CN115169740A - Sequence prediction method and system of pooled echo state network based on compressed sensing - Google Patents

Sequence prediction method and system of pooled echo state network based on compressed sensing Download PDF

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CN115169740A
CN115169740A CN202210945778.4A CN202210945778A CN115169740A CN 115169740 A CN115169740 A CN 115169740A CN 202210945778 A CN202210945778 A CN 202210945778A CN 115169740 A CN115169740 A CN 115169740A
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王梓鉴
康明磊
赵慧
郑明文
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Abstract

The invention provides a sequence prediction method and a sequence prediction system of a pooling echo state network based on compressed sensing, which belong to the technical field of network information prediction and are used for acquiring sequence data required by a prediction task; constructing a pooling echo state network model based on compressed sensing, and training the network model; inputting the acquired sequence data into a trained pooling echo state network model to obtain a prediction result; adding a pooling layer and a compressed sensing layer in a reserve pool of the pooled echo state network model, wherein the pooling layer is used for readjusting the weight of the node state of the reserve pool, and the compressed sensing layer performs sparse transformation and random sub-sampling on the nodes; based on the mechanism of the compressed sensing and pooling algorithm, the invention provides a mechanism which can effectively reduce redundant nodes and improve the node activity performance, and effectively improves the model performance of the ESN, so that the calculated amount can be reduced while the reserve pool is active, and the accuracy and the operating efficiency of model calculation are improved.

Description

Sequence prediction method and system of pooled echo state network based on compressed sensing
Technical Field
The invention belongs to the technical field of network information prediction, and particularly relates to a sequence prediction method and a sequence prediction system of a pooled echo state network based on compressed sensing.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
Today, when machine learning, deep learning technology and application are rapidly developed, echo State Network models (ESNs) are increasingly applied to various industries, such as weather prediction, stock prediction, natural language processing, wind prediction, chaotic sequence prediction and the like; compared with the traditional neural network, the echo state network uses a reserve pool mode to replace a large number of hidden layers included in the original neural network model, the prediction process of the ESN is more mainly reflected on the variation of data dimension, and the parameters are updated in a mode different from back propagation, the determination mode of most parameters of the ESN is randomly initialized in a limited range, the training modes of other parameters are in a least square solution mode to determine values, and the parameter values are not changed along with the training or the prediction of other processes after being determined. And the dimensionality of the data is also promoted to a high dimensionality after entering the reserve pool from the input layer, and then is reduced to a specified dimensionality according to the task requirement, so that the prediction process is completed.
The reserve pool mainly comprises a reserve pool node group with a graph structure and an activation function, and under the action of the nodes and the activation function, the whole echo state network can generate strong nonlinear fitting capacity.
The existing methods for reducing the nodes of the reserve pool include compressed sensing, a neural network Dropout layer and the like, but the improper way of applying the compressed sensing to sparse representation and random sampling in the ESN can cause the loss of data characteristics during sparse representation and sampling, and the direct reduction of the number of the nodes of the reserve pool can cause the deterioration of the prediction effect of the model; therefore, finding a better update method of the reserve pool node and a representation form of the node are key points for improving the model effect.
Disclosure of Invention
In order to overcome the defects of the prior art and solve the problems of how to effectively reduce node redundancy in an Echo State Network model, improve model accuracy, calculation efficiency and the like, the invention provides a sequence prediction method and a sequence prediction system of a Pool Echo State Network (PCESN) based on Compressed Sensing, which are used for increasing a Pool algorithm and Compressed Sensing for the Pool Echo State Network model, effectively reducing redundant nodes, improving node activity performance and improving the model performance of the ESN, so that the amount of calculation can be reduced while a reserve Pool is active, and the accuracy and the operation efficiency of model calculation can be improved.
To achieve the above object, one or more embodiments of the present invention provide the following technical solutions:
the invention provides a sequence prediction method of a pooling echo state network based on compressed sensing;
the sequence prediction method of the pooling echo state network based on compressed sensing comprises the following steps:
acquiring sequence data required by a prediction task;
constructing a pooling echo state network model based on compressed sensing, and training the network model;
inputting the acquired sequence data into a trained pooling echo state network model to obtain a prediction result;
the method comprises the steps that a pooling layer and a compressed sensing layer are added in a reserve pool of a pooled echo state network model, the pooling layer is used for readjusting the weight of the node state of the reserve pool, and the compressed sensing layer conducts sparse transformation and random sub-sampling on nodes.
