An intelligent control method for a microchannel continuous crystallizer

Abstract

The present invention relates to the field of intelligent control. More specifically, the present invention relates to an intelligent control method for a microchannel continuous crystallizer. The method includes: collecting crystallization images of several chemical substances and the corresponding crystallization stages of each crystallization image; obtaining a pre-trained first crystallization recognition network and a second crystallization recognition network; calculating an optimized learning rate; inputting the crystallization images of other types of chemical substances into the first crystallization recognition network, obtaining optimized gradient update values of each network parameter using the optimized learning rate of each network parameter, and performing gradient update according to the optimized gradient update values until the training is completed; so as to realize the control of the crystallizer. By adjusting the learning rate, the learning of the network for different information is controlled, thereby improving the recognition accuracy of the network.

Description

Technical Field

[0001] The present invention relates to the field of intelligent control, and more specifically, to an intelligent control method for a microchannel continuous crystallizer. Background Art

[0002] The control parameters required for each crystallization stage are different. For example, in the early stage of crystallization, when not many crystals have been precipitated, the solution should be stirred faster to allow the solution to be fully mixed and crystals to precipitate faster. In the late stage of crystallization, when many crystals have been precipitated, the solution should be stirred slower to prevent the precipitated crystals from being destroyed. Therefore, the corresponding control parameters need to be adjusted according to the crystallization stage. In order to achieve precise control of the crystallization process, the crystallization stage in the crystallization process needs to be accurately determined.

[0003] Neural networks have accurate classification and judgment functions, so neural networks are often used to judge the crystallization stage. In order for the neural network to have the function of crystallization stage judgment, the neural network needs to be trained. Training the neural network requires a large number of labeled training samples. For a chemical, it is difficult to obtain a large number of training samples, and even if a large number of samples are obtained, the workload of labeling is large, so training samples from the crystallization process of other types of chemicals are often introduced for neural network training. Although the crystallization processes of different types of chemicals are not exactly the same, there are similarities between the crystallization processes of different types of chemicals, so training samples of other types of chemicals can be used for neural network training. In order to improve the accuracy of the crystallization stage judgment of the neural network, it is necessary to control the training process of the training samples of other types of chemicals to the neural network according to the contribution of other types of chemicals to the crystallization stage judgment of this chemical.

[0004] A crystallizer liquid level automatic control simulation system is disclosed in the patent document with authorization announcement number CN106468888B. The patent document only discloses the hardware equipment required for the crystallizer and the corresponding connection relationship. The method in the patent document does not involve content related to neural network training. Therefore, the method in the patent document cannot solve the technical problem of the present invention. Summary of the invention

[0005] In order to solve the problem of how to use training samples of other types of chemicals to control the training process of the neural network to improve the accuracy of the crystallization stage judgment of the neural network, the present invention proposes an intelligent control method for a microchannel continuous crystallizer, which includes the following steps:

[0006] Collect crystallization images of several chemicals and the crystallization stages corresponding to each crystallization image;

[0007] Acquire a first crystallization recognition network and a second crystallization recognition network obtained in advance;

[0008] Calculated optimized learning rate Regarding the chemicals for current crystallization control as the target type of chemicals Denote the gray histogram of the th crystallization image of other types of chemicals at the z-th crystallization stage Denote the gray histogram of the j-th crystallization image of the target type of chemicals at the z-th crystallization stage Respectively denote the feature information vectors obtained from the i-th crystallization image of the target type of chemicals in the k-th layer of the first crystallization recognition network and the second crystallization recognition network. N represents the number of crystallization images of the target type of chemicals Denote the number of crystallization images of the target type of chemicals at the z-th crystallization stage Denote the similarity of vectors Denote the norm of vectors Linear normalization function, L0 represents the preset learning rate

[0009] Input the crystallization images of other types of chemicals into the first crystallization recognition network, obtain the optimized gradient update values of each network parameter using the optimized learning rate of each network parameter, and perform gradient update according to the optimized gradient update values until the training is completed; to achieve crystallizer control

