2D Principal Component Analysis Research Articles

A Multifaceted Independent Performance Analysis of Facial Subspace Recognition Algorithms

Face recognition has emerged as the fastest growing biometric technology and has expanded a lot in the last few years. Many new algorithms and commercial systems have been proposed and developed. Most of them use Principal Component Analysis (PCA) as a base for their techniques. Different and even conflicting results have been reported by researchers comparing these algorithms. The purpose of this study is to have an independent comparative analysis considering both performance and computational complexity of six appearance based face recognition algorithms namely PCA, 2DPCA, A2DPCA, (2D)2PCA, LPP and 2DLPP under equal working conditions. This study was motivated due to the lack of unbiased comprehensive comparative analysis of some recent subspace methods with diverse distance metric combinations. For comparison with other studies, FERET, ORL and YALE databases have been used with evaluation criteria as of FERET evaluations which closely simulate real life scenarios. A comparison of results with previous studies is performed and anomalies are reported. An important contribution of this study is that it presents the suitable performance conditions for each of the algorithms under consideration.

An e-nose made of carbon nanotube based quantum resistive sensors for the detection of eighteen polar/nonpolar VOC biomarkers of lung cancer.

A room temperature operating electronic nose (e-nose) has been developed by the assembly of conductive polymer nanocomposite (CPC) quantum resistive sensors (QRS). The fabrication of QRS by spray layer by layer (sLbL) of CPC solutions allowed us to obtain transducers with reproducible initial properties that could be easily tailored by adjusting either the number of sprayed layers and/or the solution composition. The selectivity of QRS was varied by changing the chemical nature of the polymer matrix in which carbon nanotubes (CNTs) were dispersed in solution, i.e., poly(carbonate) (PC), poly(caprolactone) (PCL), poly(lactic acid) (PLA), poly(styrene) (PS), and poly(methyl methacrylate) (PMMA). The e-nose was then successfully used to detect several volatile organic compounds (VOCs) selected among lung cancer biomarkers: a first set of seven polar vapours (water, ethanol, methanol, acetone, propanol, isopropanol, and 2-butanone), and another set of eleven less and nonpolar vapours (chloroform, toluene, benzene, styrene, cyclohexane, o-xylene, n-propane, n-decane, 1,2,4-trimethyl benzene, isoprene, and 1-hexene). The discrimination ability of the e-nose evaluated after a 3D principal component analysis (PCA) pattern recognition treatment was proved to be very good. Moreover, the quantitativity of the transducers' chemo-resistive responses was well fitted with the Langmuir-Henry-Clustering (LHC) model for both acetone and toluene vapours in a wide range of concentrations. The QRS developed in this study appear to be very good candidates to design low cost e-noses for the anticipated diagnosis of lung cancer by VOC analysis in breath, with ppm level sensitivity (tested down to 2.5 parts per million), short response time (a couple of seconds), low consumption, and a large signal to noise ratio (SNR ≥ 10).

Genetic diversity of the fungal pathogen Metarhizium spp., causing epizootics in Chinese burrower bugs in the Jingting Mountains, eastern China

Based on the internal transcribed spacer and inter-simple sequence repeats (ISSR), the phylogenetic relationship and genetic diversity of Metarhizium spp., pathogens found in Chinese burrower bugs, Schiodtella formosana, were analyzed. The results showed that the causative agents of the epizootic green muscardine disease in populations of S. formosana were actually composed of M. anisopliae and its sister species, M. robertsii. The genetic structure of Metarhizium spp. populations were assessed using ten ISSR. A 3D principal component analysis of 51 isolates sampled on different occasions revealed that the Metarhizium spp. populations were temporally heterogeneous. They differentiated into two main clades including over 71 % of all strains causing epizootics, with a similarity of 83 %. The population differentiation was relatively low (G ( ST ), 0.2080), reflecting a large proportion of gene differentiation (79.2 %) within the populations. Further knowledge of the complex species and heterogeneous populations of Metarhizium spp. may be necessary for sustainable control methods of S. formosana.