Further, the pooled echo state network model is based on a classical echo state network model and comprises three parts: an input layer, a reserve pool and an output layer;
the reserve pool is improved and divided into three layers: the method comprises a layer, a pooling layer and a compressed sensing layer.
Further, the normalization layer performs normalization processing on the input data, so that the value of the input data is mapped between 0 and 1.
Further, the pooling layer performs optimization updating on nodes of the reserve pool, and performs state adjustment on inactive or redundant nodes in the reserve pool to obtain a better node state.
Furthermore, the value of the connection parameter between the output layer and the reserve pool layer is determined by the form of least square solution.
Further, the training process of the echo state network model is mainly divided into two stages: a sampling stage and a weight calculation stage.
Further, the sampling stage is used for constructing a system state matrix and a sample data vector;
and the weight calculation stage is used for calculating an output connection weight matrix of the echo state network model.
The second aspect of the invention provides a sequence prediction system based on a compressed sensing pooled echo state network.
The sequence prediction system of the pooling echo state network based on compressed sensing comprises a data acquisition module, a model construction module and a result prediction module;
a data acquisition module configured to: acquiring sequence data required by a prediction task;
a model building module configured to: constructing a pooling echo state network model based on compressed sensing, and training the network model;
a result prediction module configured to: inputting the obtained sequence data into a trained pooling echo state network model to obtain a prediction result;
the method comprises the steps that a pooling layer and a compressed sensing layer are added in a reserve pool of a pooled echo state network model, the pooling layer is used for readjusting the weight of the node state of the reserve pool, and the compressed sensing layer conducts sparse transformation and random sub-sampling on nodes.
A third aspect of the present invention provides a computer readable storage medium having stored thereon a program which, when being executed by a processor, carries out the steps of the method for sequence prediction of a compressed sensing-based pooled echo state network according to the first aspect of the present invention.
A fourth aspect of the present invention provides an electronic device, comprising a memory, a processor and a program stored on the memory and executable on the processor, wherein the processor implements the steps of the compressed sensing-based sequence prediction method for a pooled echo state network according to the first aspect of the present invention when executing the program.
The above one or more technical solutions have the following beneficial effects:
the invention adds a normalization processing layer in a reserve pool of a network, provides a new node value updating algorithm-pooling algorithm of the reserve pool, extracts node information by using a new compressed sensing sparse representation and random sampling method, puts sequence data into a model based on a predicted task, and obtains a prediction result, namely, provides a mechanism capable of effectively reducing redundant nodes and improving the node activity performance based on the mechanisms of compressed sensing and pooling algorithms.
The pooling algorithm provided by the invention does not reduce the number of nodes, but adds a noise value on the basis of the traditional pooling method, adjusts the node state of the nodes of the reserve pool, so that redundant or inactive nodes are subjected to state adjustment, and the prediction mode of the reserve pool can be closer to the chaotic characteristic of a chaotic sequence to be predicted by the model, and finally the model achieves a better prediction effect.
Compared with the original sampling method, the new compressed sensing sparse representation and random sampling method can extract the main information of the nodes of the reserve pool more accurately and efficiently, avoid the leakage and the loss of the information to the maximum extent, effectively improve the model performance of the ESN, reduce the calculated amount while the reserve pool is active, and improve the accuracy and the operating efficiency of model calculation.
Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
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The accompanying drawings, which are incorporated in and constitute a part of this specification, are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the invention and together with the description serve to explain the invention and not to limit the invention.
FIG. 1 is a flow chart of the method of the first embodiment.
Fig. 2 is a schematic structural diagram of a classical pooling echo state network model in the first embodiment.
Fig. 3 is a schematic structural diagram of an improved pooled echo state network model in the second embodiment.
Detailed Description
The invention is further described with reference to the following figures and examples.
