WO2020118708A1 - Procédé et système de reconnaissance faciale à factorisation de matrice semi-non-négative basés sur une fonction e auxiliaire, et support de stockage - Google Patents

Procédé et système de reconnaissance faciale à factorisation de matrice semi-non-négative basés sur une fonction e auxiliaire, et support de stockage Download PDF

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WO2020118708A1
WO2020118708A1 PCT/CN2018/121289 CN2018121289W WO2020118708A1 WO 2020118708 A1 WO2020118708 A1 WO 2020118708A1 CN 2018121289 W CN2018121289 W CN 2018121289W WO 2020118708 A1 WO2020118708 A1 WO 2020118708A1
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matrix
module
iterations
training sample
base image
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PCT/CN2018/121289
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Chinese (zh)
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陈文胜
陈海涛
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深圳大学
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition

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  • the present invention relates to the field of data processing technology, and in particular, to a face recognition method, system, and storage medium based on semi-negative matrix factorization of E auxiliary functions.
  • biometrics using personal physiological and behavioral characteristics for personal identification has become one of the most active research areas.
  • biometrics using personal physiological and behavioral characteristics for personal identification has become one of the most active research areas.
  • one of the most easily accepted technologies is facial recognition technology, which is because compared with other biometrics technologies, facial recognition is non-invasive, non-mandatory, and non-contact. And concurrency.
  • Face recognition technology consists of two stages.
  • the first stage is feature extraction, which is to extract face feature information in the face image. This stage directly determines the quality of face recognition technology; the second stage is identity authentication.
  • Personal identification based on the extracted feature information.
  • Principal component analysis (PCA) and singular value decomposition (SVD) are more classic feature extraction methods, but the feature vectors proposed by these two methods usually contain negative elements, so these methods do not have the original sample is non-negative data Rationality and interpretability.
  • Non-negative matrix factorization is a feature extraction method for processing non-negative data. It is widely used, such as hyperspectral data processing and face image recognition.
  • the NMF algorithm has a non-negative limitation on the extracted features during the decomposition of the original sample non-negative data matrix, that is, all components after decomposition are non-negative, so non-negative sparse features can be extracted.
  • the essence of the NMF algorithm is to approximately decompose the non-negative matrix X into the product of the base image matrix W and the coefficient matrix H, that is, X ⁇ WH, and both W and H are non-negative matrices.
  • each column of the matrix X can be represented as a non-negative linear combination of the vectors of the columns of the matrix W, which is also consistent with the construction basis of the NMF algorithm-the perception of the whole is composed of the perception of the parts that make up the whole (pure additive) .
  • NMF requires that the original samples are non-negative data, which limits the application of the algorithm to a certain extent.
  • technologies have proposed many algorithms for deforming NMF, such as semi-negative matrix factorization (Semi-NMF) and convex nonnegative matrix factorization (Convex-NMF). These two algorithms can be used for both non-negative data and other data.
  • Si-NMF semi-negative matrix factorization
  • Convex-NMF convex nonnegative matrix factorization
  • the auxiliary function is a commonly used tool to prove the convergence of the algorithm, and its definition and properties are as follows:
  • Definition 1 For any matrix H and H (t) , if the condition is met
  • G(H,H (t) ) is called an auxiliary function of function f(H).
  • Semi-Negative Matrix Factorization does not limit the sign of the sample matrix, thereby expanding the application range of NMF.
  • matrix factorization X ⁇ WH the optimization problem that Semi-NMF needs to solve is:
  • Convex non-negative matrix factorization Convex-NMF
  • Convex-NMF The main idea of Convex-NMF is to restrict the columns in the base image matrix to be a convex combination of the columns in the original sample matrix.
  • the optimization problem that Convex-NMF needs to solve is:
  • NMF non-negative matrix factorization algorithm
  • the invention provides a face recognition method based on semi-negative matrix factorization of E auxiliary function, which includes a training step, and the training step includes the following steps:
  • the first step convert the training sample image into a training sample matrix X, set the error threshold ⁇ , the maximum number of iterations I max , and enter the training sample matrix X, the error threshold ⁇ and the maximum number of iterations I max
  • the second step initialize the base image matrix W and coefficient matrix H;
  • the fourth step update the base image matrix W and coefficient matrix H according to formula (6);
  • the sixth step determine whether the objective function F(W,H) ⁇ or the number of iterations n reaches the maximum number of iterations I max , if it is, then output the base image matrix W and the coefficient matrix H, otherwise perform the fourth step;
  • W represents the base image matrix
  • H represents the coefficient matrix
  • X represents the training sample matrix
  • the face recognition method further includes performing a recognition step after the training step, the recognition step including:
  • Step 9 Calculate the distance between the feature vector h y of the face image to be recognized and the average feature vector m j of each class. If the distance between h y and m j is the smallest, then classify the face image y to be recognized into class P;
  • Step 10 Output category P.
  • the invention also provides a face recognition system based on the semi-negative matrix factorization of the E auxiliary function, which includes a training module, and the training module includes:
  • Input module used to convert the training sample image into the training sample matrix X, set the error threshold ⁇ , the maximum number of iterations I max , and input the training sample matrix X, the error threshold ⁇ and the maximum number of iterations I max ;
  • Initialization module used to initialize the base image matrix W and coefficient matrix H;
  • Update module used to update the base image matrix W and coefficient matrix H according to formula (6);
  • Judgment module judge whether the objective function F(W,H) ⁇ or the number of iterations n reaches the maximum number of iterations I max , if it is, then output the base image matrix W and coefficient matrix H, otherwise execute the update module;
  • W represents the base image matrix
  • H represents the coefficient matrix
  • X represents the training sample matrix
  • the face recognition system further includes a recognition module executed after the training module, the recognition module includes:
