Magnetic resonance image classification method based on quantum bayesian neural network

Abstract

The present invention relates to a magnetic resonance image classification method based on a quantum Bayesian neural network, comprising: acquiring an input data set from an image data set; selecting a prior distribution and a prior confidence level of a weight parameter of a trainable circuit; calculating a posterior distribution of the weight parameter of the trainable circuit on the basis of the input data set, the prior distribution and the prior confidence level; updating the prior distribution and the prior confidence level; processing the input data set on the basis of the posterior distribution and a variational quantum circuit to obtain quantum state data; and classifying the quantum state data to form an output data set. The method has the desirable properties of Bayesian inference while maintaining prediction performance comparable to other similar models. Compared with the prior art, the magnetic resonance image classification method based on a quantum Bayesian neural network disclosed in the present application allows for a more comprehensive understanding and use of the uncertainty of quantitative prediction in input data, thereby improving the generalization ability and robustness of models.

Description

A magnetic resonance image classification method based on quantum Bayesian neural network Technical Field

[0001] The present invention relates to the technical field of magnetic resonance image classification technology, and in particular to a magnetic resonance image classification method based on quantum Bayesian neural network. Background Art

[0002] Magnetic resonance imaging (MRI), an advanced medical imaging technique, is widely used to obtain high-quality brain images. This technique is favored for its painless and non-invasive nature, as well as its ability to provide high levels of spatial and contrast resolution. It not only plays an important role in the diagnosis of various diseases, but also provides detailed information about the internal structures of the brain. However, extracting useful information from these high-quality images is a challenge due to the huge amount of data involved and the difficulty in drawing meaningful conclusions directly from the raw data. Therefore, it is necessary to rely on advanced image analysis tools to process this data in order to effectively classify normal and abnormal brain states.

[0003] In the field of medical image analysis, various deep learning-based methods have been proposed for analyzing brain MRI images for health monitoring and disease diagnosis. Meanwhile, quantum computing, as an emerging computing paradigm, demonstrates distinct advantages over traditional computing. These advantages extend beyond computational power. The development of quantum hardware has also given rise to the new field of quantum machine intelligence. To fully leverage the potential of quantum computing in artificial intelligence, researchers are exploring the applications and characteristics of quantum machine intelligence in various AI tasks. Furthermore, advances in neural architecture design are promoting the convergence of deep learning and quantum machine intelligence. In the context of quantum machine learning, frequency training is commonly used to train models based on variational circuits. Traditional frequency training involves finding point estimates for neural weights or parameterized quantum gates. At its core, frequency training is maximum likelihood estimation, which, under appropriate regularization, is equivalent to maximum a posteriori estimation. While computationally convenient in its implementation, frequency training tends to ignore the uncertainty of model parameters, which can lead to poor generalization to unseen data. A key characteristic of frequency training is its focus on finding a single optimal set of parameters, rather than considering their distribution. This approach may not be sufficient to capture the full potential of the model from a statistical learning perspective, especially when dealing with data with high uncertainty or complexity.

[0004] Summary of the Invention

[0005] In order to solve the defect of quantum frequency training in magnetic resonance imaging that ignores the uncertainty of model parameters, the present invention proposes a magnetic resonance image classification method based on quantum Bayesian neural network.

[0006] The technical solution adopted by the present invention is a magnetic resonance image classification method based on quantum Bayesian neural network, comprising:

[0007] Get the input dataset from the image dataset;

[0008] Selecting a prior distribution and a prior confidence level for trainable circuit weight parameters;

[0009] Calculating a posterior distribution of trainable circuit weight parameters based on an input dataset, a prior distribution, and a prior confidence;

[0010] Update prior distribution and prior confidence;

[0011] The input data set is processed according to the posterior distribution and the variational quantum circuit to obtain quantum state data;

[0012] The quantum state data is classified into output data sets.

[0013] Preferably, the steps of calculating the posterior distribution of the trainable circuit weight parameters based on the input data set, the prior distribution and the prior confidence, and updating the prior distribution and the prior confidence include:

[0014] The posterior distribution is proportional to the prior confidence, and the posterior distribution is inversely proportional to the product of the prior confidence and the prior distribution.