It is to be understood that the following detailed description is exemplary and is intended to provide further explanation of the invention as claimed. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the invention. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
Example one
The embodiment discloses a sequence prediction method of a pooling echo state network based on compressed sensing;
as shown in fig. 1, the sequence prediction method based on the compressed sensing pooled echo state network includes:
s1, acquiring sequence data required by a prediction task;
the pooling echo state network is applied to jobs in various scenes, such as stock prediction, wind strength prediction, signal trend prediction, industrial dynamic data soft measurement, time series classification, pattern learning and the like, so that prediction tasks and sequence data, such as stock prediction tasks and stock sequence data, chaotic sequence prediction tasks and chaotic sequence data and the like, are acquired, stock data can be acquired through a website, and the chaotic sequence data is generated through a corresponding chaotic sequence generation formula and combined with a specific numerical value.
S2, constructing a pooling echo state network model based on compressed sensing, and training the network model;
s3, inputting the acquired sequence data into a trained pooling echo state network model to obtain a prediction result;
the method comprises the following steps of constructing a pool echo state network model:
(1) Initialization: and randomly initializing an input weight and a graph structure connection weight in the reserve pool, and initializing an initial time node value of the reserve pool.
(2) Normalization: after the initialization of the nodes in the reserve pool is completed, the sequence data required by the tasks are put into a model, the data enter a normalization layer in the reserve pool for normalization processing, the values of the data are distributed between 0 and 1, the adverse effect of dimension and data value range on model prediction is eliminated, and the connection is established with the reserve pool nodes through a state updating formula of the reserve pool nodes.
(3) Pooling: and the reserve pool nodes enter a pooling layer in the reserve pool to update and optimize the state, and the state of inactive or redundant nodes in the reserve pool is adjusted to obtain a more optimal node state.
After the pooling layer is updated, the number of nodes of the reserve pool is not changed, and the node state of the original reserve pool is optimized through a pooling algorithm, so that the echo state network model can be predicted better.
(4) Compressed sensing: and the updated and optimized reserve pool nodes enter a compressed sensing layer, the compressed sensing layer performs sparse transformation and a random sub-sampling layer on the nodes, and after passing through the compressed sensing layer, the number of the reserve pool nodes is indirectly reduced, but the original node information can still be completely described.
(5) And (3) outputting: and after finishing the training of the reserve pool nodes, determining the value of a connection parameter between the output layer and the reserve pool layer, wherein the parameter is generally determined in a least square solution mode.
The invention is based on a special network-echo state network model in a recurrent neural network, and a classic ESN network is shown in figure 2 and consists of three parts, namely: an input layer, a reserve pool (hidden layer) and an output layer, wherein the network is assumed to be provided with K input units, N reserve pool internal processing units and L output units.
At the time t, the values of an input layer, a reserve pool and an output layer of the network are respectively as follows:
u(t)＝[u 1 (t),u 2 (t),······,u K (t)] T
x(t)＝[x 1 (t),x 2 (t),······,x N (t)] T
y(t)＝[y 1 (t),y 2 (t),······,y L (t)] T
aiming at each moment input u (t), the reserve pool updates the corresponding state, and the state updating formula is as follows:
x(t)＝f(W in ·u(t)+Wx(t-1)(
where u (t) is the input at the current time, x (t) is the node state of the pool at the current time, x (t-1) is the node state of the pool at the previous time, f (-) represents the activation function of the neurons inside the pool, and f (-) generally takes the hyperbolic tangent function tanh ().
The output formula of ESN is:
y(t)＝f out (W out ·x(t))
f out represents an output function of oneIn general, the output layer is linear, i.e. f out Taking an identity function.
The input-to-state variable connection weight matrix W in FIG. 2 in The (NxK dimension) represents the connection between the input layer and the reserve pool, the connection weight matrix W (NxN dimension) of the state variable to the state variable represents the connection between the neurons of the reserve pool, and the connection weight matrix W of the state variable to the output out The (L × N dimension) represents the weight of the connection between the reserve pool to the output layer. Wherein W in And W is randomly generated during the initialization phase and is fixed once generated. And W out The output layer connection weight is obtained by training according to input and output data of a system, and because the state variables and the output are in a linear relation, the output layer connection weight is generally obtained by solving a linear regression problem, namely:
W out ·x＝y
the training process of the echo state network model is mainly divided into two stages: a sampling stage and a weight calculation stage.