Pulmonary Nodules Detection in CT Scanned Images Based on Optimization Region Growing and MCSVMs

Lung CT images tumor automatic recognition method combined parameter optimization of regional growth with matMCSVMs (Matrix-mode within-class scatter support vector machine) was proposed to reduce the influence of lung CT image segmentation and support vector (SVM) identification in computer aided the tumor detection. Firstly, in view of the main problems existing in the traditional region growing, such that the initial seed point was too sensitive to select and the growth constraint criterion was difficult to determine, 2D PCA (2D principal component analysis) method was put forward. Secondly, a new growth criteria based on watershed range diagram was also designed for image segmentation. And then, aiming at the current problem that it was hard to compute the decision vector iterative operation in the matMCSVMs, a new method with a preprocessing conjugate gradient descent was used to optimize solution process and improve the classifier identification accuracy. The experimental results show that the methods are effective.

Detection of Pulmonary Nodules in CT Scanned Images Based on Region Growing with Optimization Parameters

We present a more efficient computer-aided diagnosis algorithm to detect pulmonary nodules automatically in CT (Computerized Tomography) scanned images based on region growing with optimization parameters: initial seed points and constraint condition. The former are chosen by 3D (three-dimension) PCA (principal component analysis), and the later is designed by distance map and watershed algorithms. The technique was tested against more than 200 CT images of 10 typical cases from Jilin Tumor Hospital. The results confirm the validity of technique as well as enhanced performance.

FACE RECOGNITION USING HYBRID APPROACH

In this paper, a hybrid feature extraction technique using 2D principal component analysis (2DPCA) and discrete orthogonal Krawtchouk moment (KM) are used to extract the global and local features from the face. Ensemble of RBF classifiers are used to classify the image. Decision-level fusion is done using fuzzy integral to generate more accurate classification than each of the constituent classifiers. The proposed system is evaluated using ORL and YALE databases. Experimental results show that the combination of global and local features promotes the system performance. The fusion of multiple RBFs using fuzzy integral performed better as compared to conventional aggregation rules.

Improved discriminant locality preserving projections for face and palmprint recognition

We propose in this paper two improved manifold learning methods called diagonal discriminant locality preserving projections (Dia-DLPP) and weighted two-dimensional discriminant locality preserving projections (W2D-DLPP) for face and palmprint recognition. Motivated by the fact that diagonal images outperform the original images for conventional two-dimensional (2D) subspace learning methods such as 2D principal component analysis (2DPCA) and 2D linear discriminant analysis (2DLDA), we first propose applying diagonal images to a recently proposed 2D discriminant locality preserving projections (2D-DLPP) algorithm, and formulate the Dia-DLPP method for feature extraction of face and palmprint images. Moreover, we show that transforming an image to a diagonal image is equivalent to assigning an appropriate weight to each pixel of the original image to emphasize its different importance for recognition, which provides the rationale and superiority of using diagonal images for 2D subspace learning. Inspired by this finding, we further propose a new discriminant weighted method to explicitly calculate the discriminative score of each pixel within a face and palmprint sample to duly emphasize its different importance, and incorporate it into 2D-DLPP to formulate the W2D-DLPP method to improve the recognition performance of 2D-DLPP and Dia-DLPP. Experimental results on the widely used FERET face and PolyU palmprint databases demonstrate the efficacy of the proposed methods.

2D Principal Component Analysis for Face and Facial-Expression Recognition

<p>Although it shows enormous potential as a feature extractor, 2D principal component analysis produces numerous coefficients. Using a feature-selection algorithm based on a multiobjective genetic algorithm to analyze and discard irrelevant coefficients offers a solution that considerably reduces the number of coefficients, while also improving recognition rates.</p>

Abstract 347: Gene expression signature of the gross morphology and the specific role of EpCAM in hepatocellular carcinoma

Abstract Tumor morphologies have been identified to associate with their malignant properties such as the invasive, metastatic and/or even recurrent potentials after the cancer treatment. Hepatocellular carcinoma (HCC) is known to demonstrate a variety of morphological appearances. Eggel's nodular type of HCC is morphologically subclassified into single nodular type (SN), single nodular type with extranodular growth (SNEG), and confluent multinodular type (CM), but their biomolecular differences remain unclear. In this study, the clinicopathologic characteristics as well as genome-wide gene expressions were analyzed in relation to the gross morphology of curatively resected HCC. Among 275 patients with nodular type HCC (124 SN-type, 91 SNEG-type and 60 CM-type), significantly poor prognosis was recognized in CM-type in overall survival (p=0.0020) as well as recurrence-free survival (p=0.0066) after the curative resection. The genome-wide expression patterns were evaluated by 3D principal component analysis using Kruskal-Wallis test, and p-value distribution histograms using Mann-Whitney U test. Both of the analyses on the gene expression signature revealed the significant deference in CM-type HCC compared to either SN or SNEG-type HCC. In particular, a stem cell marker EpCAM was dominantly expressed in CM-type HCC. Immunohistochemical studies confirmed the specific expression of EpCAM in HCC cancer cells of CM-type. In multivariate analysis, the gross morphology of CM type was significantly associated with EpCAM expression (p=0.0133), AFP-L3 level (p=0.0311) and the portal vein invasion (p=0.0138). Furthermore, EpCAM was predictive for poor prognosis in overall and recurrence-free survivals of patients with CM-type HCC (p=0.0082 and p=0.0043, respectively). Our studies suggested the distinct signature of gene expression closely related to the morphological progression in HCC. Especially, EpCAM might play a critical role in the aggressiveness of CM-type HCC. Citation Format: {Authors}. {Abstract title} [abstract]. In: Proceedings of the 102nd Annual Meeting of the American Association for Cancer Research; 2011 Apr 2-6; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2011;71(8 Suppl):Abstract nr 347. doi:10.1158/1538-7445.AM2011-347

