Multi-sample data dimension reduction method and device based on quantum state superposability

Abstract

The invention discloses a multi-sample data dimension reduction method and device based on quantum state superimposition, and the method comprises the steps: mapping classical data to a quantum state through a quantum coding technology, and forming a quantum data set; processing a quantum data set by using a parameterized quantum circuit, and realizing dimension reduction of data by optimizing parameters of a quantum gate; measuring the quantum data set after dimension reduction to obtain classical data after dimension reduction; and inputting the classical data subjected to dimension reduction into a machine learning model, and carrying out subsequent prediction or classification tasks.

Description

Technical Field

[0001] The present invention relates to the field of quantum dimensionality reduction technology, and in particular to a multi-sample data dimensionality reduction method and device based on quantum state superposition. Background Art

[0002] With the advent of the big data era, all industries are facing the challenge of processing and analyzing massive amounts of data. In the field of machine learning, data-driven models often take too long to run or have reduced performance due to the large dimensions of the input data, which is particularly disadvantageous for industries that require quick decision-making.

[0003] To solve this problem, traditional data dimensionality reduction techniques such as principal component analysis (PCA) are widely used, but these methods have limitations such as poor interpretability and high computational overhead. Summary of the invention

[0004] The present invention aims to solve one of the technical problems in the related art at least to a certain extent. To this end, one object of the present invention is to propose a multi-sample data dimensionality reduction method and device based on quantum state superposition, comprising: Map classical data to quantum states through quantum coding technology to form quantum data sets; Use parameterized quantum circuits to process quantum data sets and achieve data dimensionality reduction by optimizing the parameters of quantum gates; Measure the dimension-reduced quantum data set to obtain the dimension-reduced classical data; The reduced classical data is input into the machine learning model for subsequent prediction or classification tasks.

[0005] Preferably, the quantum coding technology includes at least one of angle coding, ground state coding or amplitude coding.

[0006] Preferably, the amplitude encoding normalizes the classical data and then associates it with the amplitude of the quantum state to achieve mapping of data to the quantum state.

[0007] Preferably, the parameterized quantum circuit comprises: Optimizable quantum gates can achieve data dimensionality reduction by iteratively optimizing the parameters of quantum gates.

[0008] Preferably, the parameterized quantum circuit further comprises: Quantum coding and measurement, quantum coding is used to map classical data into quantum states; Measurement is used to measure the quantum state after dimensionality reduction.

[0009] Preferably, the dimensionally reduced quantum data set is measured to obtain the dimensionally reduced classical data, which is measured using observables on quantum bits to obtain the frequency of the quantum state, which is converted into expectations through post-processing to achieve conversion of quantum states into classical data.

[0010] Preferably, the machine learning model includes: Classification model, regression model, or clustering model.

[0011] Preferably, mapping the classical data to the quantum state through quantum coding technology to form a quantum data set also includes: preprocessing the classical data, including normalization or standardization processing, to avoid the effect of quantum dimensionality reduction being affected by the excessive magnitude of a single eigenvalue.

[0012] Preferably, it includes applications in: customer intelligent marketing, precision marketing, customer default risk detection, customer matured asset prediction, and business scenarios involving high-dimensional features and data.

[0013] A device, comprising: a quantum coding module, a parameterized quantum circuit module, a measurement module and a machine learning model module; The quantum encoding module is used to map classical data to quantum states; The parameterized quantum circuit module is used to process the quantum data set to achieve data dimensionality reduction; The measurement module is used to measure the dimension-reduced quantum data set to obtain the dimension-reduced classical data; The machine learning model module is used to perform prediction or classification tasks on the classical data after dimensionality reduction.

