Intelligent control method of micro-channel continuous crystallizer

Abstract

The invention relates to the field of intelligent control, in particular to an intelligent control method of a micro-channel continuous crystallizer, which comprises the following steps: acquiring crystallization images of a plurality of chemical substances and crystallization stages corresponding to the crystallization images; obtaining a first crystallization identification network and a second crystallization identification network which are obtained in advance; calculating an optimized learning rate; inputting the crystallization images of other types of chemicals into a first crystallization identification network, obtaining an optimized gradient update value of each network parameter by using the optimized learning rate of each network parameter, and carrying out gradient update according to the optimized gradient update value until the training is completed; therefore, the crystallizer is controlled. And the learning conditions of the network for different information are controlled by adjusting the learning rate, so that the recognition accuracy of the network is improved.

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: Collect crystallization images of several chemicals and the crystallization stages corresponding to each crystallization image; Acquire a first crystallization recognition network and a second crystallization recognition network obtained in advance; Calculate the optimized learning rate , record the chemical currently controlled by crystallization as the target chemical, Indicates the crystallization stage of other types of chemicals Grayscale histogram of a crystal image, Represents the grayscale histogram of the jth crystallization image of the target chemical species at the zth crystallization stage, represents the feature information vector of the i-th crystallization image of the target chemical species obtained in the k-th layer of the first crystallization recognition network and the second crystallization recognition network, respectively. N represents the number of crystallization images of the target chemical species. represents the number of crystallization images of the target chemical species in the zth crystallization stage, represents the similarity of vectors, represents the magnitude of a vector, Linear normalization function, L0 represents the preset learning rate; The crystallization images of other types of chemicals are input into the first crystallization recognition network, and the optimized gradient update values ​​of each network parameter are obtained by using the optimized learning rates of each network parameter. The gradient is updated according to the optimized gradient update values ​​until the training is completed, so as to realize crystallizer control.

[0006] The present invention controls the network to learn more useful information for crystallization stage identification by adjusting the learning rate, and avoids the network from learning too much interference information. The network trained in this way has a higher crystallization stage identification accuracy; further, when adjusting the learning rate, by introducing the similarity between the crystallization images of other categories of chemicals and the crystallization images of the same stage of the target category of chemicals, the availability of other categories of chemicals for crystallization stage identification of the target category of chemicals is accurately determined, so as to adjust the learning rate accordingly and control the network to learn different information; further, when adjusting the learning rate, by introducing the difference value of the information extracted from the same layer of the first crystallization network and the second stage network by the crystallization image, the learning ability of each layer of network parameters in the crystallization identification network for the shared information between different types of chemicals is accurately determined, so as to adjust the learning rate of each layer of network parameters in the crystallization identification network accordingly, control the network to learn more useful information for crystallization stage identification, avoid the network from learning more interference information, and improve the network's crystallization stage identification accuracy.

[0007] Preferably, the step of obtaining the first crystallization recognition network and the second crystallization recognition network obtained in advance comprises: Constructing an initial crystallization recognition network; The crystallization stage is used as a label of the corresponding crystallization image; all crystallization images of the target chemical species are used to complete a round of training of the initial crystallization recognition network to obtain a first crystallization recognition network; A round of training of the initial crystal recognition network is completed using all crystal images of other types of chemicals to obtain a second crystal recognition network.

[0008] The first crystallization recognition network and the second crystallization recognition network trained by the present invention using different training samples have different recognition preferences, and the degree to which each layer of network parameters in the crystallization recognition network expresses the recognition preference is different. The degree to which each layer of network parameters expresses the recognition preference can reflect the learning ability of each layer of network parameters to the useful information of the target type chemical stage recognition, providing a network basis for the subsequent learning rate adjustment.

[0009] Preferably, the feature information vector includes: The crystallization image is input into the first crystallization recognition network, a number of output data of each layer is obtained in the first crystallization recognition network, dimension reduction processing is performed on all the output data, and the vector obtained after the dimension reduction processing is recorded as a feature information vector.

[0010] The present invention obtains the main information of the feature information extracted by each layer of the network through dimensionality reduction processing, and can also reduce the complexity of data processing, providing a data basis for subsequent learning rate adjustment.

