Minimum Mahalanobis Distance Research Articles

Proposed methods of image recognition depend on the PCA

This paper suggest two method of recognition, these methods depend on the extraction of the feature of the principle component analysis when applied on the wavelet domain(multi-wavelet). First method, an idea of increasing the space of recognition, through calculating the eigenstructure of the diagonal sub-image details at five depths of wavelet transform is introduced. The effective eigen range selected here represent the base for image recognition. In second method, an idea of obtaining invariant wavelet space at all projections is presented. A new recursive from that represents invariant space of representing any image resolutions obtained from wavelet transform is adopted. In this way, all the major problems that effect the image and change its characteristic are solved through calculating invariant eigen range of the recursive resolution forms of all sub-images coefficient. These approaches employed here as multi-wavelet transform identifier with minimum Mahalanobis distance. All method recognition proposed in this paper are applied on different images. Different tables of image recognition resulted in accurate and fast.

Industrial image anomaly detection based on multi Gaussian discriminant model and robust core set

Abstract To address the issue of false positive (FP) detections in image anomaly detection caused by the loss of low-frequency features when dealing with high-dimensional feature distributions, we propose the multi-layer Gaussian discriminant anomaly detection model (MGAD). This model utilizes distance metrics based on multiple normal distributions to perform anomaly detection. By mining multi-layer feature combinations from normal samples and incorporating a Gaussian mixture model strategy for pixel-by-pixel probability density estimation, a weighting mechanism is designed to emphasize the role of low-frequency features in Gaussian space. This approach effectively models data collections that do not follow a single normal distribution as a mixture of several Gaussian distributions, thereby reducing false detections. Additionally, we propose a method for calculating the minimum Mahalanobis distance based on the estimation of the minimum covariance determinant. By identifying a subset with the smallest covariance matrix determinant, this method enhances the robust estimation of the data’s central position and spread, thereby reducing the impact of outliers. On the MVTec-AD dataset, MGAD demonstrates outstanding performance with an anomaly detection area under the receiver operating characteristic curve (AUROC) of 98.8%, the anomaly localization AUROC of 98.2%, and the per-class true negative rate for normal samples of 93.1%. Compared with the state-of-the-art models, MGAD improves the detection accuracy for normal samples by 3.6%, demonstrating the best performance among all models. These results highlight the model’s excellent capability in anomaly recognition and reduction of FPs.

Quantile Regression Approach for Analyzing Similarity of Gene Expressions under Multiple Biological Conditions

Temporal gene expression data contain ample information to characterize gene function and are now widely used in bio-medical research. A dense temporal gene expression usually shows various patterns in expression levels under different biological conditions. The existing literature investigates the gene trajectory using the mean function. However, temporal gene expression curves usually show a strong degree of heterogeneity under multiple conditions. As a result, rates of change for gene expressions may be different in non-central locations and a mean function model may not capture the non-central location of the gene expression distribution. Further, the mean regression model depends on the normality assumptions of the error terms of the model, which may be impractical when analyzing gene expression data. In this research, a linear quantile mixed model is used to find the trajectory of gene expression data. This method enables the changes in gene expression over time to be studied by estimating a family of quantile functions. A statistical test is proposed to test the similarity between two different gene expressions based on estimated parameters using a quantile model. Then, the performance of the proposed test statistic is examined using extensive simulation studies. Simulation studies demonstrate the good statistical performance of this proposed test statistic and show that this method is robust against normal error assumptions. As an illustration, the proposed method is applied to analyze a dataset of 18 genes in P. aeruginosa, expressed in 24 biological conditions. Furthermore, a minimum Mahalanobis distance is used to find the clustering tree for gene expressions.

Relations Between Collision Probability, Mahalanobis Distance, and Confidence Intervals for Conjunction Assessment

Some of the most common metrics for collision risk assessment are the probability of collision, miss distance in Mahalanobis space, and confidence intervals. Sometimes they are used in combination; for example, the miss distance is used as a prescreening method to identify potentially hazardous conjunctions; other times they are used as alternative means; that is, covariance ellipse overlapping checks are employed instead of computing the probability of collision. In this work, we show that the three risk indexes are intimately connected once a suitable distance is defined. We argue that Mahalanobis miss distance is a proper metric only when the sigma-normalized hard-body size is negligible; we thus investigate the minimum Mahalanobis distance between the hard-body circle and the combined position covariance as an alternative. Its computation is fully analytic, as the most complex operation is finding the roots of a quartic polynomial. When multiplied by the sigma-normalized hard-body radius, such distance provides an upper bound to the collision probability. When used to scale the covariance matrix, it provides the largest confidence interval supporting a noncollision event. Finally, when adopted as an actionable threshold, analytical bounds on the probability of miss detection and of false alarms can be computed.

