Machine Vision and Applications

, Volume 23, Issue 5, pp 985–997

Feature extraction based on fuzzy class mean embedding (FCME) with its application to face and palm biometrics

  • Minghua Wan
  • Ming Li
  • Zhihui Lai
  • Jun Yin
  • Zhong Jin
Original Paper


In the local discriminant embedding (LDE) framework, the neighbor and class of data points were used to construct the graph embedding for classification problems. From a high-dimensional to a low-dimensional subspace, data points of the same class maintain their intrinsic neighbor relations, whereas neighboring data points of different classes no longer stick to one another. However, face images are always affected by variations in illumination conditions and different facial expressions in the real world. So, distant data points are not deemphasized efficiently by LDE and it may degrade the performance of classification. In order to solve above problems, in this paper, we investigate the fuzzy set theory and class mean of LDE, called fuzzy class mean embedding (FCME), using the fuzzy k-nearest neighbor (FKNN) and the class sample average to enhance its discriminant power in their mapping into a low dimensional space. In the proposed method, a membership degree matrix is firstly calculated using FKNN, then the membership degree and class mean are incorporated into the definition of the Laplacian scatter matrix. The optimal projections of FCME can be obtained by solving a generalized eigenfunction. Experimental results on the Wine dataset, ORL, Yale, AR, FERET face database and PolyU palmprint database show the effectiveness of the proposed method.


Local discriminant embedding (LDE) Fuzzy k-nearest neighbor (FKNN) Intrinsic neighbor relations Graph embedding 

List of symbols


The number of classes

\({x_i^j }\)

The jth training sample in class i

\({y_i^j }\)

The feature matrix of image matrix \({x_i^j }\)

\({l_i^j }\)

The \({x_i^j }\) is labeled by some class label \({l_i^j }\)


The set of the training samples


The total number of training samples


The total number of training samples in class i

\({\bar{{m}}_i }\)

The class mean vector of training samples in class i


The fuzzy intraclass neighborhood graphs

\({{G}^{\prime}_{\rm fuzzy}}\)

The fuzzy interclass neighborhood graphs

\({W_{\rm fuzzy}^G }\)

The fuzzy intraclass weight

\({W_{\rm fuzzy}^{{G}^{\prime}}}\)

The fuzzy interclass weight

\({U_{ij}^G }\)

The fuzzy intraclass membership matrix


The fuzzy interclass membership matrix


The fuzzy intraclass diagonal matrix


The fuzzy interclass diagonal matrix


The number of training samples from each class


Sample dimension


The number of the neighbors


The feature matrix dimension


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Minghua Wan
    • 1
    • 2
    • 3
  • Ming Li
    • 1
    • 2
  • Zhihui Lai
    • 3
  • Jun Yin
    • 3
  • Zhong Jin
    • 3
  1. 1.School of Information EngineeringNanchang Hangkong UniversityNanchangChina
  2. 2.Key Laboratory of Nondestructive TestingNanchang Hangkong University, Ministry of EducationNanchangChina
  3. 3.School of Computer Science and TechnologyNanjing University of Science and TechnologyNanjingChina

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