[0015] Preferably, the step of the posterior distribution being proportional to the prior confidence, and the posterior distribution being inversely proportional to the product of the prior confidence and the prior distribution, comprises:

[0016] according to Compute the posterior distribution of trainable circuit weight parameters.

[0017] Preferably, the step of processing the input data set according to the posterior distribution and the variational quantum circuit to obtain quantum state data includes:

[0018] Variational quantum circuit (U w (x)) has a data encoding circuit and trainable circuits

[0019] The data encoding circuit is parameterized by the input data;

[0020] The trainable circuit is parameterized by the posterior distribution.

[0021] Preferably, the variational quantum circuit comprises a data encoding circuit and a trainable circuit; the data encoding circuit is parameterized by input data; and the trainable circuit is parameterized by a posterior distribution, including the steps of: the overall design of the variational quantum circuit is explained as follows:

[0022]

[0023] Preferably, the step of obtaining the input data set from the image data set includes:

[0024] The input dataset has a set of random variables observed in the classical data space and a set of target variables that are mapped to the set of random variables.

[0025] Preferably, the step of classifying the quantum state data to form an output data set comprises:

[0026] Quantum state data is based on Fock space and is represented by photon numbers, which are classified into output sets.

[0027] Preferably, the step of processing the input data set according to the posterior distribution and the variational quantum circuit to obtain quantum state data includes:

[0028] The variational quantum circuit is composed of basic single-mode Gaussian gates, and a non-Gaussian gate is provided at the end of the architecture of the variational quantum circuit.

[0029] Preferably, the step of obtaining the input data set from the image data set includes:

[0030] The input data set is processed through a classic multi-layer perceptron to simplify the input data set to obtain low-dimensional feature vector input data.

[0031] Preferably, the input data set is processed by a classical multi-layer perceptron to simplify the input data set to obtain low-dimensional feature vector input data, including that each data in the low-dimensional feature vector input data can be interpreted as: a (l+1) f(W (l) a (l) +b (l) );

[0032] Among them, a (l+1) is the activation value of the l+1 layer, f is the activation function, W (l) is the weight matrix of layer l, a (l) is the activation value of layer l, b (l) is the bias vector of the lth layer.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] This application discloses a magnetic resonance image classification method based on a quantum Bayesian neural network, comprising: obtaining an input dataset from an image dataset; selecting a prior distribution and a prior confidence level for trainable circuit weight parameters; calculating a posterior distribution of the trainable circuit weight parameters based on the input dataset, the prior distribution, and the prior confidence level; updating the prior distribution and the prior confidence level; processing the input dataset according to the posterior distribution and a variational quantum circuit to obtain quantum state data; and classifying the quantum state data to form an output dataset. While extensive research on quantum neural networks has shown that the only training method is frequency-based training, Bayesian learning has been found to benefit quantum neural networks in two ways. First, compared to frequency-based training, Bayesian training models enjoy higher generalization performance due to the use of prior and posterior distributions. Second, Bayesian reasoning provides epistemic uncertainty estimation, a property particularly important for medical image analysis because it allows physicians and clinicians to assess the credibility of model predictions and make more informed decisions accordingly. It is worth noting that frequency-based quantum neural networks often lack this desirable property. During the Bayesian training process, a magnetic resonance image classification method based on a quantum Bayesian neural network can be considered as a new class of quantum neural networks (called Bayesian quantum neural networks) that possesses the desirable properties of Bayesian inference while maintaining comparable predictive performance to other similar models.

[0035] Compared with the existing technology, the magnetic resonance image classification method based on quantum Bayesian neural network disclosed in this application can achieve a more comprehensive understanding and utilization of the uncertainty of quantitative prediction in input data, thereby improving the generalization ability and robustness of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The present invention is described in detail below with reference to the embodiments and accompanying drawings, in which:

[0037] FIG1 is a schematic diagram showing a flow chart of a magnetic resonance image classification method based on a quantum Bayesian neural network according to an embodiment of the present invention;

[0038] FIG2 shows an operation flow chart of a magnetic resonance image classification method based on a quantum Bayesian neural network according to an embodiment of the present invention. DETAILED DESCRIPTION

[0039] To make the objectives, technical solutions, and advantages of the present invention more apparent, embodiments of the present invention will be described in further detail below with reference to the accompanying drawings. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar components or components having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended only to explain the present invention and are not to be construed as limiting the present invention.