[0010] The present invention controls the network to learn more useful information for crystallization stage recognition by adjusting the learning rate, avoiding the network from learning too much interference information. The network trained in this way has a high accuracy in crystallization stage recognition; further, when adjusting the learning rate, by introducing the similarity between the crystallization images of other types of chemicals and the crystallization images of the target type of chemicals at the same stage, the availability of other types of chemicals for determining the crystallization stage of the target type of chemicals can be accurately determined, so as to adaptively adjust the learning rate and control the network's learning of different information; further, when adjusting the learning rate, by introducing the difference value of the information extracted from the crystallization images in the same layer of the first crystallization network and the second stage network, the learning ability of each layer of network parameters in the crystallization recognition network for the common information between different types of chemicals can be accurately determined, so as to adaptively adjust the learning rate of each layer of network parameters in the crystallization recognition network, control the network to learn more useful information for crystallization stage recognition, avoid the network from learning more interference information, and improve the accuracy of the network in crystallization stage recognition

[0011] Preferably, the obtaining of the pre-obtained first crystallization recognition network and the second crystallization recognition network includes

[0012] Construct an initial crystallization recognition network

[0013] Use the crystallization stage as the label for the corresponding crystallization image; complete one round of training of the initial crystallization recognition network using all the crystallization images of the target type of chemical to obtain the first crystallization recognition network;

[0014] Complete one round of training of the initial crystallization recognition network using all the crystallization images of other types of chemicals to obtain the second crystallization recognition network.

[0015] In the present invention, the first crystallization recognition network and the second crystallization recognition network trained using different training samples have different recognition preferences, and each layer of network parameters in the crystallization recognition network shows different degrees of performance of the recognition preferences. The performance degree of each layer of network parameters for the recognition preferences can reflect the learning ability of each layer of network parameters for the useful information of the stage recognition of the target type of chemical, providing a network basis for subsequent learning rate adjustment.

[0016] Preferably, the feature information vector includes:

[0017] Input the crystallization image into the first crystallization recognition network, obtain several output data of each layer in the first crystallization recognition network, perform dimensionality reduction processing on all the output data, and denote the vector obtained after the dimensionality reduction processing as the feature information vector.

[0018] In the present invention, while obtaining the main information of the feature information extracted by each layer of the network through dimensionality reduction processing, it can also reduce the data processing complexity, providing a data basis for subsequent learning rate adjustment.

[0019] Preferably, the obtaining the optimized gradient update value of each network parameter using the optimized learning rate of each network parameter includes:

[0020] Use the crystallization stage as the label for the corresponding crystallization image;

[0021] Input the crystallization images of other types of chemicals into the first crystallization recognition network to obtain output data; based on the output data and the label, calculate the loss value using the loss function of the first crystallization recognition network;

[0022] Use the optimized learning rate as the learning rate of the corresponding network parameter, and based on the loss value, calculate the gradient update value of the corresponding network parameter using the gradient descent method and denote it as the optimized gradient update value.

[0023] In the present invention, by adjusting the learning rate to control the gradient update value of the network parameters, and thus controlling the information absorption situation of the network for different information, so that the network can learn the information useful for the crystallization stage recognition of the target type of chemical, and improve the accuracy of the network for the crystallization stage recognition of the target type of chemical.

[0024] Preferably, the until the training is completed includes:

[0025] The crystal images of all other types of chemicals are sequentially input into the first crystal recognition network after updating the parameters, the loss value is calculated, the optimized gradient update value of each network parameter is calculated according to the loss value, and the network parameters are updated by using the optimized gradient update value until the loss value converges and the training is completed, obtaining the trained first crystal recognition network.

[0026] Preferably, the implementation of the crystallizer control includes:

[0027] During the crystallization process of the target type of chemical, crystal images are collected in real time; the crystal images collected at the current moment are input into the trained first crystal recognition network to obtain the estimated crystallization stage of the crystal images at the current moment;

[0028] If the estimated crystallization stage of the crystal image at the current moment does not reach the preset crystallization stage, the original crystallization control parameters are used for crystallization control;

[0029] If the estimated crystallization stage of the crystal image at the current moment has reached the preset crystallization stage, the control parameters required for the new crystallization stage are used for crystallization control.

[0030] The present invention adaptively adjusts the control parameters according to the crystallization stage of the target chemical, improves the accuracy of the crystallization control of the target chemical, and realizes the crystallization control of the target chemical to be completed faster and with higher quality.