  • Distance calculation module Calculate the distance between the feature vector h y of the face image to be recognized and the average feature vector m j of each class. If the distance between h y and m j is the smallest, then classify the face image y to be recognized into category P;
  • Output module used to output category P.
  • the invention also discloses a computer-readable storage medium which stores a computer program which is configured to implement the steps of the method described in the claims when called by a processor.
  • the face recognition method of the present invention has the advantages of high recognition performance and low computational complexity. Through the experimental comparison with related algorithms in the public face database, the results show that the method developed by this patent has certain Superiority.
  • Figure 3 is the method and related algorithms (Convex-NMF and Semi-NMF) proposed by the present invention
  • FIG. 4 is a comparison diagram of the convergence curves of the method of the present invention and the Semi-NMF algorithm, where FSNMF represents the method of the present invention.
  • the present invention first proposes a new concept of the E auxiliary function of the objective function, and accordingly proposes a new basic theory and framework for constructing auxiliary functions, which greatly expands the selection range of auxiliary functions and also flexibly constructs auxiliary functions for us
  • auxiliary functions greatly expands the selection range of auxiliary functions and also flexibly constructs auxiliary functions for us
  • FSNMF fast semi-negative matrix factorization
  • Non-negative matrix factorization Non-negative Matrix Factorization, NMF
  • NMF non-negative sample matrix Approximate decomposition into the product of two non-negative matrices, namely:
  • the base image matrix and the coefficient matrix, respectively.
  • the loss function is usually defined based on the F-norm, written as:
  • the main objectives of the present invention are:
  • E(H,H (t) ) is called an E auxiliary function of function f(H).
  • Theorem 1 gives a theoretical framework and method for constructing new auxiliary functions based on E auxiliary functions, which greatly expands the selection range of auxiliary functions, and also flexibly constructs auxiliary functions for us to design new high-performance non-negative feature algorithms Provides a powerful tool.
  • FSNMF fast semi-negative matrix factorization algorithm
  • question (3) has evolved into two sub-problems, namely:
  • Is -tr ((W T W) - HH T) is an auxiliary function.
  • G(H,H (t) ) is an auxiliary function of f 2 (H).
  • the updated iteration formula can be directly derived from the auxiliary function.
  • the formula derived from the auxiliary function G(H, H (t) ) here does not satisfy non-negativity, so we need to use the E auxiliary function to reconstruct a new auxiliary function.
  • Theorem 4 Define the functions G(H,H (t) ) and E(H,H (t) ) as follows:
  • function G(H,H (t) ) is an auxiliary function of function f 2 (H)
  • function E(H,H (t) ) is function f 2 (H)
  • the updated iterative formula (6) proposed in this patent not only greatly improves the convergence speed and calculation speed, but also has a better recognition effect.
  • the present invention provides a face recognition method based on semi-negative matrix factorization of E auxiliary function, which includes a training step, and the training step includes the following steps:
  • the first step transform the training sample image into a training sample matrix X, set the error threshold ⁇ , the maximum number of iterations I max , and input the training sample matrix X, the error threshold ⁇ and the maximum number of iterations I max ;
  • the second step initialize the base image matrix W and coefficient matrix H;
  • the fourth step update the base image matrix W and coefficient matrix H according to formula (6);
  • the sixth step determine whether the objective function F(W,H) ⁇ or the number of iterations n reaches the maximum number of iterations I max , if it is, then output the base image matrix W and the coefficient matrix H, otherwise perform the fourth step;
  • W represents the base image matrix
  • H represents the coefficient matrix
  • X represents the training sample matrix
  • T represents the transpose of the matrix
  • the face recognition method further includes performing a recognition step after the training step.
  • the recognition step includes:
  • Step 9 Calculate the distance between the feature vector h y of the face image to be recognized and the average feature vector m j of each class. If the distance between h y and m j is the smallest, then classify the face image y to be recognized into class P;
  • Step 10 Output category P.
  • the output category P indicates that the face image y to be recognized is recognized as the Pth personal face category, so after the category P is output, face recognition is completed.
  • the invention also provides a face recognition system based on semi-negative matrix factorization of E auxiliary function, which includes a training module, and the training module includes:
  • Input module used to convert the training sample image into the training sample matrix X, set the error threshold ⁇ , the maximum number of iterations I max , and input the training sample matrix X, the error threshold ⁇ and the maximum number of iterations I max ;
  • Initialization module used to initialize the base image matrix W and coefficient matrix H;
  • Update module used to update the base image matrix W and coefficient matrix H according to formula (6);
  • Judgment module judge whether the objective function F(W,H) ⁇ or the number of iterations n reaches the maximum number of iterations I max , if it is, then output the base image matrix W and coefficient matrix H, otherwise execute the update module;
  • W represents the base image matrix
  • H represents the coefficient matrix
  • X represents the training sample matrix
  • T represents the transpose of the matrix
  • the face recognition system also includes a recognition module that is executed after the training module.
  • the recognition module includes:
  • Distance calculation module Calculate the distance between the feature vector h y of the face image to be recognized and the average feature vector m j of each class. If the distance between h y and m j is the smallest, then classify the face image y to be recognized into category P;
  • Output module used to output category P.
  • the invention also discloses a computer-readable storage medium which stores a computer program which is configured to implement the steps of the method described in the claims when called by a processor.
  • Table 1 compares the recognition rate (%) of the method proposed in this patent (Our Method) with convex non-negative matrix factorization (Convex-NMF) and semi-non-negative matrix factorization (Semi-NMF) on the ORL face database
  • Table 2 compares the recognition speed (seconds) of the method proposed in this patent (Our Method) with convex non-negative matrix factorization (Convex-NMF) and semi-non-negative matrix factorization (Semi-NMF) on the ORL face database
  • the present invention allows the input matrix to contain negative numbers, expanding the application range of NMF.
  • the face recognition method of the present invention has the advantages of high recognition performance and low computational complexity.

