CN108985356A - NMF-based image decomposition method - Google Patents

NMF-based image decomposition method Download PDF

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CN108985356A
CN108985356A CN201810687759.XA CN201810687759A CN108985356A CN 108985356 A CN108985356 A CN 108985356A CN 201810687759 A CN201810687759 A CN 201810687759A CN 108985356 A CN108985356 A CN 108985356A
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nmf
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coefficient
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江天
彭元喜
彭学锋
宋明辉
舒雷志
张松松
周士杰
李俊
赵健宏
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National University of Defense Technology
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Abstract

The invention discloses an NMF-based image decomposition method, which comprises the following steps: s1: acquiring an original data matrix to be decomposed, and performing SVD on the acquired original data matrix to obtain a singular value matrix and a singular vector matrix; s2: respectively initializing a base matrix and a coefficient matrix in NMF decomposition by using a singular value matrix and a singular vector matrix; s3: and performing iterative updating on the initialized base matrix and the initialized coefficient matrix to perform NMF decomposition on the original data matrix to obtain a product of the base image and the coefficient matrix. The invention has the advantages of simple realization principle, high decomposition efficiency, good decomposition effect and the like.

Description

Picture breakdown method based on NMF
Technical field
The present invention relates to digital image processing techniques field more particularly to a kind of picture breakdown methods based on NMF.
Background technique
Matrix decomposition is that higher dimensional matrix is resolved into the process of several low-dimensional matrix products, low by resolving into several The product for tieing up matrix, can effectively compress original image data, reduce the data volume for needing to store, and can be right The information etc. hidden in original image data extracts, to be further processed according to the characteristic information extracted, such as Feature extraction, text cluster etc..
Currently used matrix decomposition algorithm includes LU decomposition, SVD (singular value decomposition, Singular Value Decomposition) decompose and principal component analysis (PCA) etc., but above-mentioned decomposition method by original matrix A by approximate factorization at When the form of the UV of low-dimensional, it can be positive and can be negative in the element decomposed in obtained matrix U and matrix V, and in image data, It is not possible that there are the pixels of negative value, thus it is not suitable in image procossing.Non-negative Matrix Factorization (NMF, Non- Negative Matrix Factorizatioin) algorithm, it is that can be constrained each element during matrix decomposition non-negative, And there is good dimensionality reduction, feature extraction functions, the demand of image procossing can be better met.As shown in Figure 1, NMF is calculated Input matrix V is resolved into the matrix W of two low-dimensionals, the product of H by method, and the either element that W, H are constrained in decomposable process is all Non-negative, dimensionality reduction function can be achieved in matrix after NMF is decomposed, and reduces the data volume for needing to store, and carrying out reduction process In, there is preferable ability in feature extraction.
Ability for the feature extraction of raising matrix decomposition, the descriptive power to initial data and reduction computation complexity The problems such as, the most key solution procedure for being that matrix decomposition.NMF solution procedure is by defining suitable loss letter The solution procedure of NMF, is become the optimization problem of loss function by number, and due to loss function be it is non-convex, easily acquire Locally optimal solution rather than globally optimal solution.At present applied to image procossing NMF algorithm in solution procedure, be usually all by After the data structure of certain way adjustment original matrix, the form of random initializtion is taken to initialize split-matrix, It is iterated update again and realizes decomposition, realizes that image procossing has the following problems based on such NMF isolation:
(1) result finally acquired can be made easily to fall into locally optimal solution region using random initializtion mode, led It causes discomposing effect poor, also will increase the number of iterations in next step solution procedure, so that calculated performance is lower；
(2) need to destroy the data structure of original matrix, so that a variety of data characteristicses including directional information are broken It is bad, the loss of information is caused, the final effect of image procossing is unfavorable for.
Chinese patent application CN104867124A disclose it is a kind of based on the sparse Non-negative Matrix Factorization of antithesis it is multispectral with it is complete Color image interfusion method, the image data NMF decomposition method being directed to are exactly before decomposing to image data, first The matrix has been subjected to column vector, then the random initializtion strategy between 0 to 1, column vectorization processing are used to split-matrix Meeting causes information to be lost, while to split-matrix so that the directional information being hidden in adjacent region data in original image is destroyed Using random initializtion strategy, causes final required the number of iterations to reach 1000 times, seriously reduce the performance decomposed and realized.
