CN111639671B - Method for estimating nonnegative parameter vector of sparse multitasking adaptive network - Google Patents
Method for estimating nonnegative parameter vector of sparse multitasking adaptive network Download PDFInfo
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Abstract
The invention discloses a method for estimating non-negative parameter vectors of a sparse multi-task self-adaptive network, wherein the sparse multi-task self-adaptive network comprises K nodes, the network is divided into Q clusters, the estimated parameter vectors of each cluster are the same, the estimated parameter vectors of different clusters are different, and each node comprises a self-adaptive filter; the clusters are used for simulating the parameter distribution condition of the multi-task system, so that the parameter vector association of different task clusters is ensured; adaptive filter introduction L based on cost function 0 The norm method estimates the unknown parameter vector. The adaptive network is divided into a plurality of clusters, the estimated parameter vector of each cluster is the same, and the estimated parameter vectors of different clusters are different, but have certain similarity. The method has a high convergence rate, so that the problem that the convergence rate of the traditional method is low when a sparse system is estimated is solved.
Description
Technical Field
The invention relates to a method for estimating nonnegative parameter vector of a sparse multitasking adaptive network, in particular to a method for combining L by using mean square error 0 Parameter estimation is carried out by a norm method, and belongs to the field of wireless sensor networks.
Background
An adaptive network is a communication network consisting of a plurality of nodes dispersed over a region, each node being provided with an adaptive filter for adaptively estimating unknown parameter vectors. At present, the application of the multi-task self-adaptive network is very wide, and each node in the network can utilize the interaction information of adjacent nodes to perform independent operation, so that the accuracy of the whole network identification is improved. Multi-tasking adaptive networks have been widely used in machine learning, computer networks, and other applications.
According to the different cooperative modes of the nodes, the network can be divided into three self-adaptive network types of incremental type, diffusion type and probability type. Based on various architectures and adaptive filtering frameworks, scholars have proposed a range of distributed network approaches. In 2013, chen et al proposed a multitasking diffusion least mean square method (abbreviated as MD-LMS) [ Multitask Diffusion Adaptation over Networks [ J ]. IEEE Journal of Selected Topics in Signal Processing,2013, pp (99): 1-1 ], which effectively expands the application range of the adaptive network.
In some physical phenomena, such as concentration fields, demographics, etc., parameter vectors in a multitasking adaptive network need to satisfy non-negative constraints. The adaptive filtering method under the non-negative constraint condition is essentially an optimization problem under the solution constraint. In 2011, chen et al have proposed a non-negative least Mean Square method (abbreviated NNLMS) [ Nonnegative Least-Mean-Square Algorithm [ J ]. Signal Processing,2011,59 (11): 5225-5235 ], which enriches the theory of adaptive filters.
However, the existing multi-tasking diffusion LMS method and multi-tasking diffusion RLS method are only suitable for identifying unconstrained parameter vectors.
Therefore, there is a need to find an efficient way to do non-negative parameter vector identification for a multi-tasking adaptive network.
Disclosure of Invention
To solve the above-mentioned drawbacks, the present invention aims to: the method for estimating the non-negative parameter vector of the sparse multitask adaptive network is provided, fills the blank of the existing method for identifying the non-negative parameter vector of the sparse multitask adaptive network, and simultaneously can achieve lower steady state offset.