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  • Data Mining & Analysis (AREA)
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  • Computer Vision & Pattern Recognition (AREA)
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Abstract

La présente invention concerne un procédé et un système de reconnaissance faciale à factorisation de matrice semi-non-négative basés sur une fonction E auxiliaire, et un support de stockage. Le procédé de reconnaissance faciale comprend une première étape consistant à : convertir une image d'échantillon d'apprentissage en une matrice d'échantillon d'apprentissage X, régler un seuil d'erreur ε et le nombre maximum Imax d'itérations, et entrer la matrice d'échantillon d'apprentissage X, le seuil d'erreur ε et le nombre maximum Imax d'itérations ; une deuxième étape consistant à : initialiser une matrice d'image de base W et une matrice de coefficient H ; une quatrième étape consistant à : mettre à jour la matrice d'image de base W et la matrice de coefficient H en fonction d'une formule (6) ; et une sixième étape consistant à : déterminer si une fonction cible F(W,H)≤ε ou si le nombre d'itérations atteint le nombre maximum Imax d'itérations, et si tel est le cas, délivrer la matrice d'image de base W et la matrice de coefficient H ; dans le cas contraire, exécuter la quatrième étape. Les effets bénéfiques de la présente invention sont les suivants : le procédé de reconnaissance faciale présente une performance de reconnaissance élevée et une faible complexité de calcul ; et par comparaison expérimentale avec un algorithme associé dans une base de données faciale divulguée, le résultat indique que le procédé présente certains avantages.
PCT/CN2018/121289 2018-12-14 2018-12-14 Procédé et système de reconnaissance faciale à factorisation de matrice semi-non-négative basés sur une fonction e auxiliaire, et support de stockage WO2020118708A1 (fr)

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CN112043269A (zh) * 2020-09-27 2020-12-08 中国科学技术大学 一种手势动作过程中肌肉空间激活模式提取和识别方法
CN113378664A (zh) * 2021-05-26 2021-09-10 辽宁工程技术大学 基于半非负矩阵分解的高光谱图像变化检测方法和系统
CN114118094A (zh) * 2021-11-12 2022-03-01 国网天津市电力公司 一种基于非负矩阵分解的语义社团发现方法
CN116883226A (zh) * 2023-07-21 2023-10-13 中国国土勘测规划院 基于nmf分解的dem零水印方法、装置及介质

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CN112043269A (zh) * 2020-09-27 2020-12-08 中国科学技术大学 一种手势动作过程中肌肉空间激活模式提取和识别方法
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CN114118094A (zh) * 2021-11-12 2022-03-01 国网天津市电力公司 一种基于非负矩阵分解的语义社团发现方法
CN114118094B (zh) * 2021-11-12 2024-05-24 国网天津市电力公司 一种基于非负矩阵分解的语义社团发现方法
CN116883226A (zh) * 2023-07-21 2023-10-13 中国国土勘测规划院 基于nmf分解的dem零水印方法、装置及介质
CN116883226B (zh) * 2023-07-21 2024-01-02 中国国土勘测规划院 Dem零水印嵌入与提取方法、装置及介质

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