Summary of the invention
The technical problem to be solved in the present invention is that, for technical problem of the existing technology, the present invention provides one Kind realization principle is simple, decomposition efficiency is high and the good picture breakdown method based on NMF of discomposing effect.
In order to solve the above technical problems, technical solution proposed by the present invention are as follows:
A kind of picture breakdown method based on NMF, step include:
S1: obtaining the raw data matrix of target image, and carry out SVD decomposition to the raw data matrix of acquisition, Obtain the singular vector composition singular vector matrix that multiple singular values constitute singular value matrix and corresponding each singular value；
S2: using the singular value matrix, singular vector matrix respectively to NMF decompose in basic matrix, coefficient matrix into Row initialization；
S3: update is iterated to the basic matrix, the coefficient matrix after initial, the raw data matrix is carried out NMF is decomposed, and obtains the product of basic image Yu the coefficient matrix.
As a further improvement of the present invention: the step S2 specifically obtains specified number from the singular value matrix Singular value carries out the basic matrix, coefficient matrix using each singular value and the corresponding singular vector of acquisition Initialization.
As a further improvement of the present invention: before the step S2 is specifically obtained from the singular value matrix described in r Singular value and the corresponding singular vector initialize the basic matrix, coefficient matrix, and wherein r meets: the surprise The ratio of the sum of preceding r singular value and the sum of all singular values is less than the first preset threshold and preceding r+1 in different value matrix The ratio of the sum of singular value and the sum of all singular values is greater than the second preset threshold.
As a further improvement of the present invention: specifically basic matrix, coefficient matrix being initialized in the step S2 Expression formula are as follows:
Wherein, W0For the basic matrix after initialization, H0For the coefficient matrix after initialization, U, V are respectively the singular vector The matrix of composition, ∑ are singular value matrix, | U | expression takes absolute value to matrix U, VTFor the transposition of matrix V, | VT| it indicates to square Battle array VTIt takes absolute value.
As a further improvement of the present invention: being specifically based on CUDA in the step S1 and execute the SVD decomposition parallel.
As a further improvement of the present invention: basic matrix, coefficient matrix specifically use following formula to change in the step S3 In generation, updates；
Wherein, W is the basic matrix, and H is the coefficient matrix, and A is the raw data matrix, HTFor turning for matrix H It sets, WTFor the transposition of matrix W.
As a further improvement of the present invention: the basic matrix, the system being executed using CUDA parallel in the step S3 The iteration of each column vector updates in matrix number.
As a further improvement of the present invention: basic matrix, coefficient matrix are specifically based under CUDA use in the step S3 Formula is iterated update；
Wherein, W is the basic matrix, and H is the coefficient matrix, and A is the raw data matrix, and m is that the column of matrix H are tieed up Degree, n are the row dimension of matrix W.
Compared with the prior art, the advantages of the present invention are as follows:
1) the present invention is based on the picture breakdown methods of NMF, by carrying out SVD points first to input picture raw data matrix Solution, calculates all singular values and its corresponding all singular vectors, is supplied to the matrix that subsequent NMF is decomposed and is initialized, can To obtain the effect of more preferably globally optimal solution, and for input matrix without carrying out any data structures such as column vector Change processing, will not destroy the data structure of initial data, can retain more detailed information, directional information etc., to mention Hi-vision discomposing effect；
2) the present invention is based on the picture breakdown methods of NMF, and the unusual of specified number is further obtained from singular value matrix Value, initializes basic matrix, coefficient matrix using each singular value and corresponding singular vector of acquisition, that is, initialized The singular value of specified number is only chosen in journey and its corresponding singular vector is handled, and does not need whole singular values, greatly The data handled needed for reducing greatly, while can guarantee the precision finally decomposed；
3) the present invention is based on the picture breakdown methods of NMF, and SVD decomposable process is further used parallel computation, Neng Gouti High SVD decomposes execution efficiency, and eliminating SVD decomposition computation process bring calculation amount influences, to improve general image decomposition Efficiency；
4) the present invention is based on the picture breakdown methods of NMF, further execute the iteration of NMF split-matrix parallel using CUDA Update, by the iteration of each column vector of split-matrix update it is parallel execute, by a large amount of matrix multiple and data not phase The iterative operation of pass is executed using parallel, can further decrease delay, greatly improves the efficiency that general image decomposes.