In order to realize the scheme, the invention adopts the following technology:
a method for sparse multitasking adaptive network non-negative parameter vector estimation, characterized by: the sparse multitasking adaptive network comprises K nodes, the sparse multitasking adaptive network is divided into Q clusters, the estimated parameter vector of each cluster is the same, the estimated parameter vectors of different clusters are different,
each of the nodes comprises an adaptive filter;
the clusters are used for simulating the parameter distribution condition of the multi-task system, so that the parameter vector association of different task clusters is ensured;
the adaptive filter introduces L based on a cost function 0 The norm method estimates the unknown parameter vector. The method has a high convergence rate, so as to solve the problem of slow convergence rate of the traditional method when estimating the sparse system。
In one embodiment, the estimating comprises the steps of:
s1: solving a joint matrix C, a similarity matrix rho and a system joint parameter a of a network lk Wherein, the method comprises the steps of, wherein,
in a multitasking adaptive network, defining a neighborhood of node k (including k) as N k The cluster in which node k is located is C (k),
for nodes within the same cluster, a joint matrix is definedEach of which combines parameter c lk Satisfy c lk ≥0,
For nodes in different clusters, a similarity matrix is definedEach of which has a similarity parameter ρ kl Satisfy ρ kl ≥0,/>
S2: generating joint estimation psi of node k to unknown parameters at time n+1 k (n+1), k.epsilon. {1,2, …, K }, using w k (n) represents an estimate of the unknown parameter by node k at time n,expressed in w k The element of (n) is a diagonal matrix of diagonal elements, the input signal of node k at time n is x k (n)，
Error ofJoint estimation ψ of node k for unknown parameters at time n+1 k (n+1) is represented by the formula
Generating, wherein mu, eta and lambda are step parameters, and beta is the action range and the intensity of zero absorption factors;
s3: generating a latest estimate w of unknown parameters by node k at time n+1 k (n+1),k∈{1,2,…,K}，
Using psi l (n + 1) represents a joint estimation of the unknown parameters by node l at time n +1,
by usingGenerating the latest estimate of the unknown parameter by node k at time n+1.
In one embodiment, in step S1, a is taken lk ＝c kl 。
Advantageous effects
Compared with the scheme in the prior art, the invention has the advantages that: the method of the invention can not only keep the sparse multitask self-adaptive network to have a fast convergence speed, but also ensure that the sparse multitask self-adaptive network obtains low steady state offset. The method of the invention can be widely applied to computer networks, distributed machine learning, disaster early warning, target positioning and cognitive radio.
Drawings
The invention is further described below with reference to the accompanying drawings and examples:
fig. 1 is a schematic diagram of a multi-task adaptive network according to an embodiment of the present application;
fig. 2 is a schematic diagram of a multi-task adaptive network connection of 4 task clusters and 20 nodes according to an embodiment of the present application;
fig. 3a and 3b are schematic diagrams of weight parameter vector values of the 4 task clusters according to the embodiment of the present application;
FIG. 4 is a graph of network mean square deviation using Gaussian noise as input in an embodiment of the application;
fig. 5 is a graph of network mean square deviation using uniform noise as input in an embodiment of the present application.
Detailed Description
Examples
For a better description of the objects and advantages of the present invention, the present invention will be described in further detail with reference to the accompanying drawings and examples. The above-described aspects are further described in connection with specific embodiments in the following section. It should be understood that these examples are illustrative of the present invention and are not intended to limit the scope of the present invention. The implementation conditions employed in the examples may be adjusted according to the specific application, and the implementation conditions not noted are generally those in routine experiments.
The invention discloses a method for estimating non-negative parameter vectors of a sparse multi-task self-adaptive network, which comprises K nodes, wherein the network is divided into Q clusters, the estimated parameter vectors of each cluster are the same, the estimated parameter vectors of different clusters are different, and each node comprises a self-adaptive filter; the clusters are used for simulating the parameter distribution condition of the multi-task system, so that the parameter vector association of different task clusters is ensured; adaptive filter introduction L based on cost function 0 The norm method estimates the unknown parameter vector. The method has a high convergence rate, so that the problem that the convergence rate of the traditional method is low when a sparse system is estimated is solved. In the implementation method, the parameter vector association description of different task clusters is that the parameter vectors of different task clusters have differences and remain the similarity to a certain extent.
