherein The step of converting the obtained initial palmprint image into an HSV image and generating a complex-valued palmprint image in iHSV format through a complex-valued image conversion model includes: Obtain an initial palmprint image and convert the palmprint image in RGB format into an HSV format image , where h represents hue, S represents saturation, and V represents value; Convert the HSV format image to the iHSV complex value format image , which is achieved through the following channel settings: Hue fixed channel , with saturation S as the real axis and lightness V as the imaginary axis; Saturation-fixed channel , with brightness V as the real axis and the product of saturation and hue as the imaginary axis; Brightness fixed channel , generated by polar coordinate transformation; Separating and recombining the real and imaginary parts of the three channels to generate a complete complex-valued image.

3. The method according to claim 1, wherein The complex-valued residual block contains at least two types of residual structures: Residual structure 1: Making the number of input and output channels consistent through complex-valued convolution and complex-valued normalization, and performing weighted fusion; Residual structure 2: Processing the input data through a complex-valued activation function and then performing weighted fusion with the original input.

4. The method according to claim 1, wherein Each layer in the complex-valued dense block receives the outputs of all previous layers as inputs and is processed by a non-linear transformation module, and the non-linear transformation module is composed of complex-valued normalization, a complex-valued activation function, and complex-valued convolution.

5. The method according to claim 1, characterized in that, The complex-valued dynamic activation function is defined as: ； Among them, a plurality of ; ; ； Indicates the restricted area for dynamically adjusting a plurality of phases, Indicates the activation threshold for dynamically adjusting ReLU.

6. The method according to claim 1, wherein The complex-valued dynamic loss function is composed of a complex-valued cross-entropy loss function and a complex-valued weighted triplet loss function as follows: ； Where: ； ； Complex outputs of the representation model; ； Among them, represents an anchor sample, represents a positive sample, represents a negative sample, and represent the positive and negative sample weights respectively.

7. The method according to claim 6, wherein The distance metric in the complex-valued weighted triple loss function is calculated by the following formula: 。

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