[0011] Preferably, the step of obtaining the optimized gradient update value of each network parameter by using the optimized learning rate of each network parameter comprises: The crystallization stages are used as labels for the corresponding crystallization images; Inputting crystal images of other types of chemicals into the first crystal recognition network to obtain output data; and calculating a loss value using a loss function of the first crystal recognition network based on the output data and the label; The optimized learning rate is used as the learning rate of the corresponding network parameters. Based on the loss value, the gradient descent method is used to calculate the gradient update value of the corresponding network parameters and record it as the optimized gradient update value.

[0012] The present invention controls the gradient update value of the network parameters by adjusting the learning rate, thereby controlling the network's absorption of different information, so that the network can learn useful information for identifying the crystallization stage of target type chemicals, thereby improving the network's accuracy in identifying the crystallization stage of target type chemicals.

[0013] Preferably, the step of completing the training includes: The crystal images of all other types of chemicals are sequentially input into the first crystallization recognition network after parameter update, and 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 gradient updated using the optimized gradient update value until the loss value converges and the training is completed, thereby obtaining the trained first crystallization recognition network.

[0014] Preferably, the method for achieving crystallizer control comprises: During the crystallization process of the target chemical, a 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 an estimated crystallization stage of the crystallization image at the current moment; If the estimated crystallization stage of the crystallization image at the current moment does not reach the preset crystallization stage, the original crystallization control parameters are used to perform crystallization control; If the estimated crystallization stage of the crystallization image at the current moment has reached the preset crystallization stage, crystallization control is performed using the control parameters required for the new crystallization stage.

[0015] The present invention adjusts the control parameters accordingly according to the crystallization stage of the target chemical, thereby improving the accuracy of the crystallization control of the target chemical and achieving faster and higher-quality completion of the crystallization control of the target chemical.

[0016] Preferably, the method for obtaining the grayscale histogram includes: The crystallization image is grayed to obtain a grayscale image of the crystallization image. The grayscale values ​​in the grayscale image are counted to obtain the frequency of occurrence of each grayscale value. The frequency of occurrence of all grayscale values ​​is arranged in ascending order of the grayscale values, and the obtained vector is recorded as a grayscale histogram.

[0017] Preferably, the similarity of the vectors is the cosine similarity of the two vectors.

[0018] The present invention has the following beneficial effects: The present invention controls the network to learn more useful information for crystallization stage recognition by adjusting the learning rate, thereby preventing the network from learning too much interference information. The network trained in this way has a higher crystallization stage recognition accuracy. Furthermore, when adjusting the learning rate, by introducing the similarity between the crystallization images of other categories of chemicals and the crystallization images of the target category of chemicals at the same stage, the availability of other categories of chemicals for determining the crystallization stage of the target category of chemicals can be accurately determined, thereby adjusting the learning rate accordingly and controlling the network's learning of different information; Furthermore, when adjusting the learning rate, by introducing the difference value of the information extracted from the same layer of the first crystallization network and the second stage network of the crystallization image, 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 adjust the learning rate of each layer of network parameters in the crystallization recognition network accordingly, control the network to learn more useful information for learning crystallization stage recognition, avoid the network learning more interference information, and improve the network's crystallization stage recognition accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] By reading 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 accompanying 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: Figure 1 It is a flow chart of the steps of an intelligent control method of a microchannel continuous crystallizer according to an embodiment of the present invention. DETAILED DESCRIPTION

[0020] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of the present invention.

[0021] The specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0022] See also Figure 1 , which shows a flow chart of the steps of an intelligent control method for a microchannel continuous crystallizer provided by an embodiment of the present invention, the method comprising the following steps: S1: Collect crystallization images of several chemicals and the crystallization stages corresponding to each crystallization image.

[0023] Specifically, a crystallization image of each chemical substance in the crystallization process is obtained, and the corresponding crystallization stage in the crystallization image is manually determined. The crystallization image is labeled according to the crystallization stage of the crystallization image. For example, the crystallization process of a chemical substance includes 5 crystallization stages. When the crystallization image is in 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 the fourth crystallization stage, its corresponding label is , when the crystallization image is the fifth crystallization stage, its corresponding label is .

[0024] S2: Acquire a first crystallization recognition network and a second crystallization recognition network obtained in advance.