Geometric Features of 3D Face and Recognition of It by PCA

The extraction algorithms for geometric features of 3D face and recognition of the face by PCA (Principal Component Analysis) is proposed. Firstly, by normalizing the original scattered 3D face point cloud, much less amount of the points is acquired, which still contains the main characteristics of the face. Secondly, by calculating and analyzing the curvatures of pre-processed 3D face profiles, which are extracted from the normalized point cloud, the facial feature points are located. And then the 3D geometric features are obtained by the facial feature points. Finally, some merging strategies are performed to recognize the face, where we use the 3D geometric features and implement the scheme of 2D PCA. The experimental results on 3DFACE-XMU and ZJU-3DFED databases show ed that, the merging strategy which uses the identification results via the geometric features then to screen out the candidates for the recognition by PCA performed on 2D equalized gray image improves recognition accuracy, and the strategy is more robust on expression changes.

Mel- and Mellin-cepstral Feature Extraction Algorithms for Face Recognition

In this article, an image feature extraction method based on two-dimensional (2D) Mellin cepstrum is introduced. The concept of one-dimensional (1D) mel-cepstrum that is widely used in speech recognition is extended to two-dimensions using both the ordinary 2D Fourier transform and the Mellin transform. The resultant feature matrices are applied to two different classifiers such as common matrix approach and support vector machine to test the performance of the mel-cepstrum-and Mellin-cepstrum-based features. The AR face image database, ORL database, Yale database and FRGC database are used in experimental studies, which indicate that recognition rates obtained by the 2D mel-cepstrum-based method are superior to that obtained using 2D principal component analysis, 2D Fourier-Mellin transform and ordinary image matrix-based face recognition in both classifiers. Experimental results indicate that 2D cepstral analysis can also be used in other image feature extraction problems.

Synergistic Combinations of Histone Deacetylase Inhibitors and Decitabine Induce a Unique Gene Expression and Epigenetic Profile In Models of Diffuse Large B-Cell Lymphoma