[0014] The above solution of the present invention includes at least the following beneficial effects: Improve the efficiency of data dimensionality reduction: By using quantum coding to efficiently map classical data to quantum states and using variational quantum circuits to manipulate quantum states, rapid data dimensionality reduction at the quantum level is achieved; this process significantly shortens the time required for data dimensionality reduction and improves overall data processing efficiency; Reduce computing resource consumption: Compared with traditional data dimensionality reduction methods, this invention uses the parallelism of quantum computing and the superposition of quantum states to process multiple data points in one quantum operation, thereby reducing computing resource consumption; this is particularly important for processing large-scale data sets and helps reduce the cost of data processing; Enhance the interpretability and generalization ability of the model: Through quantum dimensionality reduction, redundant information and noise in the original data are effectively removed, retaining the information that best reflects the essential characteristics of the data; this makes the data after dimensionality reduction easier to be understood and used by machine learning models, improving the interpretability and generalization ability of the model.

[0015] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying creative work.

[0017] Figure 1 It is a structural schematic diagram of a multi-sample data dimensionality reduction method based on quantum state superposition provided in an embodiment of the present invention; Figure 2 is a schematic diagram of a structure of a parameterized quantum circuit provided in an embodiment of the present invention; Figure 3 The first prediction graph of the model provided in the embodiment of the present invention; Figure 4 The second prediction graph of the model provided in the embodiment of the present invention; Figure 5 The third prediction graph of the model provided in the embodiment of the present invention; Figure 6 The fourth prediction graph of the model provided in the embodiment of the present invention; Figure 7 A comparison chart of model effect indicators is provided in an embodiment of the present invention; Figure 8 It is a running time diagram provided in an embodiment of the present invention.

[0018] The realization of the purpose, functional features and advantages of the present invention will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0019] The embodiments of the present invention are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, but are not to be construed as limiting the present invention. All other embodiments obtained by ordinary technicians in the field without creative work based on the embodiments of the present invention are within the scope of protection of the present invention.

[0020] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "clockwise", "counterclockwise", "axial", "circumferential", "radial" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the referred device or element must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as limiting the present invention.

[0021] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0022] In the present invention, unless otherwise clearly specified and limited, the terms "installed", "connected", "connected", "fixed" and the like should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be an indirect connection through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0023] In the present invention, unless otherwise clearly specified and limited, a first feature being "above" or "below" a second feature may include that the first and second features are in direct contact, or may include that the first and second features are not in direct contact but are in contact through another feature between them. Moreover, a first feature being "above", "above" and "above" a second feature includes that the first feature is directly above and obliquely above the second feature, or simply indicates that the first feature is higher in level than the second feature. A first feature being "below", "below" and "below" a second feature includes that the first feature is directly below and obliquely below the second feature, or simply indicates that the first feature is lower in level than the second feature.

[0024] A multi-sample data dimensionality reduction method and device based on quantum state superposition according to an embodiment of the present invention will be described in detail below with reference to the accompanying drawings.

[0025] See also Figure 1In this embodiment, the method includes: mapping classical data to quantum states through quantum coding technology to form a quantum data set; processing the quantum data set using a parameterized quantum circuit, and achieving data dimension reduction by optimizing the parameters of the quantum gate; measuring the dimension-reduced quantum data set to obtain dimension-reduced classical data; inputting the dimension-reduced classical data into a machine learning model to perform subsequent prediction or classification tasks; Improve the efficiency of data dimensionality reduction: By using quantum coding to efficiently map classical data to quantum states and using variational quantum circuits to manipulate quantum states, rapid data dimensionality reduction at the quantum level is achieved; this process significantly shortens the time required for data dimensionality reduction and improves overall data processing efficiency; Reduce computing resource consumption: Compared with traditional data dimensionality reduction methods, this invention uses the parallelism of quantum computing and the superposition of quantum states to process multiple data points in one quantum operation, thereby reducing computing resource consumption; this is particularly important for processing large-scale data sets and helps reduce the cost of data processing; Enhance the interpretability and generalization ability of the model: Through quantum dimensionality reduction, redundant information and noise in the original data are effectively removed, retaining the information that best reflects the essential characteristics of the data; this makes the data after dimensionality reduction easier to be understood and used by machine learning models, improving the interpretability and generalization ability of the model.