[0025] Preferably, as an example, obtaining the first crystallization recognition network and the second crystallization recognition network obtained in advance includes: Constructing an initial crystallization recognition network, wherein the initial crystallization recognition network is a VGGNet network; A crystal image of a target category chemical is input into the initial crystallization recognition network, and output data is obtained. Based on the output data and the label, the loss value is calculated using the loss function of the initial crystallization recognition network, and the initial crystallization recognition network is reversely updated with the gradient descent method based on the loss value. Each crystal image of the target category chemical is sequentially input into the initial crystallization recognition network after the parameters are updated, and the initial crystallization recognition network after the parameters are updated is reversely updated with the gradient, completing one round of training of the initial crystallization recognition network to obtain the first crystallization recognition network.

[0026] In the same way, all crystallization images of other types of chemicals are sequentially input into the initial crystallization recognition network, and a round of training of the initial crystallization recognition network is completed to obtain the second crystallization recognition network.

[0027] It should be noted that the VGGNet network is an existing network and will not be described in detail here.

[0028] S3: Calculate the optimized learning rate.

[0029] It should be noted that each layer of the neural network learns information differently. The earlier the number of layers of the neural network, the stronger its ability to learn common information, and the later the number of layers, the stronger its ability to learn individual information. The individual information of the crystallization images of different types of chemicals mainly reflects the distinguishing information between the crystallization images of different types of chemicals. This information is useless for crystallization stage recognition and will interfere with 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. This common information can help recognize the crystallization stage, so the network needs to learn more of this information. Therefore, it is necessary to perform different training controls on each layer according to the learning of the common information by each layer of the neural network.

[0030] It should be further explained that the crystallization processes of some different types of chemicals are relatively similar, while the crystallization processes of some types of chemicals are quite different. In order to accurately identify the crystallization stage of chemicals to be controlled for crystallization, the crystallization recognition network needs to learn more crystallization information of chemicals with higher similarity. Therefore, it is necessary to use training samples to control the network training process differently according to the similarity of the crystallization images of other types of chemicals with the type to be controlled for crystallization.

[0031] Preferably, as an example, calculating the optimized learning rate includes:

[0032] Among them, the chemical substance currently under crystallization control is recorded as the target chemical substance. Indicates the crystallization stage of other types of chemicals Grayscale histogram of a crystal image, Represents the grayscale histogram of the jth crystallization image of the target chemical species at the zth crystallization stage, represents the feature information vector of the i-th crystallization image of the target chemical species obtained in the k-th layer of the first crystallization recognition network and the second crystallization recognition network, respectively. N represents the number of crystallization images of the target chemical species. represents the number of crystallization images of the target chemical species in the zth crystallization stage, represents the similarity of vectors, represents the magnitude of a vector, represents a linear normalization function; L0 represents a preset learning rate, which is a fixed learning rate traditionally set based on experience. Indicates the crystallization stage of other types of chemicals The optimized learning rate of the k-th layer network parameters when the first crystal recognition network is trained with crystal images.

[0033] Understandably, It reflects the similarity between the crystallization image of another type of chemical and the crystallization image of the target type of chemical at the same stage. The larger the value, the more similar the crystallization process of the other type of chemical is to the target type of chemical. The crystallization information of the other type of chemical is more helpful for identifying the crystallization stage of the target type of chemical, and has less interference with the identification of the crystallization stage of the target type of chemical. The network should learn more about the crystallization image information of this type of chemical, so the learning rate should be increased.

[0034] Both crystallization recognition networks have the function of recognizing the crystallization stage, but the first crystallization recognition network is trained using training samples of target type chemicals, while the second crystallization recognition network is trained using training samples of other types of chemicals. The first crystallization recognition network has a higher recognition accuracy for the crystallization stage of target type chemicals, while the second crystallization recognition network has a higher recognition accuracy for the crystallization stage of other types of chemicals. The two crystallization recognition networks have different recognition preferences. Although there are preference differences between the two crystallization recognition networks, specifically within the network, only some layers have strong individual information extraction capabilities, and some layers have strong common information extraction capabilities. Therefore, the common information capabilities of each layer need to be judged separately. If a layer of the two crystallization recognition networks extracts common information that reflects the crystallization process of all types of chemicals, the information similarity of a crystal image extracted should be relatively large. Therefore, the common information extraction capabilities of each layer in the crystallization recognition network can be judged based on this. It reflects the difference in information extracted by the two crystallization recognition networks in the same layer. The smaller the value, the more common information the two crystallization recognition networks have extracted in this layer. Therefore, in order to allow the crystallization recognition network to learn more information, the learning rate of this layer should be increased.