A sampling stage: firstly, arbitrarily selecting an initial state of a network, wherein the initial state of the selected network is 0 under a normal condition, namely x (0) =0; connecting the weight matrix W via inputs in And (3) adding training samples u (n) (n =1,2, ·, M) into the reserve pool, and sequentially completing the calculation and collection of the state variable x (t) and the output y (t) according to corresponding equations. Assume that the system state is collected from a certain time m and in a vector (x) 1 (i),x 2 (i),···,x N (i) (i = M, M +1, ·, M) forms a matrix X (M-M +1, n) for the rows, and corresponding sample data Y (n) is also collected and forms a column vector Y (M-M +1, 1) for subsequent calculation of the output connection weight matrix.
A weight calculation stage: calculating an output connection weight matrix W of the echo state network model according to the state matrix and the output collected in the sampling stage out . State variable x (t) and prediction output
Figure BDA0003787367220000081
With linear management between, using predicted output
Figure BDA0003787367220000082
Approximation desired output y (t):
Figure BDA0003787367220000083
the mean square error of the echo state network model is minimized when the calculated weight matrix is satisfied, and the target equation is as follows:
Figure BDA0003787367220000084
further, the resolvable form is:
W out ＝(X -1 Y) T
to solve this linear regression problem, a ridge regression method can be used, as follows:
W out ＝(X T X+C -1 I) -1 X T Y
wherein, X = [ X (m) T ,x(m+1) T ,···,x(M) T ] T ,Y＝[y(m) T ,y(m+1) T ,···,yMT]T, p is sampling starting time, and M is the number of training samples; t represents a matrix transposition operation; the effect of C is at X T And applying a regular term coefficient to the X, if C is properly selected, effectively balancing the complexity of an error term and a model, and improving the performance of the echo state network.
The prediction task inputs the sequence data into the pooling echo state network model to obtain a prediction result, and specifically comprises the following steps:
firstly, a prediction task and time sequence data are obtained, and a training set and a test set are divided according to the data size.
Then, establishing a pooling echo state network model, which comprises the following steps: the method comprises the steps of establishing an echo state network model which can effectively optimize node state information and reduce the number of nodes by a layer, a pooling layer and a compressed sensing layer; and initializing an input connection weight matrix and an internal connection weight matrix of the reserve pool. And training the network, and solving an output weight matrix by using a least square method.
And finally, inputting the time sequence data into the pooling echo state network model based on the prediction task to obtain a prediction result.
For example, a prediction task V and time or chaotic sequence data P are obtained, a pooling echo state network model based on compressed sensing is constructed, an input connection weight matrix and a reserve pool internal connection weight matrix are initialized randomly, the spectrum radius (the absolute value of the characteristic value with the maximum matrix) of the reserve pool internal connection weight matrix is ensured to be less than 1, and a proper pooling layer parameter is selected to obtain a pooling echo state network model A; as shown in fig. 3, the reserve pool of the compressed sensing-based pooled echo state network model is different from that of the classical echo state network model, and the reserve pool of the compressed sensing-based pooled echo state network model is divided into three layers, namely, a merging layer, a pooling layer and a compressed sensing layer. Normalizing the input data in a layer to map the value of the input data between 0 and 1, and eliminating the adverse effect of dimension and data value range on model prediction; the pooling layer performs optimization updating on the nodes of the original reserve pool through a pooling algorithm, and performs state adjustment on the inactive or redundant nodes in the reserve pool to obtain a better node state; the compressed sensing layer compresses and represents the characteristics of the original reserve pool nodes by using a compressed sensing technology, and extracts information capable of describing the states of the original reserve pool nodes through sparse transformation and random sub-sampling, so that the model calculation complexity is reduced, and the prediction accuracy of the model is improved.
In the training process, the input connection weight of the ESN and the internal connection weight of the reserve pool are kept unchanged, and only the output connection weight is trained; and finally, inputting the time sequence data P to the pooling echo state network model A based on the prediction task V to obtain a prediction result S, and calculating a prediction error to finish prediction.
Normalizing the input data by one layer to map the data between 0 and 1, comprising:
normalizing the input data, wherein the formula is as follows:
Figure BDA0003787367220000091
where DATA _ MAX and DATA _ MIN are the maximum and minimum values of the DATA set, respectively.