Detailed description of the invention
Fig. 1 is the decomposition principle schematic diagram of NMF algorithm.
Fig. 2 is the implementation process schematic diagram of picture breakdown method of the present embodiment based on NMF.
Fig. 3 is the detailed implementation process schematic diagram of the picture breakdown method in the specific embodiment of the invention based on NMF.
Fig. 4 is the realization principle schematic diagram that NMF split-matrix iteration updates in the specific embodiment of the invention.
Fig. 5 is the schematic illustration for the CUDA platform programming hierarchical model that the present embodiment uses.
Fig. 6 is the reconstruction result contrast schematic diagram of the decomposed and reconstituted mode of difference NMF in the specific embodiment of the invention.
Specific embodiment
Below in conjunction with Figure of description and specific preferred embodiment, the invention will be further described, but not therefore and It limits the scope of the invention.
As shown in Figure 2,3, picture breakdown method and step of the present embodiment based on NMF includes:
S1: the data matrix of image to be decomposed is obtained, and SVD decomposition is carried out to the data matrix of acquisition, obtains singular value Matrix and singular vector matrix.
There is following form since NMF is decomposed:
An×m=Wn×rHr×m (1)
Wherein A is raw data matrix, i.e., matrix to be decomposed, W is basic matrix, and H is coefficient matrix.It is decomposed by NMF, n The raw data matrix A of × m is broken down into the product of the coefficient matrix H of the basic matrix W and r × m of n × r.
SVD, which is decomposed, has following form:
Wherein, A is raw data matrix, i.e., matrix to be decomposed, and U, V are respectively the matrix that singular vector is constituted, VTFor square The transposition of battle array V, ∑ is singular value matrix.
From SVD decomposition computation formula (2) as can be seen that the form of its calculated result is similar with NMF calculated result, if being The result of dry matrix multiple.Similar characteristic and picture number of the present embodiment based on SVD Yu two kinds of matrix decomposition algorithms of NMF According to nonnegativity characteristic, establish the relational expression as shown in formula (3) between two kinds of matrix decompositions of SVD and NMF:
Wherein W0For the initial value of basic matrix, H0For the initial value of coefficient matrix, ∑ VTFor matrix ∑ and matrix VTMultiply Product.
It can be obtained by formula (3), singular vector matrix U, V and the singular value matrix ∑ decomposed by SVD is available The initial basic matrix and initial coefficients matrix of NMF decomposition are obtained, that is, realizes the initialization of basic matrix W and coefficient matrix H.
The present embodiment by input picture raw data matrix introduce SVD decompose mechanism, calculate all singular values and its Corresponding all singular vectors are initialized with being supplied to the matrix that subsequent NMF is decomposed, and can not only be obtained more preferably global The effect of optimal solution, and the change for being not necessarily to carry out any data structures such as column vector for input matrix is handled, and will not be broken The data structure of bad initial data can retain more detailed information, directional information etc., improve picture breakdown effect.
Due to introducing SVD decomposition algorithm before NMF is decomposed, SVD, which is decomposed, will increase calculation amount, and the solution that SVD is decomposed Process is the process of a continuous iteration updated value, comprising largely can be with the part of parallel computation.The present embodiment passes through SVD points Solution preocess uses parallel computation, by SVD can parallel computation part by parallel executing, can be improved SVD decomposition and execute effect Rate, eliminating SVD decomposition computation process bring calculation amount influences, to improve the efficiency of general image decomposition.