[0035] The above embodiments involve a grayscale histogram, a feature information vector, and the similarity of a vector. The following describes a method for determining a grayscale histogram, a feature information vector, and the similarity of a vector.

[0036] The grayscale histogram acquisition method includes: The crystallization image is grayed to obtain a grayscale image of the crystallization image. The grayscale values ​​in the grayscale image are counted to obtain the frequency of occurrence of each grayscale value. The frequency of occurrence of all grayscale values ​​is arranged in ascending order of the grayscale values, and the obtained vector is recorded as a grayscale histogram.

[0037] In addition, the method for obtaining the feature information vector includes: The crystallization image is input into the first crystallization recognition network, a number of output data of each layer is obtained in the first crystallization recognition network, dimension reduction processing is performed on all the output data, and the vector obtained after the dimension reduction processing is recorded as a feature information vector.

[0038] For example, several feature images are obtained in the first convolutional layer of the first crystal recognition network, and the vectors obtained by splicing the rows of the feature images together are recorded as analysis vectors. The principal component analysis algorithm is used to perform dimensionality reduction processing on all analysis vectors, and the obtained vectors are recorded as feature information vectors.

[0039] In addition, this embodiment uses the cosine similarity of vectors to reflect the similarity of vectors.

[0040] S4: Inputting crystallization images of other types of chemicals into the first crystallization recognition network, using the optimized learning rate of each network parameter to obtain the optimized gradient update value of each network parameter, and performing gradient update according to the optimized gradient update value until the training is completed; so as to realize crystallizer control.

[0041] S40: Inputting crystal images of other types of chemicals into the first crystal recognition network, obtaining optimized gradient update values ​​of each network parameter using the optimized learning rates of each network parameter, and performing gradient update according to the optimized gradient update values.

[0042] Preferably, as an example, a crystallization image of other types of chemicals is input into the first crystallization recognition network, and the optimized gradient update value of each network parameter is obtained by using the optimized learning rate of each network parameter, and the gradient is updated according to the optimized gradient update value, including: Inputting crystal images of other types of chemicals into the first crystal recognition network to obtain output data; and calculating a loss value using a loss function of the first crystal recognition network based on the output data and the label; The optimized learning rate is used as the learning rate of the corresponding network parameters. Based on the loss value, the gradient descent method is used to calculate the gradient update value of the corresponding network parameters and record it as the optimized gradient update value.

[0043] The network parameters are updated using the optimized gradient update values.

[0044] It should be noted that, when the learning rate is known, using the gradient descent method to calculate the update value of each network parameter based on the loss value is an existing technology and will not be described in detail here.

[0045] It can be understood that by adjusting the learning rate to further adjust the gradient update value, the network's learning of different information can be controlled, so that the network can learn information that is helpful for identifying the crystallization stage of the target type of chemicals, and avoid learning some irrelevant interference information, thereby improving the network's accuracy in identifying the crystallization stage of the target type of chemicals.

[0046] S41: until the training is completed.

[0047] Preferably, as an example, until the training is completed, it includes: The crystal images of all other types of chemicals are sequentially input into the first crystallization recognition network after parameter update, and 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 gradient updated using the optimized gradient update value until the loss value converges and the training is completed, thereby obtaining the trained first crystallization recognition network.

[0048] S42: To achieve crystallizer control.

[0049] It should be noted that in order to achieve accurate control of the crystallizer, the control parameters need to be adjusted in time according to the crystallization stage of the chemical, so as to achieve higher quality crystallization of the chemical.

[0050] Preferably, as an example, to achieve crystallizer control, the method includes: During the crystallization process of the target chemical, a 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 an estimated crystallization stage of the crystallization image at the current moment; If the estimated crystallization stage of the crystallization image at the current moment does not reach the preset crystallization stage, the original crystallization control parameters are used to perform crystallization control; If the estimated crystallization stage of the crystallization image at the current moment has reached the preset crystallization stage, crystallization control is performed using the control parameters required for the new crystallization stage.

[0051] For example, the crystallization stage before the current moment is the first crystallization stage, and the second crystallization stage is used as the preset crystallization stage. If it is determined through judgment that the crystallization image at the current moment is the second crystallization stage, it means that the first crystallization stage has been completed and has entered the second crystallization stage. At this time, the control parameters need to be adjusted to adapt to the second crystallization stage.