[0031] Preferably, the method for obtaining the grayscale histogram includes:

[0032] The crystal image is grayscale processed to obtain the grayscale image of the crystal image, the grayscale values in the grayscale image are statistically counted to obtain the occurrence frequency of each grayscale value, and the occurrence frequencies of all grayscale values are arranged in ascending order of the grayscale values, and the obtained vector is denoted as the grayscale histogram.

[0033] Preferably, the similarity of the vectors is the cosine similarity of the two vectors.

[0034] The present invention has the following beneficial effects:

[0035] The present invention controls the network to learn more useful information for crystal stage recognition by adjusting the learning rate, avoiding the network from learning too much interference information, and the network trained in this way has a high crystal stage recognition accuracy;

[0036] Furthermore, when adjusting the learning rate, by introducing the similarity between the crystal images of other types of chemicals and the crystal images of the same stage of the target type of chemical, the availability of other types of chemicals for the crystal stage determination of the target type of chemical is accurately determined, so as to adaptively adjust the learning rate and control the learning situation of the network for different information;

[0037] Further, when adjusting the learning rate, by introducing the difference value of the information extracted from the crystallization images in the same layer of the first crystallization network and the second-stage network, the learning ability of each layer of network parameters in the crystallization recognition network for the common information between different types of chemical substances can be accurately determined. Thus, the learning rate of each layer of network parameters in the crystallization recognition network can be adaptively adjusted to control the network to learn more useful information for crystallization stage recognition, avoid the network from learning more interference information, and improve the crystallization stage recognition accuracy of the network. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] By referring to the following detailed description with reference to the accompanying drawings, the above and other objects, features, and advantages of the exemplary embodiments of the present invention will become readily understood. In the drawings, several embodiments of the present invention are shown in an exemplary and non-limiting manner, and the same or corresponding reference numerals represent the same or corresponding parts, wherein:

[0039] Figure 1 is a flowchart of the steps of an intelligent control method for a microchannel continuous crystallizer according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0040] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0041] The following will describe the specific embodiments of the present invention in detail with reference to the accompanying drawings.

[0042] Please refer to Figure 1 , which shows a flowchart of the steps of an intelligent control method for a microchannel continuous crystallizer provided by an embodiment of the present invention. The method includes the following steps:

[0043] S1: Collect crystallization images of several chemical substances and the corresponding crystallization stages of each crystallization image.

[0044] Specifically, obtain the crystallization images during the crystallization process of each chemical substance, manually determine the corresponding crystallization stage in the crystallization image, and label the crystallization image according to the crystallization stage of the crystallization image. For example, the crystallization process of the chemical substance includes a total of 5 crystallization stages. When the crystallization image is the first crystallization stage, its corresponding label is , when the crystallization image is the second crystallization stage, its corresponding label is , when the crystallization image is the third crystallization stage, its corresponding label is , when the crystallization image is in the fourth crystallization stage, its corresponding label is , when the crystallization image is in the fifth crystallization stage, its corresponding label is .

[0045] S2: Obtain the pre-obtained first crystallization recognition network and second crystallization recognition network.

[0046] Preferably, as an example, obtaining the pre-obtained first crystallization recognition network and second crystallization recognition network includes:

[0047] Construct an initial crystallization recognition network, and the initial crystallization recognition network is a VGGNet network;

[0048] Input a crystallization image of a target category chemical into the initial crystallization recognition network, and obtain output data. Based on the output data and the label, calculate the loss value using the loss function of the initial crystallization recognition network, and perform backpropagation gradient update on the initial crystallization recognition network using the gradient descent method; Input each crystallization image of the target category chemical into the initial crystallization recognition network with updated parameters in sequence, and perform backpropagation gradient update on the initial crystallization recognition network with updated parameters to complete one round of training of the initial crystallization recognition network to obtain the first crystallization recognition network.

[0049] In the same way, input all crystallization images of other types of chemicals into the initial crystallization recognition network in sequence to complete one round of training of the initial crystallization recognition network to obtain the second crystallization recognition network.

[0050] It should be noted that the VGGNet network is an existing network and will not be elaborated here.