[0026] In this embodiment, the quantum coding technology includes at least one of angle coding, ground state coding or amplitude coding; Angle coding mainly relies on the phase information of quantum bits to encode information. In quantum computing, the state of a quantum bit consists of two base states (usually denoted as and ), and the phase of the superposition state can be adjusted by rotating the quantum bit. Angle coding uses this feature to encode information by changing the phase of the quantum bit, thereby realizing the quantization of information. Ground state coding is a more intuitive coding method that maps classical information to the ground state of the quantum bit, that is, the quantum bit is selected according to the value of the information. state or state; In amplitude coding, classical information is encoded in the amplitude of the quantum bit, that is, when the quantum bit is in a superposition state, its State and The amplitude of the state reflects the value of classical information. This encoding method can make full use of the superposition and coherence of quantum states to achieve efficient processing and transmission of information.

[0027] In this embodiment, amplitude coding normalizes the classical data and associates it with the amplitude of the quantum state to achieve the mapping of data to the quantum state; Amplitude coding technology means that data is encoded into the amplitude of a quantum state. It associates the classical information in the normalized real vector with the quantum amplitude; a normalized classical Dimensional data points By one The amplitude of the quantum state of the bit express: ; in , yes No. elements, It is A calculation ground state; For example, to amplitude encode a 4D floating point array: , the first step is to normalize it, , at least qubits to encode, so two qubits are used to represent The corresponding amplitude encoding is: The main advantage of amplitude coding is that in amplitude coding methods, the large Hilbert space of quantum devices is properly utilized; amplitude coding can be used Bits represent a dimensional data points; if the quantum machine learning algorithm is The polynomial (or qubit efficiency) of , its running time depends logarithmically on the size of the data set. For example, a 4-dimensional data point can be run with 2; Another advantage of amplitude coding is that due to the superposition of quantum states, this method can encode multiple sample points at a time; in addition, in the process of converting classical information into quantum states, the original data is stored in a small number of quantum bits in quantum form. In other words, the data dimension reduction model based on amplitude coding is based on the data dimension compression of the full vector space, without the concept of information loss. See also Figure 2 , parameterized quantum circuits, including: optimizable quantum gates, which can achieve data dimension reduction by iteratively optimizing the parameters of quantum gates; parameterized quantum circuits, also include: quantum coding and measurement, quantum coding is used to map classical data to quantum states; measurement is used to measure the quantum states after dimension reduction; the quantum data sets after dimension reduction are measured to obtain the classical data after dimension reduction; the observables on the quantum bits are used to measure, and the frequency of the quantum state is obtained, which is converted into expectations through post-processing to achieve the conversion of quantum states to classical data; Mapping classical data to quantum states through quantum coding technology to form a quantum data set also includes: preprocessing classical data, including normalization or standardization, to avoid a single eigenvalue that is too large to affect the effect of quantum dimensionality reduction Quantum computers process data by applying a set of universal quantum gates that can simulate the rotation of any quantum state vector. Parameterized quantum circuits can be viewed as a series of parameterized unitary operations acting on n quantum bits. As shown in the figure, the variational quantum circuit in quantum dimensionality reduction consists of three parts: The first part is the process of quantum coding, which is responsible for encoding classical data into quantum states that can be input into quantum circuits; The second part is a quantum circuit composed of a series of quantum gates. By designing quantum gates and parameters, different structures can be defined. Some quantum gates contain optimizable parameters θ. The third part represents the measurement operation used to obtain observable quantities, which is performed at the end of one or more quantum circuits. After the observation, the frequency of each quantum state is obtained and converted into expectations through post-processing, thus realizing the process of converting the input classical vector into the data after quantum dimensionality reduction.