[0052] It is understandable that this method can timely adjust the control parameter information according to the needs of the crystallization stage, thereby achieving higher quality crystallization of chemicals. At this point, this embodiment is completed.

[0053] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the principles of the present invention should be included in the protection scope of the present invention.

Claims

1. An intelligent control method for a microchannel continuous crystallizer, characterized in that: include: Collect crystallization images of several chemicals and the crystallization stages corresponding to each crystallization image; Acquire a first crystallization recognition network and a second crystallization recognition network obtained in advance; Calculate the optimized learning rate , record the chemical currently controlled by crystallization as the target chemical, Indicates the crystallization stage of other types of chemicals The grayscale histogram of a crystal image, Represents the grayscale histogram of the jth crystallization image of the target chemical species at the zth crystallization stage, represents the feature information vector of the i-th crystallization image of the target chemical species obtained in the k-th layer of the first crystallization recognition network and the second crystallization recognition network, respectively. N represents the number of crystallization images of the target chemical species. represents the number of crystallization images of the target chemical species in the zth crystallization stage, represents the similarity of vectors, represents the magnitude of a vector, Linear normalization function, L0 represents the preset learning rate; The crystallization images of other types of chemicals are input into the first crystallization recognition network, and the optimized gradient update values ​​of each network parameter are obtained by using the optimized learning rates of each network parameter. The gradient is updated according to the optimized gradient update values ​​until the training is completed, so as to realize crystallizer control.

2. The intelligent control method of a microchannel continuous crystallizer according to claim 1, characterized in that: The obtaining of the first crystallization recognition network and the second crystallization recognition network obtained in advance comprises: Constructing an initial crystallization recognition network; The crystallization stage is used as a label of the corresponding crystallization image; all crystallization images of the target chemical species are used to complete a round of training of the initial crystallization recognition network to obtain a first crystallization recognition network; A round of training of the initial crystal recognition network is completed using all crystal images of other types of chemicals to obtain a second crystal recognition network.

3. The intelligent control method of a microchannel continuous crystallizer according to claim 1, characterized in that: The feature information vector includes: The crystallization image is input into the first crystallization recognition network, a number of output data of each layer is obtained in the first crystallization recognition network, dimension reduction processing is performed on all the output data, and the vector obtained after the dimension reduction processing is recorded as a feature information vector.

4. The intelligent control method of a microchannel continuous crystallizer according to claim 1, characterized in that: The method of obtaining the optimized gradient update value of each network parameter by using the optimized learning rate of each network parameter includes: The crystallization stages are used as labels for the corresponding crystallization images; Inputting crystal images of other types of chemicals into the first crystal recognition network to obtain output data; and calculating a loss value using a loss function of the first crystal recognition network based on the output data and the label; The optimized learning rate is used as the learning rate of the corresponding network parameters. Based on the loss value, the gradient descent method is used to calculate the gradient update value of the corresponding network parameters and record it as the optimized gradient update value.

5. The intelligent control method of a microchannel continuous crystallizer according to claim 1, characterized in that: The training is completed, including: The crystal images of all other types of chemicals are sequentially input into the first crystallization recognition network after parameter update, and 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 gradient updated using the optimized gradient update value until the loss value converges and the training is completed, thereby obtaining the trained first crystallization recognition network.

6. The intelligent control method of a microchannel continuous crystallizer according to claim 1, characterized in that: The method of realizing the crystallizer control comprises: During the crystallization process of the target chemical, a 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 an estimated crystallization stage of the crystallization image at the current moment; If the estimated crystallization stage of the crystallization image at the current moment does not reach the preset crystallization stage, the original crystallization control parameters are used to perform crystallization control; If the estimated crystallization stage of the crystallization image at the current moment has reached the preset crystallization stage, crystallization control is performed using the control parameters required for the new crystallization stage.

7. The intelligent control method of a microchannel continuous crystallizer according to claim 1, characterized in that: The method for obtaining the grayscale histogram comprises: The crystallization image is grayed to obtain a grayscale image of the crystallization image. The grayscale values ​​in the grayscale image are counted to obtain the frequency of occurrence of each grayscale value. The frequency of occurrence of all grayscale values ​​is arranged in ascending order of the grayscale values, and the obtained vector is recorded as a grayscale histogram.

8. 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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