[0040] The present invention discloses a magnetic resonance image classification method based on a quantum Bayesian neural network, referring to FIG1 and FIG2 , comprising:

[0041] S10, obtaining an input data set from an image data set;

[0042] S20, selecting a prior distribution and a prior confidence level of trainable circuit weight parameters;

[0043] S30, calculating the posterior distribution of the trainable circuit weight parameters according to the input data set, the prior distribution and the prior confidence;

[0044] S40, updating the prior distribution and prior confidence;

[0045] S50, processing the input data set according to the posterior distribution and the variational quantum circuit to obtain quantum state data;

[0046] S60. Classify the quantum state data to form an output data set.

[0047] By observing the extensive research on quantum neural networks, the only training method is based on frequency training. It is found that Bayesian learning benefits quantum neural networks in two ways. First, compared with frequency training, Bayesian training models enjoy a higher level of generalization due to the use of prior and posterior distributions. Second, Bayesian reasoning provides epistemic uncertainty estimation, which is particularly important for medical image analysis because it allows doctors and clinicians to assess the credibility of model predictions and make more informed decisions accordingly. It is worth mentioning that quantum neural networks trained by frequency training usually lack this desirable property. During the Bayesian training process, a magnetic resonance image classification method based on quantum Bayesian neural networks can be considered as a new type of quantum neural network (called Bayesian quantum neural network), which has the desirable properties of Bayesian reasoning while maintaining predictive performance comparable to other similar models.

[0048] Compared with the existing technology, the magnetic resonance image classification method based on quantum Bayesian neural network disclosed in this application can achieve a more comprehensive understanding and utilization of the uncertainty of quantitative prediction in input data, thereby improving the generalization ability and robustness of the model.

[0049] In step S10, an input dataset is obtained from an image dataset. The image dataset refers to images captured using magnetic resonance imaging (MRI), i.e., the images required for recognition, judgment, and classification. The image dataset is converted from image form into a form suitable for computation. Furthermore, during the learning process, the image dataset can be obtained from image data that has already been judged to have typical features, achieving faster training results.

[0050] For step S20, the prior distribution and prior confidence of the trainable circuit weight parameters are selected. The range of selection is the distribution parameters commonly used in the field of magnetic resonance technology. If certain diseases that are extremely rare in the database are analyzed, the prior distribution can be defined as a Gaussian distribution, and the distribution relationship of the prior confidence can be defined as a multinomial distribution or a Bernoulli distribution. It should be noted that the parameters of the prior distribution and prior confidence defined in this step can be updated according to the posterior distribution of the trainable circuit weight parameters obtained after calculation, so as to train the prior distribution and prior confidence. The prior distribution and prior confidence are predefined before the input data set is observed. The posterior distribution is subsequently calculated based on the input data set, and then the training parameters are continuously updated through network training.

[0051] In step S30, the posterior distribution of the trainable circuit weight parameters is calculated based on the input data set, the prior distribution, and the prior confidence level. The posterior distribution of the trainable circuit weight parameters is calculated based on the input data set, the prior distribution, and the prior confidence level. This approach can effectively analyze historical symptom data and the causes of the symptoms, thereby achieving a more comprehensive understanding and utilization of the uncertainty of quantitative predictions in the input data.

[0052] Regarding the updating of the prior distribution and prior confidence in step S40, the core idea of ​​our proposed variational quantum circuit framework is to incorporate randomness and uncertainty into the design and training of quantum circuits. The key to this approach is to model the quantum circuit weights ω probabilistically, rather than treating them as fixed values. This approach enables us to more fully understand and utilize uncertainty in the data, thereby improving the model's generalization and robustness.

[0053] In step S50, the input data set is processed according to the posterior distribution and the variational quantum circuit to obtain quantum state data. After obtaining the posterior distribution, the posterior distribution needs to be substituted into the variational quantum circuit for calculation, and the quantum state data is obtained after processing. Specifically, the step of encoding classical data into quantum data can be implemented by an encoder.