[0028] In this embodiment, the machine learning model includes: a classification model, a regression model or a clustering model; Classification models are the most common type of models in machine learning. They are mainly used to predict the category to which a data point belongs. They classify new unknown data points by learning the features and boundaries of each category from historical data. Classification models are widely used in image recognition, text classification, spam detection and other fields. For example, in image recognition, a classification model can identify whether the object in the picture is a cat or a dog; in text classification, it can determine whether an email is a work email or a spam email. Regression models are mainly used to predict numerical data, that is, the target variable is continuous rather than discrete; regression models predict the target value of new data points by analyzing the relationship between independent variables (features) and dependent variables (targets); in the financial field, regression models can be used to predict stock prices; in the medical field, it can be used to predict the progression of a patient's disease or the effect of treatment; Clustering models are different from classification models and regression models. They are mainly used to discover natural groups or patterns in data without defining categories or target values ​​in advance. Clustering models divide data points into different groups by calculating the similarities or distances between data points. These groups may represent potential patterns or categories in the data. Clustering models are widely used in market research, social network analysis and other fields. For example, in market research, clustering models can help companies identify different customer groups and develop corresponding marketing strategies.

[0029] See also Figures 3~8 , in this embodiment, includes applications in: customer intelligent marketing, precision marketing, customer default risk detection, customer maturity asset prediction involving high-dimensional features and data business scenarios; For example, when applied to customer default risk detection: Test indicators: True Positive (TP): The number of samples in the test sample that the model predicts as True. False Negative (FN): The number of samples where the model predicts True type samples in the test sample as False; False Positive (FP): The number of samples in the test sample where the model predicts the False type samples as True; True Negative (TN): The number of samples in the test sample where the model predicts the False type as False; (I) Accuracy: It describes the proportion of samples predicted correctly by the model (including true positive examples, positive and negative examples) to the total number of samples. The specific formula is as follows:

[0030] The accuracy can only indicate the quality of a model to a certain extent. If the number of positive and negative samples in the test data set is unbalanced, the model will mark all samples as the same category. In this case, the accuracy must be very high, but it does not mean that the model's prediction is very accurate. Therefore, other test criteria should be introduced. (ii) Recall: It indicates the proportion of all positive examples that are correctly predicted. The specific formula is as follows:

[0031] The higher the recall rate, the stronger the model's ability to find the correct samples in the test samples. If the model predicts all test samples as correct samples, the recall rate is 1; Test environment and methods: Based on the Qiskit open source software development kit, the AerSimulator simulator is used to simulate the quantum environment locally; Dataset introduction: We use a public dataset of loan risk scenarios for quantum data conversion, model training and testing, and use a classification model to minimize the risk of loss when lending to customers. The dataset has 307, 511 rows and 122 columns, including 120 dimensions of features for prediction, including basic information of customers when applying, such as assets, income, gender, age, etc. The labels used for prediction are about whether the customer has difficulty repaying the loan. Methods: First, the model prediction results based on the original data set are used as a benchmark; based on the original data set, the maximum probability estimation method (automatically retaining the most original data information) and the cut-off method (manually intercepting the retained feature dimensions) in the traditional principal component analysis (Principal Components Analysis) dimensionality reduction method and the quantum dimensionality reduction method are used to reduce the dimensions of the original data set respectively; the reduced-dimensional data sets are put into the model for loan default detection, and the results are compared and verified after they are obtained; Test results: (I) Benchmark: The model prediction accuracy of the original data set (120 features) is 95.498%; the recall rate of risky customers is 0.76; the recall rate of risk-free customers is 0.97; the running time is 12.91 seconds; (ii) The prediction accuracy of the model based on principal component analysis (PCA)-maximum probability estimation method (119 eigenvalues) is 95.701%; the recall rate of risky customers is 0.74; the recall rate of risk-free customers is 0.98; and the running time is 32.33 seconds.