In the formula, u represents input layer data, y represents a label value corresponding to u, values of u and y are mapped into a value range from 0 to 1 through normalization processing, the influence of the dimension of the input data and the value range on model prediction is eliminated after the normalization processing, the training speed of the model is improved, and the prediction precision of the model is improved.
The node state is updated and optimized through the pooling layer, state adjustment is carried out on inactive or redundant nodes, more optimal node information is obtained, the node state comprises the steps of sequentially grabbing original reserve pool nodes according to the set number cross of the original reserve pool nodes grabbed each time and the grabbing interval step each time, and if the number of the original reserve pool nodes grabbed sequentially is not enough, the nodes with the state of 0 are supplemented.
And performing state enhancement on each group of captured nodes by using a pooling algorithm, wherein the noise value in a certain range is added on the basis of average pooling, and the noise value is generally 10 times of the learning rate:
xa＝mean(xc)*r
wherein xa is the node after pooling, xc is a group of captured node information, mean () is an obtained average function, r is a parameter for optimizing the node state, and the numerical value is ten times of the learning rate.
Compress and the feature expression to the reserve pool node through the compressed sensing layer, through sparse transform and random subsampling, extract the information that can describe the reserve pool node state originally, improve ESN model prediction performance, include:
1) And (3) signal sparse representation, wherein node information passing through the pooling layer is sparsely represented through discrete Fourier transform, and the discrete Fourier transform formula is as follows:
Figure BDA0003787367220000101
wherein f is n Is a finite sequence of length M, and N is the number of data points.
2) And designing an observation matrix, and observing the compressed signals by using a random Gaussian measurement matrix.
Figure BDA0003787367220000102
Wherein phi is a Gaussian random measurement matrix, RN is the number of nodes of the compressed reserve tank, N is the number of nodes of the original reserve tank before compression, cross is the number of nodes captured each time by the pooling operation, and randn (x, y) function generates an x multiplied by y matrix consisting of random numbers.
Further comprising training the pooled echo state network model, comprising:
acquiring a sample set, dividing the sample data set into a training set and a testing set, and initializing all parameter information in the pooled echo state network model: initializing the node number N of the reserve pool and the node number RN of the reserve pool after passing through a compressed sensing layer, initializing the self-connection weight W of the reserve pool according to the parameters of N, spectrum radius and sparsity, and inputting the weight W in And (4) initializing at random, and initializing cross and step of pooling parameters.
And inputting the data in the training set into a reserve pool through an input layer, and recording the state information of the nodes passing through the compressed sensing layer and the corresponding labels.
Calculating an output weight matrix W by a ridge regression method according to the recorded state information of the nodes passing through the compressed sensing layer and the corresponding labels out 。
Finally, the trained pooled echo state network model is obtained and used in the time sequence prediction process of the actual scene, and the prediction effect of the prediction model in various time sequences is shown in table 1:
table 1. Model effect predicted in time series based on compressed sensing of pooled echo state networks.
Figure BDA0003787367220000111
The data of the chaotic sequence and the chaotic system are measured into 10000000 pieces, and the closing price of 200 stocks is intercepted from stock data, wherein 828799 pieces of data are total.
In conclusion, by acquiring the prediction task and the time series data; constructing a pooling echo state network model based on compressed sensing; normalizing the input data by one layer to eliminate the adverse effect of dimension and data value range on model prediction; performing state adjustment on inactive or redundant nodes in the original reserve pool through a pooling layer, and obtaining a better node state through optimizing and updating the nodes of the original reserve pool; the nodes of the original reserve pool are compressed and characterized by the compressed sensing layer, so that the number of the nodes of the original reserve pool is reduced, and the training speed of the model is improved. And inputting the time sequence data into the network model based on the prediction task to obtain a prediction result.
Example two
The embodiment discloses a sequence prediction system of a pooling echo state network based on compressed sensing;
the sequence prediction system of the pooling echo state network based on compressed sensing comprises a data acquisition module, a model construction module and a result prediction module;
a data acquisition module configured to: acquiring sequence data required by a prediction task;
a model building module configured to: constructing a pooling echo state network model based on compressed sensing, and training the network model;
a result prediction module configured to: inputting the obtained sequence data into a trained pooling echo state network model to obtain a prediction result;
the method comprises the steps that a pooling layer and a compressed sensing layer are added in a reserve pool of a pooled echo state network model, the pooling layer is used for readjusting the weight of the node state of the reserve pool, and the compressed sensing layer conducts sparse transformation and random sub-sampling on nodes.