AbstractAbstract 435Diffuse large B-cell lymphoma (DLBCL) is the most common type of lymphoid malignancy, representing approximately 30–40% of all lymphomas. While significant progress has been made in treating this disease over the past decade, it is still regarded as a heterogeneous disease which, after being classified as relapsed or refractory, is fatal in about one-third of patients. Histone deacetylase inhibitors (HDACI) are presently approved for the treatment of relapsed or refractory cutaneous T- cell lymphomas (CTCL), and have marked activity in peripheral T-cell lymphomas (PTCL), though their effectiveness in DLBCL is less established. DNA methyltransferases (DNMTs) are known to recruit and cooperate with histone deacetylases to induce gene silencing. Combinations of drugs affecting these pathways have emerged as active and important, mostly in myeloid leukemias. We hypothesized that the combination of HDACI and DNMT inhibitors (DNMTI) in DLBCL may be active only in combination and not as single agents. We examined the interaction between a broad range of HDACI including vorinostat, depsipeptide, panobinostat and DNMTI using in vivo and in vitro models of DLBCLs, clearly confirming that these agents are in fact synergistic with decitabine. Synergy was measured by relative risk ratio (RRR) and the values obtained were as low as 0.01, representing very strong synergy. This combination of drugs, specifically panobinostat and decitabine, was also shown to be strongly synergistic in a murine xenograft model of DLBCL. In addition, we analyzed the molecular basis for this synergistic effect by evaluating the global gene expression and methylation using microarrays on the cells treated with the single agents and combination in DLBCL. Three DLBCL lines (OCI-Ly1, OCI-Ly10 and Su-DHL6) were treated with decitabine alone (2.5 μ M), panobinostat alone (2.5 nM) or their combination for 48h hours. DNA and RNA from untreated and treated cells were used for genome wide methylation analysis through Illumina Humanmethyation27 platform and gene expression profiling analysis with Illumina HumanHT-12 v3 Expression arrays. 3D principal component analysis clearly clustered the samples treated with panobinostat and combination therapy together and at greater distances from untreated samples and samples treated by decitabine alone. Therefore, the contribution to the gene expression phenotype of the combination was greater from the HDACI than with DNMTI. Consistent with this observation, the top network of genes differentially expressed (p<0.05) by panobinostat involved critical transcription factors like GATA1, GATA4, SMAD and DNMT3A. Additionally, network-functional analysis of genes perturbed by the combination treatments enriched for critical pathways involved in cell death, cell development and cellular proliferation. Surprisingly, differentially expressed genes and networks identified by each of the treatment conditions and by combination therapy were unique with few overlapping genes as shown in Venn diagram in Figure 1a. Genome wide methylation analysis produced similar results with greater contribution to global methylation changes in cells treated by the combination therapy and decitabine as compared to HDACI. Again, methylation status of a distinct set of genes was altered by combination therapy as compared to the individual drugs (Figure 1b). Correlation between genome wide methylation analysis and gene expression profiling identified 16 overlapping genes in the samples treated by the combination of panobinostat and decitabine including known tumor suppressor genes like VHL, DIRAS3 and WT1. Taken together, integrative genomic analysis has provided insights into the relative contribution of independent epigenetic therapies to the combination phenotype. These findings may provide important leads in identifying unique biomarkers of response specific to the combination of panobinostat and decitabine in DLBCL. [Display omitted] Disclosure:O'Connor:Millennium Pharmaceuticals, Inc.: Membership on an entity's Board of Directors or advisory committees, Research Funding.

Block-wise 2D kernel PCA/LDA for face recognition

Direct extension of (2D) matrix-based linear subspace algorithms to kernel-induced feature space is computationally intractable and also fails to exploit local characteristics of input data. In this letter, we develop a 2D generalized framework which integrates the concept of kernel machines with 2D principal component analysis (PCA) and 2D linear discriminant analysis (LDA). In order to remedy the mentioned drawbacks, we propose a block-wise approach based on the assumption that data is multi-modally distributed in so-called block manifolds. Proposed methods, namely block-wise 2D kernel PCA (B2D-KPCA) and block-wise 2D generalized discriminant analysis (B2D-GDA), attempt to find local nonlinear subspace projections in each block manifold or alternatively search for linear subspace projections in kernel space associated with each blockset. Experimental results on ORL face database attests to the reliability of the proposed block-wise approach compared with related published methods.

Ear recognition based on improved 2D principal component analysis and neural network

Since the human ear feature extraction method of 2 Dimensional Principal Component Analysis (2DPCA) gets relatively bigger features dimension,which leads to poor real-time capability and lack of data storage space,the authors proposed a new approach. First of all,pretreatment of human ear pictures was completed. Then an improved 2DPCA algorithm was used to compress feature dimension. Finally,BP neural network was used in ear classification. Experimental results show that this method is of real-time and can save feature data storage space,and also maintains the recognition rate.

Temperature-dependent infrared spectrum of (Bu 4N) 2[Ru(dcbpyH) 2-(NCS) 2] on nanocrystalline TiO 2 surfaces

The thermal degradation behavior of the self-assembled thin films of (Bu 4N) 2[Ru(dcbpyH) 2-(NCS) 2] (N719) anchoring on TiO 2 surfaces via its carboxylate group has been studied using temperature-dependent diffuse reflectance infrared Fourier transform (DRIFT) spectroscopy. Our analysis indicate that the decomposition temperature of N719 appeared to be at ≈270 °C on TiO 2 surfaces, whereas such decompositions occurred at temperatures higher than ≈340 °C in their solid states as line with the thermal analysis data. This change was also found to be irreversible, if heated above 100 °C on TiO 2 surfaces. Our 2D correlation spectroscopy and principal component analysis (PCA) applied to the temperature-dependent DRIFT spectra supported that the thermal degradation mechanism for N719 should differ in its solid state and on TiO 2 powder surfaces. The NCS stretching vibrational intensities of the neat N719 vibrations were found to shift from 2102 to 1975 cm −1 increase with increase in temperatures, whereas similar vibration changes from 2095 to 2008 cm −1 were observed for N719 attached to TiO 2. Referring from the open-circuit potential, short-circuit, fill factor, and efficiency measurements for the N719 dye-loaded photoelectrodes depending on temperature, the NCS stretching band at ∼2008 cm −1 on TiO 2 surfaces appeared to be correlated with the thermal degradation of the DSSCs.