[0054] Regarding step S60 of classifying the quantum state data to form output data sets, it should be noted that the quantum state data needs to be classified to obtain output data sets for different diseases. In other embodiments, the quantum state data can also be converted into classical data again and then classified to obtain output data sets for different diseases.

[0055] It is important to note that the prior distribution of the variational quantum circuit parameter ω reflects a prior understanding of the parameter's likely values ​​before any data is observed. Furthermore, a prior confidence measure of predictive power is defined, which represents the model's ability to predict the output given an input dataset and the parameter ω. Finally, the focus is on the posterior distribution of the parameter ω.

[0056] In some embodiments, the steps of calculating the posterior distribution of the trainable circuit weight parameters based on the input data set, the prior distribution, and the prior confidence, and updating the prior distribution and the prior confidence include:

[0057] The posterior distribution is proportional to the prior confidence, and the posterior distribution is inversely proportional to the product of the prior confidence and the prior distribution.

[0058] In some specific embodiments, the step of making the posterior distribution proportional to the prior confidence and the posterior distribution inversely proportional to the product of the prior confidence and the prior distribution includes:

[0059] according to Compute the posterior distribution of trainable circuit weight parameters.

[0060] In this framework, we first define a variational quantum circuit U parameterized by learnable weights ω w (x), which can adjust the behavior of the variational quantum circuit according to the input χ. This variational quantum circuit design can map classical data into quantum states and process them through quantum computing.

[0061] Next, we define the prior distribution p(ω) of the quantum circuit parameter ω. The prior distribution reflects our prior understanding of the possible values ​​of the parameter before observing any data. In addition, we define the prior confidence p(y|x, ω) of the predictive ability, which represents the ability of the model to predict the output y given the input dataset χ and the parameter ω. Finally, we focus on the posterior distribution p(ω|D) of the parameter ω.

[0062] This is an updated understanding of the parameters ω after observing a dataset D. The dataset D is calculated by combining the prior distribution and the evidence obtained from the input dataset χ. The dataset D not only suggests which parameter values ​​(prior distribution and prior confidence) are more likely, but also suggests the uncertainty about these parameter values ​​(prior distribution and prior confidence).

[0063] In some embodiments, the step of processing the input data set according to the posterior distribution and the variational quantum circuit to obtain quantum state data includes:

[0064] Variational quantum circuit (U w (x)) has a data encoding circuit and trainable circuits

[0065] The data encoding circuit is parameterized by the input data;

[0066] The trainable circuit is parameterized by the posterior distribution.

[0067] In some specific embodiments, the variational quantum circuit comprises a data encoding circuit and a trainable circuit; the data encoding circuit is parameterized by input data; and the trainable circuit is parameterized by a posterior distribution. The overall design of the variational quantum circuit is explained as follows:

[0068] The core idea of ​​quantum neural networks is to use quantum circuits to perform functions similar to those of neurons in traditional neural networks. In a quantum neural network, each quantum circuit can be viewed as a "neuron" that minimizes a target loss function through adjustable parameters. This design enables quantum approximate optimization algorithms to verify the effectiveness of quantum machine learning algorithms on simulated machines.

[0069] For a set of random variables observed in the classical data space χ and a set of related target variables

[0070] Circuit-based quantum machine learning models process these classical data by mapping them into a high-dimensional Hilbert space.

[0071] Circuit-based quantum machine learning models are interpreted as variational quantum circuits U w (x), where ω is a classical trainable parameter with the implementation χ.

[0072] Mathematically speaking, the mapping of input data is defined as: x→U w (x)|0>=|φ w (x)>

[0073] where |φ w (x)> is the quantum representation of the input χ in the high-dimensional quantum Hilbert space. w The structure of (x) involves the data encoding circuit and trainable circuits The structure of the quantum classifier consists of a stack of N variable quantum circuits, where is parameterized by the input features, and is parameterized by the model's weights. In particular, It is formed by gates of the form exp(-ixH), where H is the time-evolving Hamiltonian (total energy) that generates the data encoding.

[0074] Therefore, the overall design of a quantum circuit can be interpreted as:

[0075] The unified representation of the quantum model can be written as:

[0076] where |φ w (x)><φ w (x)| is the density matrix of the quantum state, |φ w (x)> and is the Hermitian operator corresponding to the quantum observable associated with the measurement.

