Advanced variations of two-dimensional principal component analysis for face recognition

Although two-dimensional principal component analysis (2DPCA) extracts image features directly from 2D image matrices rather than one dimensional vectors, 2DPCA is only based on the whole images to preserve total variances by maximizing the trace of feature covariance matrix. Thus, 2DPCA cannot extract localized components, which are usually important for face recognition. Inspired by nonnegative matrix factorization (NMF), which is based on localized features, we propose a novel algorithm for face recognition called two-dimensional nonnegative principal component analysis (2DNPCA) to extract localized components and maintain the maximal variance property of 2DPCA. 2DNPCA is a matrix-based algorithm to preserve the local structure of facial images and has the nonnegative constraint to learn localized components. Therefore, 2DNPCA has both advantages of 2DPCA and NMF. Furthermore, 2DNPCA solves the time-consuming problem by removing the restriction of minimizing the cost function and extracting only the base matrix. The nearest neighbor (NN) classifier and linear regression (LR) classifier are used for classification and extensive experimental results show that 2DNPCA plus NN and 2DNPCA plus LR are both very efficient approaches for face recognition.

In this paper, based on the study of the Two-Dimensional Principal Component Analysis (2DPCA), Two-Dimensional Principal Component Analysis (2DPCA) and fuzzy set theory, we propose a integrated face recognition algorithm based on wavelet subspace. This method can make good use of the advantages of each single method, and also can make up for the defect of each other. The comparison of the results of the different methods identification effect on the ORL、YALE and FERET face database show, the integrated method proposed in this paper improves the recognition rate, and it also reduces the training and classification time as well. Key word: face recognition; Two-Dimensional Principal Component Analysis (2DPCA); Two-Dimensional Linear Discriminant Analysis (2DLDA); fuzzy set theory; feature extraction be divided into several categories:the method based on geometric features、the method based on model、the method based on the statistical、the method based on neural network method and the method of combining multiple classifiers, this paper mainly focuses on the method based on statistics. The method based on statistical faced the image as random vector, thus using some statistical methods to analyze the face model, the most representative methods include the eigenface method based on principal component analysis which proposed by Turk M (2)

In this paper, based on face recognition, the core algorithm is studied, which was applied in access control system. This algorithm carries on two-dimensional principal component analysis (2DPCA), singular value decomposition (SVD) and the fusion of 2DPCA and SVD, which the main characteristic vector of the PCA is fused to form a new one that is taken as the distinction standard. The experiment results, by means of ORL and Yale face database, the recognition rate is up to 87% and 98.9%, respectively. The effectiveness of the proposed face recognition algorithm and its insensitivity to the facial expression, illumination and posture are shown in terms of both the absolute performance indices and the comparative performance against some popular face recognition schemes such as singular value decomposition based method.

The traditional two-Dimensional Principal Component Analysis(2DPCA) only extracts the in-line features of data of face image, the direction of feature extraction is relatively simple, and the feature extraction in other directions is not considered. In order to extract the features of the image from multiple angles and provide more abundant information for recognition, a new method of 2DPCA face recognition is proposed. The new algorithm first self-corrects the face image, at the same time, it extracts the low frequency information of the image, and then it uses the Perceptual hash technique to obtain the ‘fingerprint’ of the image. Then, the new algorithm will rotate multi-angle images from the self-corrected face images and extract the features separately to get multi-angle feature information. Finally, the training sample pictures are classified again for each category, and the images of similar expressions or features are classified to retain the special expressions or features. The numerical experiments in the ORL human face databases show that the improved algorithm is superior to the traditional 2DPCA algorithm.

In this paper, the improved face recognition method based on two-directional 2DPCA (two-dimensional principal component analysis) in each block of face images is proposed. Firstly, the face image is divided into several sub-images, and then the sub-image features of each corresponding block are extracted by two-directional 2DPCA according to the number of sub-images. Finally, using the support vector machine to improve the recognition rate. Experimental results on ORL face database and YALE face database show that the proposed method is superior to any other 2DPCA methods in face recognition rate.

Recently, many approaches of face recognition have been proposed due to its broad applications. The generalized low rank approximation of matrices(GLRAM) was proposed in [1], and a necessary condition for the solution of GLRAM was presented in [2]. In addition to all these developments, the Two-Dimensional Principal Component Analysis (2DPCA) model is proposed and proved to be an efficient approach for face recognition [5]. In this paper, we proposed Double Sides 2DPCA algorithm via investigating the 2DPCA algorithm and GLRAM algorithm, experiments showed that the Double Sides 2DPCA’s performance is as good as 2DPCA’s and GLRAM’s. Furthermore, the computation cost of recognition is less than 2DPCA and the computation speed is faster than that for GLRAM. Further, we present a new constructive method for incrementally adding observation to the existing eigen-space model for Double Sides 2DPCA, called incremental doubleside 2DPCA. An explicit formula for such incremental learning is derived. In order to illustrate the effectiveness of the proposed approach, we performed some typical experiments.KeywordsFace RecognitionRecognition AccuracyFace DatabaseFace Recognition AlgorithmBatch AlgorithmThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Two-dimensional feature extraction methods such as two-dimensional principal component analysis (2DPCA) and two-dimensional linear discriminant analysis (2DLDA) have been extensively studied in the past several years. Numerous experimental results demonstrate that these two-dimensional feature extraction methods are generally more efficient than and at least as effective as their one-dimensional counterparts in face recognition. However, in contrary to the large number of studies in two-dimensional feature extraction methods, studies in two-dimensional pattern classification are quite few. In this paper we propose two kinds of two-dimensional nearest neighbor classifiers and test their performance in face recognition. Extensive experimental studies conducted on four benchmark face image databases: OR, Yale, FERET, and AR demonstrate that the proposed classifiers can achieve higher recognition accuracies than the nearest neighbor classifier in general.