[0051] S3: Calculate the optimized learning rate.

[0052] It should be noted that each layer of the neural network learns information differently. Among them, the earlier the layer of the neural network, the stronger its learning ability for common information, and the later the layer, the stronger its learning ability for individual information. The individual information of the crystallization images of different types of chemicals mainly reflects the discrimination information between the crystallization images of different types of chemicals, and these information are useless for crystallization stage recognition and will instead interfere with the recognition. Therefore, the learning of individual information should be reduced. The common information between the crystallization images of different types of chemicals reflects the common information between the crystallization images of different types of chemicals, and these common information can help with crystallization stage recognition. Therefore, the network needs to learn more of this kind of information. Therefore, different training controls need to be performed on each layer according to the learning situation of each layer of the neural network for common information.

[0053] It should be further noted that the crystallization processes of some different types of chemical substances are relatively similar, while those of some types of chemical drugs vary greatly. In order to accurately identify the crystallization stage of the chemical drug to be crystallized, the crystallization recognition network needs to learn more crystallization information of chemical drugs of types with high similarity to it. Therefore, different controls need to be performed on the network training process using training samples according to the similarity of the crystallization images of other types of chemical drugs to those of the chemical drug to be crystallized.

[0054] Preferably, as an example, calculating the optimized learning rate includes:

[0055]

[0056] Among them, the chemical substance currently under crystallization control is denoted as the target type of chemical substance. represents the gray-level histogram of the th crystallization image of other types of chemical substances in the z-th crystallization stage. represents the gray-level histogram of the j-th crystallization image of the target type of chemical substance in the z-th crystallization stage. respectively represent the feature information vectors obtained from the k-th layer of the first crystallization recognition network and the second crystallization recognition network for the i-th crystallization image of the target type of chemical substance. N represents the number of crystallization images of the target type of chemical substance. represents the number of crystallization images of the target type of chemical substance in the z-th crystallization stage. represents the similarity of the vectors. represents the norm of the vector. represents the linear normalization function; L0 represents the preset learning rate, which is a fixed learning rate set conventionally according to experience. represents the optimized learning rate of the network parameters of the k-th layer when the th crystallization image of other types of chemical substances in the z-th crystallization stage is used to train the first crystallization recognition network.

[0057] It can be understood that reflects the similarity between the crystallization image of an other type of chemical substance and the crystallization image of the target type of chemical substance in the same stage. The larger this value is, the more similar the crystallization process of this other type of chemical substance is to that of the target type of chemical substance. The crystallization information of this other type of chemical substance is more helpful for identifying the crystallization stage of the target type of chemical substance and less interfering with the identification of the crystallization stage of the target type of chemical substance. Therefore, the network should learn more crystallization image information of this type of chemical substance, so the learning rate should be increased.

[0058] Both of the two crystal recognition networks have the function of recognizing the crystal stage. The first crystal recognition network is trained using the training samples of the target type of chemical, while the second crystal recognition network is trained using the training samples of other types of chemicals. The first crystal recognition network has a higher recognition accuracy for the crystal stage of the target type of chemical, and the second crystal recognition network has a higher recognition accuracy for the crystal stage of other types of chemicals. The two crystal recognition networks have differences in recognition preferences. Although there are preference differences between the two crystal recognition networks, specifically within the network, only some layers have a strong ability to extract individual information, and there are also some layers with a strong ability to extract common information. Therefore, it is necessary to determine the common information ability of each layer separately. If a certain layer of the two crystal recognition networks extracts the common information reflecting the crystal processes of all types of chemicals, the information similarity of a crystal image it extracts should be relatively large. Therefore, it can be based on this to determine the common information extraction ability of each layer in the crystal recognition network. It reflects the difference situation of the information extracted by the two crystal recognition networks in the same layer. The smaller this value is, the more common information the two crystal recognition networks extract in this layer. Therefore, in order to enable the crystal recognition network to learn more information, the learning rate of this layer should be increased.

[0059] The above embodiments involve the gray histogram, the feature information vector, and the similarity of vectors. Next, the determination methods of the gray histogram, the feature information vector, and the similarity of vectors will be described.