Assessment of image registration accuracy in three‐dimensional transrectal ultrasound guided prostate biopsy

Prostate biopsy, performed using two-dimensional (2D) transrectal ultrasound (TRUS) guidance, is the clinical standard for a definitive diagnosis of prostate cancer. Histological analysis of the biopsies can reveal cancerous, noncancerous, or suspicious, possibly precancerous, tissue. During subsequent biopsy sessions, noncancerous regions should be avoided, and suspicious regions should be precisely rebiopsied, requiring accurate needle guidance. It is challenging to precisely guide a needle using 2D TRUS due to the limited anatomic information provided, and a three-dimensional (3D) record of biopsy locations for use in subsequent biopsy procedures cannot be collected. Our tracked, 3D TRUS-guided prostate biopsy system provides additional anatomic context and permits a 3D record of biopsies. However, targets determined based on a previous biopsy procedure must be transformed during the procedure to compensate for intraprocedure prostate shifting due to patient motion and prostate deformation due to transducer probe pressure. Thus, registration is a critically important step required to determine these transformations so that correspondence is maintained between the prebiopsied image and the real-time image. Registration must not only be performed accurately, but also quickly, since correction for prostate motion and deformation must be carried out during the biopsy procedure. The authors evaluated the accuracy, variability, and speed of several surface-based and image-based intrasession 3D-to-3D TRUS image registration techniques, for both rigid and nonrigid cases, to find the required transformations. Our surface-based rigid and nonrigid registrations of the prostate were performed using the iterative-closest-point algorithm and a thin-plate spline algorithm, respectively. For image-based rigid registration, the authors used a block matching approach, and for nonrigid registration, the authors define the moving image deformation using a regular, 3D grid of B-spline control points. The authors measured the target registration error (TRE) as the postregistration misalignment of 60 manually marked, corresponding intrinsic fiducials. The authors also measured the fiducial localization error (FLE), the effect of segmentation variability, and the effect of fiducial distance from the transducer probe tip. Lastly, the authors performed 3D principal component analysis (PCA) on the x, y, and z components of the TREs to examine the 95% confidence ellipsoids describing the errors for each registration method. Using surface-based registration, the authors found mean TREs of 2.13 +/- 0.80 and 2.09 +/- 0.77 mm for rigid and nonrigid techniques, respectively. Using image-based rigid and non-rigid registration, the authors found mean TREs of 1.74 +/- 0.84 and 1.50 +/- 0.83 mm, respectively. Our FLE was 0.21 mm and did not dominate the overall TRE. However, segmentation variability contributed substantially approximately50%) to the TRE of the surface-based techniques. PCA showed that the 95% confidence ellipsoid encompassing fiducial distances between the source and target registra- tion images was reduced from 3.05 to 0.14 cm3, and 0.05 cm3 for the surface-based and image-based techniques, respectively. The run times for both registration methods were comparable at less than 60 s. Our results compare favorably with a clinical need for a TRE of less than 2.5 mm, and suggest that image-based registration is superior to surface-based registration for 3D TRUS-guided prostate biopsies, since it does not require segmentation.

Upper airway detection and visualization from cone beam image slices

This paper describes a method developed to assist in the detection and reconstruction of a three dimensional (3D) model of the human upper airway using cone beam computed tomography (CBCT) image slices and a 3D Gaussian smoothing kernel. The segmented and reconstructed volumetric airway is characterized by the corresponding three principal axes that are selected for viewing direction orientation via rotation and translation. These axes are derived using the 3D Principal Component Analysis (PCA) result of the rendered volume. To finely adjust the view and access airway, the major and minor axes of each slice are also computed using the two dimensional (2D) PCA in the respective planes. The exterior volume view is visualized in two modes, namely, a solid surface (volume details transparent to user) view and a nontransparent (volume detail accessible) view. This functionality provides an application driven use of the 3D airway in CBCT based anatomy studies. The extracted information may be useful as an imaging biomarker in the diagnostic assessment of patients with upper airway respiratory conditions such as obstructive sleep apnea, allergic rhinitis, and other related diseases; as well as planning orthopedic/orthodontic therapies.