In a particular embodiment, specifically used CUDA platform executes SVD decomposition parallel, to be based on CUDA platform according to parallel Mode complete SVD decomposition.The parallel execution that SVD is decomposed is realized based on CUDA, required development cost is low, and execution efficiency is high, CuSolverDN function library can be directly based upon and realize the parallel execution that SVD is decomposed, further simplify the realization of SVD decomposition.
S2: basic matrix, the coefficient matrix in NMF decomposition are carried out just respectively using singular value matrix, singular vector matrix Beginningization.
The effect that NMF is decomposed, depend on following two aspect: the 1. initialization matter of split-matrix, initialization matter will be straight Connect the iterative process after influencing last discomposing effect and initialization；2. determine the order for decomposing obtained split-matrix, it is different The discomposing effect that order obtains may be different.
For initialization matter, due to image data be all non-negative and NMF decompose in need restraint each of W, H Element be all it is non-negative, then after all singular values and its corresponding all singular vectors that obtain original image matrix by step S1, also Need to be further processed in NMF matrix decomposition basic matrix W and coefficient matrix H initialize, NMF decompose group moment Battle array W and coefficient matrix H final initialization formula are as follows:
The split-matrix of NMF is initialized by the way of taking absolute value by the result that SVD is decomposed, after initialization It is subsequent also to need to execute iteration update, therefore this takes absolute value and will not influence final discomposing effect.
For split-matrix order the problem of, that is, determine basic matrix W, coefficient matrix H dimension r, by SVD decompose property It is found that singular value is bigger, it includes original matrix in energy information it is also more, while singular value reduce it is especially fast, Such as 90% of sum greater than the sum of whole singular values of preceding 10% or even 1% singular value in many cases, thus merely with portion Divide singular value can approximate description matrix.The present embodiment introduces principal component analysis (PCA) thought, specifically from singular value matrix Obtain the singular value of specified number, such as several maximum singular values, using acquisition each singular value and it is corresponding it is unusual to Amount initializes basic matrix, coefficient matrix, i.e., the singular value of specified number and its corresponding is only chosen in initialization procedure Singular vector is handled, and whole singular values is not needed, the data handled needed for greatly reducing, while can be guaranteed most The precision decomposed eventually.
In concrete application embodiment, r singular value carries out just basic matrix, coefficient matrix before taking from singular value matrix Beginningization, and the sum of meet r singular value, is (specific desirable less than the first preset threshold with the ratio of the sum of all singular values 90%) and the sum of preceding r+1 singular value, with the ratio of the sum of singular value it is greater than the second preset threshold (specifically can use 90%), Expression are as follows:
sumr/sump< 90%&&sumr+1/sump>=90% (5)
Wherein, p is the total number for the singular value that SVD decomposition computation obtains, and sumr is the sum of preceding r singular value, and sump is The sum of all singular values.First preset threshold, the specific value of the second preset threshold can also be set as it according to actual needs He is worth.
In concrete application embodiment, after SVD is decomposed, the singular value that SVD is decomposed is obtained by program, according to above formula (5) it can automatically determine to obtain the value of optimal decomposition rank number r, discomposing effect can be further increased.It is few due to only needing Several singular values can meet the regular demand of formula (5), and r value is smaller in actual implementation, and good dimensionality reduction function may be implemented Energy.
S3: being iterated update to basic matrix, coefficient matrix, by image to be decomposed progress NMF be decomposed into basic image with The product of coefficient matrix.
It is iterated solution after initializing to basic matrix W, coefficient matrix H, to obtain optimal discomposing effect.Having In body Application Example, basic matrix W, coefficient matrix H specifically use following formula to be iterated update:
Wherein, W is basic matrix, and H is coefficient matrix, and A is raw data matrix, HTFor the transposition of matrix H, WTFor matrix W Transposition, WikFor (i, k) a element of matrix W, HkjFor (k, j) a element of matrix H.
Update constantly is iterated to basic matrix W, coefficient matrix H according to iterative formula (6), until basic matrix W, coefficient square Error between the product and raw data matrix A of battle array H is less than preset threshold, i.e., the iteration for realizing matrix simultaneously updates, with And constantly reduce error between the product and raw data matrix A of updated basic matrix W, coefficient matrix H, it is final to meet most Big error constraints.