In this embodiment, MD-L is used 0 Adaptive network of NNLMS method (abbreviated as MD-L 0 -NNLMS) to identify an unknown parameter vector and compare its performance with that of an adaptive network employing the MD-NNLMS method (abbreviated as MD-NNLMS) which will make use of MD-L as proposed in the present application 0 The NNLMS method uses the mean square error as a cost function. In the implementation method, the performance of the normalized mean square deviation NMSD relative to different methods (algorithms) is used for evaluation, and the normalized mean square deviation NMSD is defined as
In decibels (dB), whereinFor an optimal solution without negative values, all experimental curves are the results of 20 averages. FIG. 1 is a schematic diagram of a multitasking adaptive network; fig. 2 is a schematic diagram of a multi-task adaptive network used in experiments, the network comprising 4 task clusters and 20 nodes. Because of the similarity between neighboring clusters, a linear model is usedl epsilon {1,2,3,4} acquires the weight parameter vector of cluster C (l), in this embodiment, a 4-task cluster and a 20-node multi-task adaptive network are adopted, and in other embodiments, the method is not limited to the application occasion. Q is 3-10, K is 10-50.
FIG. 3a is w used in the experiment * FIG. 3b shows Δw for different clusters, as a fixed part in the linear model C(l) Therefore, the parameter vector selected by each cluster is not identical, but the same original parameter vector is contained, so that the parameter value condition of the multi-task self-adaptive network is reasonably reflected.
The principle of the embodiment of the application is as follows: using KKT conditions, diffusion methods and L 0 The regularized theory designs a multitasking self-adaptive method under a non-negative constraint condition. The measurement indexes of the adaptive network comprise two kinds of convergence speed and steady state offset, wherein the convergence speed determines the time required by the adaptive network to estimate the unknown parameter vector, and the steady state offset determines the accuracy achieved by the adaptive network to estimate the unknown parameter vector. The proposed method also requires a faster convergence speed or a lower steady state offset than the conventional least mean square method.
In this embodiment, MD-L is used 0 Adaptive network pair unknown parameter vector w of NNLMS method o The estimation comprises the following steps:
s1: solving a joint matrix C, a similarity matrix rho and a system joint parameter a of a network lk
In a multitasking adaptive network, a neighborhood of node k is definedThe domain (including k) is N k The cluster in which node k is located is C (k). For nodes within the same cluster, a joint matrix is definedEach of which combines parameter c lk Satisfy c lk ≥0,For nodes in different clusters, a similarity matrix is definedEach of which has a similarity parameter ρ kl Satisfy ρ kl ≥0,/>To simplify the system joint parameters, take a lk ＝c kl ；
S2: generating joint estimation psi of node k to unknown parameters at time n+1 k (n+1), k.epsilon. {1,2, …, K } uses w k (n) represents an estimate of the unknown parameter by node k at time n,expressed in w k The element of (n) is a diagonal matrix of diagonal elements, the input signal of node k at time n is x k (n), error->Joint estimation ψ of node k for unknown parameters at time n+1 k (n+1) can be represented by the formula
Generating, wherein mu, eta and lambda are step parameters, and beta is zero absorption factor;
s3: generating a latest estimate w of unknown parameters by node k at time n+1 k (n+1),k∈{1,2,…,K}
Using psi l (n+1) represents a joint estimation of the unknown parameters by node l at time n+1, thenGenerating the latest estimate of the unknown parameter by node k at time n+1.
In this embodiment, the parameter vector to be estimated is a sparse vector with a length of m=20 and a negative value, w * The vector quantity value is 0, 0.3, 0, 0.5, 0.2, 0, 0.5, 0, -0.3, 0, 0.1, 0, 0.5, 0, 0.3, -0.2. The filters in all nodes are of the same length. For joint parameter c lk And similarity parameter ρ lk We uniformly apply the average rule, i.e. c lk ＝|N l ∩C(l)| -1 ,k∈N l ∩C(l)，ρ lk ＝|N k \C(k)| -1 ,l∈N k C (k). In the embodiment, gaussian noise is used as input, and the average value is 0.5 and the standard deviation is 0.1; the system noise is selected from Gaussian noise and uniform noise with average value of 0.05 and standard deviation of 0.001 respectively.