Multi‐Channel Piezoelectric Quartz Crystal Sensor with Principal Component Analysis and Back‐Propagation Neural Network for Organic Pollutants from Petrochemical Plants

AbstractA multi‐channel piezoelectric quartz crystal gas sensor comprising arrays coated with various organic materials and a home‐made computer interface for data processing were prepared and employed to detect six kinds of common organic pollutants from petrochemical plants including benzene, styrene, chloroform, octane, hexene and hexyne. The principal component analysis (PCA) method was employed to select six kinds of appropriate coating materials for these organic pollutants from 22 adsorbents onto piezoelectric crystals. After performing a PCA assay, six representative coating materials, namely Polyisobutylene, Poly(dimethylsiloxane) (SE30), 4‐tert‐Butylcalix[6]arene, Cholesteryl chloroformate, C60‐Polyphenyl acetylene (C60‐PPA) and Ag(I)/cryptand‐2,2/Ethylene diamine/NH3/Polyvinyl chloride were selected. Moreover, effects of coating load of adsorbents and concentration of pollutants were also investigated. Three kinds of recognition techniques including 2D PCA score map, radar plot and back‐propagation neural network (BPN) were employed for qualitative analysis of these organic pollutants, and a quantitative analysis method could be established by creating calibration curves for each organic pollutant. This homemade multi‐channel piezoelectric quartz crystal gas sensor showed a good detection limit of 0.068‐1.127 mg/L for these organic pollutants. The multi‐channel piezoelectric gas sensor exhibited good reproducibility with a relative standard deviation (RSD) of 1.1‐9.6%. Furthermore, this multi‐channel piezoelectric crystal detection system with BPN recognition technique was also utilized to successfully distinguish and identify each component of the mixture of organic gas samples. Multivariate linear regression (MLR) analysis was employed to quantitatively compute the concentration of species in the organic mixtures.

MPCA: Multilinear Principal Component Analysis of Tensor Objects

This paper introduces a multilinear principal component analysis (MPCA) framework for tensor object feature extraction. Objects of interest in many computer vision and pattern recognition applications, such as 2-D/3-D images and video sequences are naturally described as tensors or multilinear arrays. The proposed framework performs feature extraction by determining a multilinear projection that captures most of the original tensorial input variation. The solution is iterative in nature and it proceeds by decomposing the original problem to a series of multiple projection subproblems. As part of this work, methods for subspace dimensionality determination are proposed and analyzed. It is shown that the MPCA framework discussed in this work supplants existing heterogeneous solutions such as the classical principal component analysis (PCA) and its 2-D variant (2-D PCA). Finally, a tensor object recognition system is proposed with the introduction of a discriminative tensor feature selection mechanism and a novel classification strategy, and applied to the problem of gait recognition. Results presented here indicate MPCA's utility as a feature extraction tool. It is shown that even without a fully optimized design, an MPCA-based gait recognition module achieves highly competitive performance and compares favorably to the state-of-the-art gait recognizers.

Horizontal and Vertical 2DPCA-Based Discriminant Analysis for Face Verification on a Large-Scale Database

This paper first discusses some theoretical properties of 2D principal component analysis (2DPCA) and then presents a horizontal and vertical 2DPCA-based discriminant analysis (HVDA) method for face verification. The HVDA method, which applies 2DPCA horizontally and vertically on the image matrices (2D arrays), achieves lower computational complexity than the traditional PCA and Fisher linear discriminant analysis (LDA)-based methods that operate on high dimensional image vectors (1D arrays). The horizontal 2DPCA is invariant to vertical image translations and vertical mirror imaging, and the vertical 2DPCA is invariant to horizontal image translations and horizontal mirror imaging. The HVDA method is therefore less sensitive to imprecise eye detection and face cropping, and can improve upon the traditional discriminant analysis methods for face verification. Experiments using the face recognition grand challenge (FRGC) and the biometric experimentation environment system show the effectiveness of the proposed method. In particular, for the most challenging FRGC version 2 Experiment 4, which contains 12\thinspace776 training images, 16 028 controlled target images, and 8014 uncontrolled query images, the HVDA method using a color configuration across two color spaces, namely, the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">YIQ</i> and the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">YCbCr</i> color spaces, achieves the face verification rate (ROC III) of 78.24% at the false accept rate of 0.1%.