The present embodiment specifically uses alternating iteration update mode, is iterated update to basic matrix W, coefficient matrix H, such as schemes Shown in 4, by taking the iterative process of coefficient matrix H as an example, coefficient matrix H is made of m column vector, and iterative process is single with column vector Member is handled, and each column vector is multiplied in a thread with basic matrix W, then carries out phase with raw data matrix A It removes, division result is multiplied with the transposition of basic matrix W, finally corresponding with coefficient matrix H that preceding an iteration obtains Column vector is multiplied to get to the result after current iteration.The iterative solution process of basic matrix W changes with above-mentioned coefficient matrix H It is consistent for resolution principle.Compared to traditional multiplication iterative method and Projected descent method etc., the above-mentioned alternating of the present embodiment changes For update mode, computation complexity is low, it is easy to accomplish and it is parallel to accelerate, and fast convergence rate, required the number of iterations are few.
From the above, it can be seen that in the iterative process of basic matrix W, coefficient matrix H, there are a large amount of matrix multiple and numbers According to incoherent iterative operation etc., the present embodiment is updated using the iteration that CUDA executes above-mentioned NMF split-matrix parallel, will be a large amount of Matrix multiple and the incoherent iterative operation of data executed using parallel, delay can be further decreased, after decomposition Meet maximum error constraints.
It is illustrated in figure 5 the programming hierarchical model of CUDA, the programming hierarchical model of CUDA is by Grid, Block, Thread structure At storage includes global memory, constant memory and shared drive etc., each thread has oneself privately owned memory, together Thread with the shared drive shared between Thread in Shi Tongyi Block, and for the shared drive, in other Block It can not all access, the global memory that inside the same Grid there are all threads can access.The above-mentioned hardware configuration of CUDA Feature allows to easily carry out parallel Programming, the power function run in CUDA according to the feature of procedure operation number As Kernel function, Kernel function need to complete to initialize by host (host), and the present embodiment is by between CPU and GPU Cooperation realizes that above-mentioned SVD is decomposed and the iteration of NMF split-matrix updates jointly.
The iterative formula as shown in formula (6) is made of matrix multiple and algebraic operation, then the CUDA according to shown in Fig. 4 Platform programs hierarchical model, and matrix multiple can fast implement in a parallel fashion；Simultaneously analyze iterative formula (6) it is found that Can also be executed parallel between iteration twice, such as in the renewal process of matrix W, the t column for the W that rear an iteration generates only with it is low The t for the matrix W that t-1 iteration obtains shows pass, and uncorrelated to other column vectors, and the present embodiment is based on the characteristic, passes through Multiple thread parallels are updated each column vector, i.e., execute each column in basic matrix W, coefficient matrix H parallel by CUDA The iteration of vector updates, and further increases the execution efficiency of picture breakdown.Traditional needs to carry out column vector to original matrix Mode can not execute parallel accelerate due to needing to carry out column vector based on column vector.When using above-mentioned parallel mode, parallel Degree limited by column vector number in W, the determination of r value will directly affect whole decomposability, in conjunction with above-mentioned split-matrix The method of determination and decomposition parallel mode of order r value, then while picture breakdown efficiency can be improved, guarantee discomposing effect.
To meet the above-mentioned requirement to Parallel Implementation, the present embodiment, which has, to be changed based on CUDA using following iterative formula In generation, updates:
Wherein, m is the column dimension of matrix H, and n is the row dimension of matrix W,For matrix AijHpjJth column element Sum.
Above-mentioned iterative formula (7) can be more suitable for the hardware characteristics of CUDA, thus can obtain higher parallel execution Performance.
As shown in fig. 6, the selection rule based on r value above is decomposed compared to being manually set with better discomposing effect The error of matrix is smaller after reconstruct.