[0060] Among them, the method for obtaining the gray histogram includes:

[0061] Perform gray-scale processing on the crystal image to obtain the gray-scale image of the crystal image, count the gray-scale values in the gray-scale image to obtain the occurrence frequency of each gray-scale value, arrange the occurrence frequencies of all gray-scale values in ascending order of the gray-scale values, and record the obtained vector as the gray histogram.

[0062] In addition, the method for obtaining the feature information vector includes:

[0063] Input the crystal image into the first crystal recognition network, obtain a number of output data for each layer in the first crystal recognition network, perform dimensionality reduction processing on all the output data, and record the vector obtained after the dimensionality reduction processing as the feature information vector.

[0064] For example, obtain a number of feature images in the first convolutional layer of the first crystal recognition network, record the vector obtained by splicing the rows of the feature images together as the analysis vector, perform dimensionality reduction processing on all the analysis vectors using the principal component analysis algorithm, and record the obtained vector as the feature information vector.

[0065] In addition, in this embodiment, the cosine similarity of vectors is used to reflect the similarity of vectors.

[0066] S4: Input the crystal images of other types of chemical substances into the first crystal recognition network, obtain the optimized gradient update values of each network parameter using the optimized learning rate of each network parameter, and perform gradient update according to the optimized gradient update values until the training is completed; to achieve crystallizer control.

[0067] S40: Input the crystal images of other types of chemical substances into the first crystal recognition network, obtain the optimized gradient update values of each network parameter using the optimized learning rate of each network parameter, and perform gradient update according to the optimized gradient update values.

[0068] Preferably, as an example, input the crystal images of other types of chemical substances into the first crystal recognition network, obtain the optimized gradient update values of each network parameter using the optimized learning rate of each network parameter, and perform gradient update according to the optimized gradient update values, including:

[0069] Input the crystal images of other types of chemical substances into the first crystal recognition network to obtain output data; based on the output data and labels, calculate the loss value using the loss function of the first crystal recognition network;

[0070] Take the optimized learning rate as the learning rate of the corresponding network parameter, and based on the loss value, calculate the gradient update value of the corresponding network parameter using the gradient descent method and record it as the optimized gradient update value.

[0071] Update the network parameters using the optimized gradient update values.

[0072] It should be noted that in the case of a known learning rate, calculating the update values of each network parameter based on the loss value using the gradient descent method is a prior art and will not be elaborated here.

[0073] It can be understood that by adjusting the learning rate to further adjust the gradient update value, thereby controlling the learning situation of the network for different information, so that the network can learn information helpful for the recognition of the crystal phase of the target type of chemical substance, avoid learning some irrelevant interference information, and thus improve the accuracy of the network in recognizing the crystal phase of the target type of chemical substance.

[0074] S41: Until the training is completed.

[0075] Preferably, as an example, until the training is completed, including:

[0076] Input the crystal images of all other types of chemical substances into the first crystal recognition network with updated parameters in sequence, calculate the loss value, calculate the optimized gradient update values of each network parameter according to the loss value, and perform gradient update on the network parameters using the optimized gradient update values until the loss value converges and the training is completed to obtain the trained first crystal recognition network.

[0077] S42: To achieve mold control.

[0078] It should be noted that, in order to achieve accurate control of the mold, the control parameters need to be adjusted in a timely manner according to the crystallization stage of the chemical substance, so as to achieve higher-quality crystallization of the chemical substance.

[0079] Preferably, as an example, to achieve mold control, it includes:

[0080] During the crystallization process of the target type of chemical substance, the crystallization image is collected in real time; the crystallization image collected at the current moment is input into the trained first crystallization recognition network to obtain the estimated crystallization stage of the crystallization image at the current moment;

[0081] If the estimated crystallization stage of the crystallization image at the current moment has not reached the preset crystallization stage, the original crystallization control parameters are used for crystallization control;

[0082] If the estimated crystallization stage of the crystallization image at the current moment has reached the preset crystallization stage, the control parameters required for the new crystallization stage are used for crystallization control.

[0083] For example, if the crystallization stage before the current moment is the first crystallization stage, and the second crystallization stage is taken as the preset crystallization stage, and if it is determined that the crystallization image at the current moment is the second crystallization stage, it means that the first crystallization stage has been completed and the second crystallization stage has been entered. At this time, the control parameters need to be adjusted to be suitable for the second crystallization stage.