[0032] (III) The prediction accuracy of the model based on principal component analysis (PCA)-cut-off method (7 eigenvalues) is 94.677%; the recall rate of risky customers is 0.67; the recall rate of risk-free customers is 0.97; the running time is 8.55 seconds; (IV) The prediction accuracy of the model based on quantum dimensionality reduction (7 features) is 97.342%; the recall rate of risky customers is 0.72; the recall rate of risk-free customers is 1; and the running time is 6.19 seconds. Quantum coding can compress the original features exponentially, reducing the number of features by nearly 95% (120 dimensions reduced to 7 dimensions); Test summary: After comparative verification, it can be seen that the model running time is significantly reduced after applying the quantum dimensionality reduction method compared with the traditional principal component analysis (PCA) dimensionality reduction method; the prediction accuracy of the loan default risk detection model after applying the quantum dimensionality reduction method reaches 97.342%, which is higher than the benchmark and the traditional principal component analysis dimensionality reduction method; at the same time, in terms of the prediction recall rate of the risk customer group, the quantum dimensionality reduction method is not much different from the benchmark and the traditional principal component analysis dimensionality reduction method.

[0033] Compared with the benchmark and the results of classical principal component analysis (PCA) dimensionality reduction, the model running time is shorter on the dataset after quantum coding conversion, showing lower model training and running costs.

[0034] A device, comprising: a quantum coding module, a parameterized quantum circuit module, a measurement module and a machine learning model module; The quantum coding module is used to map classical data to quantum states. The quantum coding module is the starting link of quantum dimensionality reduction technology. Its core function is to map classical data to quantum states. In classical computing, information is stored in the form of bits (binary numbers), while in quantum computing, information is stored in quantum bits (qubits) as the basic unit. The quantum coding module converts classical data into quantum states through specific coding methods, such as angle coding, ground state coding or amplitude coding. This conversion not only provides the necessary information input for quantum computing, but also makes full use of the superposition and entanglement characteristics of quantum states, providing possibilities for subsequent data processing. Amplitude coding is an important coding method in quantum coding modules. In amplitude coding, classical data is normalized and then associated with the amplitude of the quantum state. In this way, a high-dimensional classical data point can be compressed into a small number of quantum bits, thereby achieving exponential compression of data. This compression not only reduces the cost of data storage and transmission, but also provides an important premise for quantum dimensionality reduction. The parameterized quantum circuit module is used to process quantum data sets to achieve data dimensionality reduction. In quantum dimensionality reduction, the parameterized quantum circuit module receives the quantum state generated by the quantum coding module as input and transforms the quantum state through a series of quantum gates; these quantum gates include fixed gates and adjustable gates, where the parameters of the adjustable gates can be adjusted through optimization algorithms to achieve the best dimensionality reduction effect; after the transformation of the quantum gates, the dimension of the quantum state is reduced, thereby achieving data dimensionality reduction; The design and optimization of parameterized quantum circuit modules are the key to quantum dimensionality reduction technology. Through reasonable circuit structure and parameter settings, effective dimensionality reduction of quantum data can be achieved while maintaining the main features and structural information of the data; this not only improves the efficiency of data processing, but also provides better input data for subsequent machine learning models; The measurement module is used to measure the quantum data set after dimensionality reduction to obtain the classical data after dimensionality reduction. In quantum dimensionality reduction, the measurement module measures the quantum state after being processed by the parameterized quantum circuit module. Due to the superposition and entanglement of quantum states, the measurement results may have certain randomness and uncertainty. However, through multiple measurements and statistical analysis, stable measurement results can be obtained, and the classical data after dimensionality reduction can be inferred based on them. The design and implementation of the measurement module need to consider many factors, including the choice of measurement method, measurement accuracy and efficiency. A reasonable measurement strategy can improve the accuracy and reliability of data and provide better input data for subsequent machine learning models. The machine learning model module is used to perform prediction or classification tasks on the classical data after dimensionality reduction. The machine learning model module can receive the classical data after dimensionality reduction as input and apply various machine learning algorithms to perform prediction or classification tasks. Since the data after dimensionality reduction has lower dimensions and higher quality, the machine learning model can more easily learn and identify the characteristics of the data, thereby improving the accuracy and efficiency of prediction or classification. In the application of quantum dimensionality reduction technology, the selection and optimization of machine learning model modules depends on the specific application scenarios and requirements. Through reasonable model selection and parameter setting, the optimal use of reduced dimensionality data can be achieved, providing strong support for various practical applications.