EXAMPLE III
An object of the present embodiment is to provide a computer-readable storage medium.
A computer-readable storage medium, on which a computer program is stored, which when executed by a processor implements the steps in the compressed sensing-based sequence prediction method for a pooled echo state network according to embodiment 1 of the present disclosure.
Example four
An object of the present embodiment is to provide an electronic device.
An electronic device comprising a memory, a processor and a program stored on the memory and executable on the processor, wherein the processor when executing the program implements the steps of the method for sequence prediction based on a compressed sensing pooled echo state network according to embodiment 1 of the present disclosure.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (10)

1. The sequence prediction method of the pooling echo state network based on compressed sensing is characterized by comprising the following steps:
acquiring sequence data required by a prediction task;
constructing a pooling echo state network model based on compressed sensing, and training the network model;
inputting the obtained sequence data into a trained pooling echo state network model to obtain a prediction result;
the method comprises the steps that a pooling layer and a compressed sensing layer are added in a reserve pool of a pooled echo state network model, the pooling layer is used for readjusting the weight of the node state of the reserve pool, and the compressed sensing layer conducts sparse transformation and random sub-sampling on nodes.
2. The sequence prediction method for a pooled echo state network based on compressed sensing as claimed in claim 1, wherein the pooled echo state network model is based on a classical echo state network model and comprises three parts: an input layer, a reserve pool and an output layer;
the reserve pool is improved and divided into three layers: the method comprises a layer, a pooling layer and a compressed sensing layer.
3. The compressed sensing-based sequence prediction method for a pooled echo state network according to claim 2, wherein the normalization layer normalizes the input data to map values of the input data between 0 and 1.
4. The sequence prediction method of claim 2, wherein the pooling layer performs an optimized update of nodes in the pool, and performs a state adjustment of inactive or redundant nodes in the pool to obtain a better node state.
5. The compressed sensing-based sequence prediction method for the pooled echo state network according to claim 1, wherein a connection parameter value between the output layer and the reserve pool layer is determined by a least squares solution.
6. The method as claimed in claim 1, wherein the training process of the echo state network model is mainly divided into two stages: a sampling stage and a weight calculation stage.
7. The compressed sensing-based sequence prediction method for a pooled echo state network according to claim 1, wherein the sampling phase is used for constructing a system state matrix and a sample data vector;
and the weight calculation stage is used for calculating an output connection weight matrix of the echo state network model.
8. The sequence prediction system of the pooling echo state network based on compressed sensing is characterized in that: the system comprises a data acquisition module, a model construction module and a result prediction module;
a data acquisition module configured to: acquiring sequence data required by a prediction task;
a model building module configured to: constructing a pooling echo state network model based on compressed sensing, and training the network model;
a result prediction module configured to: inputting the acquired sequence data into a trained pooling echo state network model to obtain a prediction result;
the method comprises the steps that a pooling layer and a compressed sensing layer are added in a reserve pool of a pooled echo state network model, the pooling layer is used for readjusting the weight of the node state of the reserve pool, and the compressed sensing layer conducts sparse transformation and random sub-sampling on nodes.
9. Computer readable storage medium, having a program stored thereon, which program, when being executed by a processor, is adapted to carry out the steps of the method for sequence prediction based on a compressed perceptual pooling echo state network of any of the claims 1-7.
10. Electronic device comprising a memory, a processor and a program stored on the memory and executable on the processor, characterized in that the processor implements the steps of the compressed sensing-based sequence prediction method of a pooled echo state network according to any of claims 1-7 when executing the program.
CN202210945778.4A 2022-08-08 2022-08-08 Sequence prediction method and system of pooled echo state network based on compressed sensing Pending CN115169740A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116485003A (en) * 2023-03-03 2023-07-25 大连海事大学 Multi-step channel water level prediction method and device based on echo algorithm and storage medium

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116485003A (en) * 2023-03-03 2023-07-25 大连海事大学 Multi-step channel water level prediction method and device based on echo algorithm and storage medium

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