For the validity of the above-mentioned picture breakdown method of the verifying present invention, traditional three kinds of modes and the present invention are used respectively Above-mentioned picture breakdown method decomposes same piece image, and reconstruct after compare reconstruction result, comparing result as shown in fig. 6, Wherein figure (a) corresponds to complete matrix decomposition reconstruct using random fashion initialization and multiplication iteration, and the value of r is 30, note For method one；(b) is schemed for input picture is carried out column vector first, is then initialized using SVD and is finally used multiplication iteration more The reconstruction result newly obtained handles due to using column vectorization, so r value can only take 1, is denoted as method two；Scheming (c) is to use Reconstruction result after the above-mentioned picture breakdown method of the present invention is decomposed and reconstituted, figure (a), (b), (c) are obtained after iteration 100 times As a result；Figure (e) is input image to be decomposed.It can be seen from the figure that after being reconstructed using picture breakdown method of the present invention Reconstructed image effect be substantially better than traditional approach shown in figure (a), (b).
As shown in fig. 6, figure (d) is to complete matrix decomposition reconstruct using method identical with the above method one, difference is The order r's of split-matrix is that empirically value is 10, and comparison diagram (a), (d) two width figure can be seen that the order r's of split-matrix takes Value has large effect to reconstruction result, meanwhile, the order r of split-matrix is determined using aforesaid way of the present invention, compared to straight It connects and order r is manually set, better quality reconstruction can be obtained.
The error amount of above-mentioned various modes, error calculation formula are calculated separately using formula (8) specifically:
Wherein | | | |FFor the Frobenius norm of matrix.
The error size that each mode obtains is as shown in table 1, wherein method one be it is above-mentioned use random fashion initialize with And multiplication iteration completes the mode of matrix decomposition reconstruct, method two is above-mentioned first by input picture progress column vector, then By SVD initialize finally updated with multiplication iteration in the way of, method three be the present invention is based on the picture breakdown method of NMF, Method four is as using the present invention is based on the picture breakdown methods of NMF, while the order r of split-matrix takes 10.
Table 1: error size contrast table.
Method one Method two Method three Method four
Error (err) 0.1617 0.3416 0.1125 0.1973
It can be obtained by table 1, using the above-mentioned picture breakdown method of the present invention, error is minimum, and discomposing effect is substantially better than traditional NMF isolation.
Above-mentioned only presently preferred embodiments of the present invention, is not intended to limit the present invention in any form.Although of the invention It has been disclosed in a preferred embodiment above, however, it is not intended to limit the invention.Therefore, all without departing from technical solution of the present invention Content, technical spirit any simple modifications, equivalents, and modifications made to the above embodiment, should all fall according to the present invention In the range of technical solution of the present invention protection.

Claims (8)

1. a kind of picture breakdown method based on NMF, which is characterized in that step includes:
S1: the raw data matrix of target image is obtained, and SVD decomposition is carried out to the raw data matrix of acquisition, is obtained Multiple singular values constitute singular value matrix and the singular vector of corresponding each singular value constitutes singular vector matrix；
S2: basic matrix, the coefficient matrix in NMF decomposition are carried out just respectively using the singular value matrix, singular vector matrix Beginningization；
S3: updates is iterated to the basic matrix, the coefficient matrix after initial, by raw data matrix progress NMF It decomposes, obtains the product of basic image Yu the coefficient matrix.
2. the picture breakdown method according to claim 1 based on NMF, which is characterized in that the step S2 is specifically from institute State the singular value that specified number is obtained in singular value matrix, using acquisition each singular value and it is corresponding it is described it is unusual to Amount initializes the basic matrix, coefficient matrix.
3. the picture breakdown method according to claim 2 based on NMF, it is characterised in that: the step S2 is specifically from institute It states and obtains the preceding r singular values and the corresponding singular vector in singular value matrix to the basic matrix, coefficient matrix It is initialized, wherein r meets: the sum of preceding r singular value in the singular value matrix, small with the ratio of the sum of all singular values It is greater than the second preset threshold in the ratio of the sum of the first preset threshold and preceding r+1 singular value and the sum of all singular values.