[0035] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0036] The above description is only a preferred embodiment of the present invention, and does not limit the patent scope of the present invention. All equivalent structural changes made by using the contents of the present invention specification and drawings under the inventive concept of the present invention, or directly / indirectly applied in other related technical fields are included in the patent protection scope of the present invention.

Claims

1. A multi-sample data dimensionality reduction method based on quantum state superposition, characterized in that: include: Map classical data to quantum states through quantum coding technology to form quantum data sets; Use parameterized quantum circuits to process quantum data sets and achieve data dimensionality reduction by optimizing the parameters of quantum gates; Measure the dimension-reduced quantum data set to obtain the dimension-reduced classical data; The reduced classical data is input into the machine learning model for subsequent prediction or classification tasks.

2. The multi-sample data dimensionality reduction method based on quantum state superposition according to claim 1 is characterized in that: The quantum coding technology includes at least one of angle coding, ground state coding or amplitude coding.

3. The multi-sample data dimensionality reduction method based on quantum state superposition according to claim 2 is characterized in that: The amplitude coding normalizes the classical data and associates it with the amplitude of the quantum state to achieve the mapping of data to the quantum state.

4. The multi-sample data dimensionality reduction method based on quantum state superposition according to claim 1, characterized in that: The parameterized quantum circuit comprises: Optimizable quantum gates can achieve data dimensionality reduction by iteratively optimizing the parameters of quantum gates.

5. The multi-sample data dimensionality reduction method based on quantum state superposition according to claim 4 is characterized in that: The parameterized quantum circuit further includes: Quantum coding and measurement, quantum coding is used to map classical data into quantum states; Measurement is used to measure the quantum state after dimensionality reduction.

6. The multi-sample data dimensionality reduction method based on quantum state superposition according to claim 1, characterized in that: The reduced-dimensional quantum data set is measured to obtain reduced-dimensional classical data, which is measured using observable measurements on quantum bits to obtain the frequency of the quantum state, which is converted into expectations through post-processing to achieve conversion from quantum state to classical data.

7. The multi-sample data dimensionality reduction method based on quantum state superposition according to claim 1, characterized in that: The machine learning model comprises: Classification model, regression model, or clustering model.

8. The multi-sample data dimensionality reduction method based on quantum state superposition according to claim 1, characterized in that: The method of mapping the classical data to the quantum state through quantum coding technology to form a quantum data set also includes: preprocessing the classical data, including normalization or standardization processing, to avoid the effect of quantum dimensionality reduction being affected by the excessive magnitude of a single eigenvalue.

9. The multi-sample data dimensionality reduction method based on quantum state superposition according to claim 1, characterized in that: It includes applications in: customer intelligent marketing, precision marketing, customer default risk detection, customer matured asset prediction, and business scenarios involving high-dimensional features and data.

10. A device, using the multi-sample data dimensionality reduction method based on quantum state superposition as described in claims 1 to 9, characterized in that: include: Quantum coding module, parameterized quantum circuit module, measurement module and machine learning model module; The quantum encoding module is used to map classical data to quantum states; The parameterized quantum circuit module is used to process the quantum data set to achieve data dimensionality reduction; The measurement module is used to measure the dimension-reduced quantum data set to obtain the dimension-reduced classical data; The machine learning model module is used to perform prediction or classification tasks on the classical data after dimensionality reduction.

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