[0077] In some embodiments, the step of obtaining an input dataset from an image dataset includes:

[0078] The input dataset has a set of random variables observed in the classical data space and a set of target variables that are mapped to the set of random variables.

[0079] In some embodiments, the step of classifying the quantum state data into an output data set includes:

[0080] Quantum state data is based on Fock space and is represented by photon numbers, which are classified into output sets.

[0081] The output of the quantum classifier is based on a representation in Fock space. Fock space is a mathematical framework used in quantum mechanics to describe quantum states, particularly when dealing with the quantum states of photons or other bosons. In Fock space, quantum states can be represented by the number of photons (or other bosons).

[0082] In this framework, the structure of the quantum classifier is based on photon number measurement. Since the output is fixed in the Fock basis, for example, the class "healthy child" is assigned to a single photon in the first mode, while the second mode corresponds to the class "tuberous sclerosis patient."

[0083] In some embodiments, the step of processing the input data set according to the posterior distribution and the variational quantum circuit to obtain quantum state data includes:

[0084] The variational quantum circuit is composed of basic single-mode Gaussian gates, and a non-Gaussian gate is provided at the end of the architecture of the variational quantum circuit.

[0085] In contrast to the design of discrete variable quantum models, the basic single-mode Gaussian gates used for continuous variable quantum gates include the phase space squeezing gate S(r), the N-mode interferometer The Kerr gate K(k) at the end of the architecture is a non-Gaussian gate that achieves nonlinearity and versatility.

[0086] In some embodiments, the step of obtaining an input dataset from an image dataset includes:

[0087] The input data set is processed through a classic multi-layer perceptron to simplify the input data set to obtain low-dimensional feature vector input data.

[0088] In some specific embodiments, the input data set is processed by a classical multi-layer perceptron to simplify the input data set to obtain low-dimensional feature vector input data, including that each data in the low-dimensional feature vector input data can be interpreted as: a (l+1) f(W (l) a (l) +b (l) );

[0089] Among them, a (l+1) is the activation value of the l+1 layer, f is the activation function, W (l) is the weight matrix of layer l, a (l) is the activation value of layer l, b (l) is the bias vector of the lth layer.

[0090] This network architecture consists of two main parts. The first part is the classic multilayer perceptron (MLP). The MLP consists of multiple layers, each containing a large number of neurons that are able to capture and learn features from the input data. Each neuron performs the following calculations: a (l+1) =f(W (l) a (l) +b (l) )

[0091] Here a (l+1) is the activation value of the l+1 layer, f is the activation function, W (l) is the weight matrix of layer l, a (l) is the activation value of layer l, and b (l) is the bias vector of the lth layer.

[0092] This classic multilayer perceptron is used to take raw data and convert it into a low-dimensional representation. This low-dimensional representation, often called a feature vector, encapsulates key information about the input data. For example, referring to Figure 2, the multilayer perceptron outputs a 14-dimensional feature vector. This vector is then used as the input parameters (the input parameters from the input dataset) of the parameterized quantum gates in the variational quantum circuit.

[0093] In this specification, the use of terms such as "Embodiment 1," "this embodiment," and "in one embodiment" indicates that the specific features, structures, materials, or characteristics described in conjunction with that embodiment or example are included in the invention or at least one embodiment or example of the invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example; furthermore, the specific features, structures, materials, or characteristics described may be appropriately combined in any one or more embodiments or examples.

[0094] In the description of this specification, the terms "connect," "install," "fix," "dispose," and "have" are to be understood in a broad sense. For example, "connect" can mean 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 an indirect connection through an intermediate medium, or it can be internal communication between two components. Those skilled in the art will understand the specific meanings of the above terms in this application based on specific circumstances.

[0095] In the description of this specification, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises", "comprising" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or apparatus comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article or apparatus comprising the element.