In this embodiment, the parameters are selected as follows:
s1: when the system noise is Gaussian noise, the parameters of the MD-NNLMS method are mu=0.035, eta=0.001, and MD-L is adopted 0 The parameters of the NNLMS method are taken as μ=0.035, η=0.001, λ=0.001, β=5; when the input is uniform noise, the parameters of the MD-NNLMS method are set to be mu=0.035, eta=0.001, and MD-L is used 0 The parameters of the NNLMS method were taken as μ=0.035, η=0.001, λ=0.001, β=5. In other embodiments, the μ selection range is 0.02-0.05, η selection range is 0.0001-0.003, λ selection range is 0.0001-0.003, and β selection range is 1-10.
Fig. 4 and 5 are normalized mean square deviation curves when gaussian noise and uniform noise are used as system noise, respectively. From the experimental results, it can be seen that: under the condition of the same steady state disorder, the invention discloses a Machine Direction (MD) -L based Machine Direction (MD) -L 0 The sparse multitasking adaptive network of the NNLMS method has the fastest convergence speed.
One of the above methods for sparse multitasking adaptive network non-negative parameter vector estimation is also referred to as an algorithm for sparse multitasking adaptive network non-negative parameter vector estimation.
The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement the same according to the content of the present invention, and are not intended to limit the scope of the present invention. All modifications made according to the spirit of the main technical proposal of the invention should be covered in the protection scope of the invention.
Claims (5)
1. A method for sparse multitasking adaptive network non-negative parameter vector estimation, characterized by: the sparse multitasking adaptive network comprises K nodes, the sparse multitasking adaptive network is divided into Q clusters, the estimated parameter vector of each cluster is the same, the estimated parameter vectors of different clusters are different,
each of the nodes comprises an adaptive filter;
the clusters are used for simulating the parameter distribution condition of the multi-task system, so that the parameter vector association of different task clusters is ensured;
the adaptive filter is based on introducing L to the cost function 0 A method of norms estimates an unknown parameter vector, the estimation comprising the steps of:
s1: solving a joint matrix C, a similarity matrix rho and a system joint parameter a of a network lk Wherein, the method comprises the steps of, wherein,
in a multitasking adaptive network, defining a neighborhood of node k (including k) as N k The cluster in which node k is located is C (k),
for nodes within the same cluster, a joint matrix is definedEach of which combines parameter c lk Satisfy the following requirements
For nodes in different clusters, a similarity matrix is definedEach of which has a similarity parameter ρ kl Satisfy ρ kl ≥0,
S2: generating joint estimation psi of node k to unknown parameters at time n+1 k (n+1), k.epsilon. {1,2, …, K }, using w k (n) represents an estimate of the unknown parameter by node k at time n,expressed in w k The element of (n) is a diagonal matrix of diagonal elements, the input signal of node k at time n is x k (n)，
Error ofJoint estimation ψ of node k for unknown parameters at time n+1 k (n+1) is represented by the formula
Generating, wherein mu, eta and lambda are step parameters, and beta is zero absorption factor;
s3: generating a latest estimate w of unknown parameters by node k at time n+1 k (n+1),k∈{1,2,…,K}，
Using psi l (n + 1) represents a joint estimation of the unknown parameters by node l at time n +1,
by usingGenerating the latest estimate of the unknown parameter by node k at time n+1.
2. The method according to claim 1The method is characterized in that: in the step S1, a is taken lk ＝c kl 。
3. The method according to claim 1, characterized in that: in the method, the Q value is between 3 and 10, and the K value is between 10 and 50.
4. A method according to claim 3, characterized in that: in the method, the Q value is 4, and the K value is 20.
5. The method according to claim 1, characterized in that: in the step S2:
mu is selected to be between 0.02 and 0.05, eta is selected to be between 0.0001 and 0.003, lambda is selected to be between 0.0001 and 0.003, and beta is selected to be between 1 and 10.
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