This paper proposes a two-dimensional color uncorrelated principal component analysis algorithm(2DCUPCA) for unsupervised subspace learning directly from color face images. The 2DCUPCA can be used to explore uncorrelated properties among color-based features, which contain minimum redundancy and ensure linear independence among features. Furthermore, the proposed 2DCUPCA provided the theoretical foundations analysis and proved the uncorrelated property between color-based features in theory. This makes it sure that the extracted features directly from three color image matrices will be uncorrelated. Finally, experimental results on the AR and FRGC-2 color face databases show that 2DCUPCA achieves better recognition performance than other color face recognition methods.KeywordsPattern recognitionface recognitionuncorrelated principal component analysisfeature extraction

The ionospheric total electron content (TEC) data from 05 to 10 January 2013 (UT) were examined by two-dimensional principal component analysis (2DPCA) and revealed a TEC anomaly related to the volcanic eruption in Colima, Mexico on 06 January, 2013. A TEC anomaly was detected above the volcano from 21:00 to 21:05 on 06 January 2013 (UT). The anomaly occurred for at least 5 minutes, during this time period we could identify the equatorial ionization anomaly (EIA). The shock acoustic wave produced by eruption-induced seismic activity may be the cause of the observed TEC anomaly. We show that it is possible to monitor or predict volcanic eruptions and their associated seismic activity through the use of two-dimensional principal component analysis of the resulting TEC anomalies.

In Brief

Dimensionality reduction methods play an important role in face recognition. Principal component analysis (PCA) and two-dimensional principal component analysis (2DPCA) are two kinds of important methods in this field. Recent research seems like that 2DPCA method is superior to PCA method. To prove if this conclusion is always true, a comprehensive comparison study between PCA and 2DPCA methods was carried out. A novel concept, called column-image difference (CID), was proposed to analyze the difference between PCA and 2DPCA methods in theory. It is found that there exist some restrictive conditions when 2DPCA outperforms PCA. After theoretical analysis, the experiments were conducted on four famous face image databases. The experiment results confirm the validity of theoretical claim.

Since two-dimensional principal component analysis has been used in face recognition, many approaches in 2D-based method have been developed. However, less attention is spent in the classification methods based on 2D image matrix. Considering that the feature extracted from 2DPCA based is a matrix instead of a single vector as in PCA based, a new measurement distance is proposed which considers the rows of the feature matrix. Unlike the previous methods which are depending on the columns or the whole matrix of the feature matrix, the proposed method is combined with the k-nearest neighbour instead of the 1-nearest neighbour. Moreover, by using the proposed method, the drawback of 2DPCA based algorithms compared to PCA based algorithms, which is the increment of the coefficient numbers, can be alleviated. Experimental results on a famous face databases show that by increasing the number of training images per class, the proposed method accuracy is also increased until it surpasses all methods in terms of accuracy and storage capacity.

This paper presents a comparison between one-dimensional component analysis (1D-PCA) and two-dimensional principal component analysis (2D-PCA) under two different types of classification techniques namely k-nearest neighbor (kNN) and Support Vector Machines (SVM). These two techniques differ in the method to determine the image covariance matrix. 2DPCA used 2D image matrices instead of column vectors in 1DPCA. The eigenvectors derived from these matrices will result in images in reduced dimensions to be used for classification. K-nearest neighbor algorithm (kNN) and Support Vector Machines (SVM) were used for classification. The performance measures used for comparison were classification accuracy and computational time. The tests were performed on the ORL image database. The experimental results indicate that 2DPCA outperforms in terms of classification accuracy and computational complexity.

The equivalence of two-dimensional PCA to line-based PCA

Two-dimensional Principal Component Analysis (2DP-CA) has been widely used for face image representation and recognition. However, 2DPCA, which is based on F-norm square, is sensitive to the presence of outliers. To enhance the robustness of 2DPCA model, we proposed a novel Robust 2DPCA objective function, called R-2DPCA. The criterion of R-2DPCA is maximizing the covariance of data in the projected subspace, while minimizing the reconstruction error of data. In addition, we use the efficient non-greedy optimization algorithms solving our objective function. Extensive experiments are done on the AR, CMU-PIE, Extended Yale B face image databases, and results illustrate that our method is more effective and robust than other robust 2DPCA algorithms, such as L1-2DPCA, L1-2DPCA-S, and N-2DPCA.