[0084] It can be understood that through this method, the control parameter information can be adjusted in a timely manner according to the requirements of the crystallization stage, so as to achieve higher-quality crystallization of the chemical substance.

[0085] So far, this embodiment is completed.

[0086] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. An intelligent control method for a microchannel continuous crystallizer, characterized in that, Including: Collecting crystal images of several chemical substances and their corresponding crystallization stages; Obtaining a pre-obtained first crystal recognition network and a second crystal recognition network, including: Constructing an initial crystal recognition network; Using the crystallization stage as the label corresponding to the crystal image; using all crystal images of the target type of chemical substance to complete one round of training of the initial crystal recognition network to obtain the first crystal recognition network; Using all crystal images of other types of chemical substances to complete one round of training of the initial crystal recognition network to obtain the second crystal recognition network; Calculated optimized learning rate , denote the chemical substance for current crystallization control as the target type chemical substance, denote the gray scale histogram of the th crystallization image of other type chemical substances in the z-th crystallization stage, denote the gray scale histogram of the j-th crystallization image of the target type chemical substance in the z-th crystallization stage, respectively denote the feature information vectors obtained in the k-th layer of the first crystallization recognition network and the second crystallization recognition network for the i-th crystallization image of the target type chemical substance, N denotes the number of crystallization images of the target type chemical substance, denote the number of crystallization images of the target type chemical substance in the z-th crystallization stage, denote the similarity of vectors, denote the norm of the vector, linear normalization function, L0 denotes the preset learning rate; Inputting the crystal images of other types of chemical substances into the first crystal recognition network, and obtaining the optimized gradient update values of each network parameter using the optimized learning rate of each network parameter, including: Using the crystallization stage as the label corresponding to the crystal image; Inputting the crystal images of other types of chemical substances into the first crystal recognition network to obtain output data; based on the output data and the label, calculating the loss value using the loss function of the first crystal recognition network; Using the optimized learning rate as the learning rate of the corresponding network parameter, and based on the loss value, calculating the gradient update value of the corresponding network parameter using the gradient descent method, which is denoted as the optimized gradient update value; Performing gradient update according to the optimized gradient update value until the training is completed; to achieve crystallizer control; the "until the training is completed" includes: Sequentially inputting the crystal images of all other types of chemical substances into the first crystal recognition network with updated parameters, calculating the loss value, calculating the optimized gradient update values of each network parameter according to the loss value, and using the optimized gradient update values to perform gradient update on the network parameters until the loss value converges and the training is completed, obtaining the trained first crystal recognition network.

2. The intelligent control method of a microchannel continuous crystallizer according to claim 1, characterized in that, The feature information vector includes: Inputting the crystal image into the first crystal recognition network, obtaining several output data of each layer in the first crystal recognition network, performing dimensionality reduction processing on all output data, and denoting the vector obtained after dimensionality reduction processing as the feature information vector.

3. The intelligent control method of a microchannel continuous crystallizer according to claim 1, characterized in that, The "to achieve crystallizer control" includes: During the crystallization process of the target type of chemical substance, collecting crystal images in real time; inputting the crystal image collected at the current moment into the trained first crystal recognition network to obtain the estimated crystallization stage of the crystal image at the current moment; If the estimated crystallization stage of the crystal image at the current moment has not reached the preset crystallization stage, using the original crystallization control parameters to perform crystallization control; If the estimated crystallization stage of the crystal image at the current moment has reached the preset crystallization stage, using the control parameters required for the new crystallization stage to perform crystallization control.

4. The intelligent control method of a microchannel continuous crystallizer according to claim 1, characterized in that The method for obtaining the gray histogram includes: Performing gray-scale processing on the crystal image to obtain the gray-scale image of the crystal image, counting the gray-scale values in the gray-scale image to obtain the occurrence frequency of each gray-scale value, arranging the occurrence frequencies of all gray-scale values in ascending order of gray-scale values, and denoting the obtained vector as the gray histogram.

5. The intelligent control method of a microchannel continuous crystallizer according to claim 1, characterized in that, The similarity of the vectors is the cosine similarity of the two vectors.

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