[0096] The above description of the embodiments is to facilitate ordinary technicians in this technical field to understand and apply the technology of this case. People familiar with the technology in this field can obviously make various modifications to these examples easily and apply the general principles described here to other embodiments without having to go through creative work. Therefore, this case is not limited to the above embodiments. Modifications to the following situations should all be within the scope of protection of this case: ① A new technical solution implemented based on the technical solution of the present invention and combined with existing common knowledge, the technical effect produced by the new technical solution does not exceed the technical effect of the present invention; ② The equivalent replacement of some features of the technical solution of the present invention with the known technology, the technical effect produced is the same as the technical effect of the present invention; ③ The technical solution of the present invention is expandable, and the substantive content of the expanded technical solution does not exceed the technical solution of the present invention; ④ The equivalent transformation made by the content of the description and drawings of the present invention is directly or indirectly applied to other related technical fields.

Claims

1. A magnetic resonance image classification method based on quantum Bayesian neural network, characterized in that: include: Get the input dataset from the image dataset; Selecting a prior distribution and a prior confidence level for trainable circuit weight parameters; Calculating a posterior distribution of trainable circuit weight parameters based on an input dataset, a prior distribution, and a prior confidence; Update prior distribution and prior confidence; The input data set is processed according to the posterior distribution and the variational quantum circuit to obtain quantum state data; The quantum state data is classified into output data sets.

2. The magnetic resonance image classification method based on quantum Bayesian neural network according to claim 1, characterized in that: The steps of calculating the posterior distribution of the trainable circuit weight parameters according to the input data set, the prior distribution and the prior confidence, and updating the prior distribution and the prior confidence include: The posterior distribution is proportional to the prior confidence, and the posterior distribution is inversely proportional to the product of the prior confidence and the prior distribution.

3. The magnetic resonance image classification method based on quantum Bayesian neural network according to claim 2, characterized in that: The steps of making the posterior distribution proportional to the prior confidence and the posterior distribution inversely proportional to the product of the prior confidence and the prior distribution include: according to Compute the posterior distribution of trainable circuit weight parameters.

4. The magnetic resonance image classification method based on quantum Bayesian neural network according to claim 1, characterized in that: The steps of processing the input data set according to the posterior distribution and the variational quantum circuit to obtain quantum state data include: Variational quantum circuit (U w (x)) has a data encoding circuit and trainable circuits The data encoding circuit is parameterized by the input data; The trainable circuit is parameterized by the posterior distribution.

5. The magnetic resonance image classification method based on quantum Bayesian neural network according to claim 4, characterized in that: The variational quantum circuit comprises a data encoding circuit and a trainable circuit; the data encoding circuit is parameterized by input data; the trainable circuit is parameterized by a posterior distribution, and the overall design of the variational quantum circuit is explained as follows:

6. The magnetic resonance image classification method based on quantum Bayesian neural network according to claim 1, characterized in that: The steps to obtain the input dataset from the image dataset include: The input dataset has a set of random variables observed in the classical data space and a set of target variables that are mapped to the set of random variables.

7. The magnetic resonance image classification method based on quantum Bayesian neural network according to claim 1, characterized in that: The steps of classifying the quantum state data into an output data set include: Quantum state data is based on Fock space and is represented by photon numbers, which are classified into output sets.

8. The magnetic resonance image classification method based on quantum Bayesian neural network according to claim 1, characterized in that: The steps of processing the input data set according to the posterior distribution and the variational quantum circuit to obtain quantum state data include: The variational quantum circuit is composed of basic single-mode Gaussian gates, and a non-Gaussian gate is provided at the end of the architecture of the variational quantum circuit.

9. The magnetic resonance image classification method based on quantum Bayesian neural network according to any one of claims 1 to 8, characterized in that: The steps to obtain the input dataset from the image dataset include: The input data set is processed through a classic multi-layer perceptron to simplify the input data set to obtain low-dimensional feature vector input data.

10. The magnetic resonance image classification method based on quantum Bayesian neural network according to claim 9, characterized in that: The input data set is processed by a classic multi-layer perceptron to simplify the input data set to obtain low-dimensional feature vector input data, including that each data in the low-dimensional feature vector input data can be interpreted as: a (l+1) =f(W (l) a (l) +b (l) ); Among them, a (l+1) is the activation value of the l+1 layer, f is the activation function, W (l) is the weight matrix of layer l, a (l) is the activation value of layer l, b (l) is the bias vector of the lth layer.

Images