4. the picture breakdown method according to claim 1 or 2 or 3 based on NMF, it is characterised in that: in the step S2 The expression formula that specifically basic matrix, coefficient matrix are initialized are as follows:
Wherein, W0For the basic matrix after initialization, H0For the coefficient matrix after initialization, U, V are respectively that the singular vector is constituted Matrix, ∑ is singular value matrix, | U | expression take absolute value to matrix U, VTFor the transposition of matrix V, | VT| it indicates to matrix VT It takes absolute value.
5. the picture breakdown method according to claim 1 or 2 or 3 based on NMF, which is characterized in that in the step S1 It is specifically based on CUDA and executes the SVD decomposition parallel.
6. the picture breakdown method according to claim 1 or 2 or 3 based on NMF, it is characterised in that: in the step S3 Basic matrix, coefficient matrix specifically use following formula to be iterated update；
Wherein, W is the basic matrix, and H is the coefficient matrix, and A is the raw data matrix, HTFor the transposition of matrix H, WT For the transposition of matrix W.
7. the picture breakdown method according to claim 1 or 2 or 3 based on NMF, which is characterized in that in the step S3 Execute that the basic matrix, the iteration of each column vector updates in the coefficient matrix parallel using CUDA.
8. the picture breakdown method according to claim 7 based on NMF, which is characterized in that basic matrix in the step S3, Coefficient matrix is specifically based on CUDA and is iterated update using following formula；
Wherein, W is the basic matrix, and H is the coefficient matrix, and A is the raw data matrix, and m is the column dimension of matrix H, n For the row dimension of matrix W.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112004238A (en) * 2020-08-07 2020-11-27 天津师范大学 Wireless sensor network optimization method based on NMF and 2-SVD-QR

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103955926A (en) * 2014-04-22 2014-07-30 西南交通大学 Method for remote sensing image change detection based on Semi-NMF
CN104732535A (en) * 2015-03-18 2015-06-24 河海大学 Sparse constraint non-negative matrix factorization method
US20160106311A1 (en) * 2014-10-16 2016-04-21 New York University Method And System For Simultaneous Decomposition Of Multiple Hyperspectral Datasets And Signal Recovery Of Unknown Fluorophores In A Biochemical System
CN108846357A (en) * 2018-06-13 2018-11-20 蔡竞 A kind of face identification method based on improvement increment type Non-negative Matrix Factorization

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103955926A (en) * 2014-04-22 2014-07-30 西南交通大学 Method for remote sensing image change detection based on Semi-NMF
US20160106311A1 (en) * 2014-10-16 2016-04-21 New York University Method And System For Simultaneous Decomposition Of Multiple Hyperspectral Datasets And Signal Recovery Of Unknown Fluorophores In A Biochemical System
CN104732535A (en) * 2015-03-18 2015-06-24 河海大学 Sparse constraint non-negative matrix factorization method
CN108846357A (en) * 2018-06-13 2018-11-20 蔡竞 A kind of face identification method based on improvement increment type Non-negative Matrix Factorization

Non-Patent Citations (5)

* Cited by examiner, † Cited by third party
Title
DANIEL D. LEE ET AL: "Algorithms for non-negative matrix factorization", 《ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 13》 *
EDGARDO MEJÍA-ROA ET AL: "NMF-mGPU: non-negative matrix factorization on multi-GPU systems", 《BMC BIOINFORMATICS》 *
HANLI QIAO: "New SVD Based Initialization Strategy for Non-negative Matrix Factorization", 《PATTERN RECOGNITION LETTERS》 *
MINGHUI SONG ET AL: "Accelerated image factorization based on improved NMF algorithm", 《JOURNAL OF REAL TIME IMAGE PROCESSING》 *
陈剑军等: "基于SVD确定NMF初始化矩阵维数", 《电脑知识与技术》 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112004238A (en) * 2020-08-07 2020-11-27 天津师范大学 Wireless sensor network optimization method based on NMF and 2-SVD-QR
CN112004238B (en) * 2020-08-07 2024-01-26 天津师范大学 NMF and 2-SVD-QR based wireless sensor network optimization method

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