Monitoring of Forest Resource Health in Akure Reserve, Ondo State Nigeria

Remote sensing and Geographic Information System (GIS) over the years play great role when integrated in the right way to study changes taken place on the planet. Most times, these changes are natural and beyond human interaction but often times too, the changes are occasioned by human factor in the search for development and daily survival. In achieving this, the forest is made to suffer unnecessarily thereby reducing its health status through excessive forest resources depletion. This study focusses on the monitoring of forest resource health in Akure forest reserve between 1972 and 2013 using Landsat MSS of 11/11/1972, Landsat TM of 17/12/1986, Landsat ETM+ of 03/01/2002, and Landsat ETM+ of 02/02/2013 downloaded from USGS website. Minimum Mahalanobis distance supervised classification was used to categorize land use pattern in the study area while ILWIS 3.2 Academic GIS was deployed to perform NDVI image classification analysis with a precision of 0.01m to determine the health status of the forest reserve. The analysis revealed that the total annual rate of depletion for 41 years stood at 2.46% while forest health status diminished during the study period as NDVI value ranged between -0.04to +0.44 (1972) to -1.0to +1.0 in 2013. The study recommends that open areas which are not homogeneous forest (shrub/grass land) detected in this study should be re-planted with varieties of tree species without delay to allow carbon sequestration for overall human benefits.

Robust generalised quadratic discriminant analysis

Quadratic discriminant analysis (QDA) is a widely used statistical tool to classify observations from different multivariate Normal populations. The generalized quadratic discriminant analysis (GQDA) classification rule/classifier, which generalizes the QDA and the minimum Mahalanobis distance (MMD) classifiers to discriminate between populations with underlying elliptically symmetric distributions competes quite favorably with the QDA classifier when it is optimal and performs much better when QDA fails under non-Normal underlying distributions with heavy tail, e.g. Cauchy distribution. However, the classification rule in GQDA is still based on the sample mean vector and the sample dispersion matrix of a training set, which are extremely non-robust under data contamination. In real world, however, it is quite common to face data which are highly vulnerable to outliers and so the lack of robustness of the classical estimators of the mean vector and the dispersion matrix reduces the efficiency of the GQDA classifier significantly, increasing the misclassification errors. The present paper investigates the performance of the GQDA classifier when the classical estimators of the mean vector and the dispersion matrix used therein are replaced by various robust counterparts. Applications to various real data sets as well as simulation studies reveal far better performance of the proposed robust versions of the GQDA classifier. A comparative study has been made to advocate the appropriate choice of the robust estimators to be used in a specific situation.

Optimizing the MFlex monitoring system using Mahalanobis-Taguchi system

Methadone Flexi Dispensing Service (MFlex) has been officially re-branded from Methadone 1Malaysia Service (M1M) since 2nd January 2019. Patients under MFlex are frequently taking their methadone according to a plan provided by pharmacist at public clinic. From the dose monitoring taken annually, pharmacists can predict critical patients based on high monthly dose increases. However, the current monitoring system is written documentation with total doses that cannot accurately measure addiction levels and slow down the distribution process to appropriate incentives as provided by the government. The main objective of this work is to develop a new data monitoring system by evaluating all factors contributed to the addiction level. Mahalanobis-Taguchi System (MTS) is a method of predicting and diagnosing system performance using multivariate data in order to make quantitative decisions with the construction of a multivariate measurement scale using an analytical method. The results show that the minimum Mahalanobis Distance (MD) for healthy data is 0.2245 while the maximum is 2.3380. The minimum and maximum MD of unhealthy data is 0.6077 and 24.5719 respectively. Thus, parameters of blood, bilirubin, nitrite, specific gravity, leukocytes are considered as significant parameters by considering positive value signal-to-noise ratio (SNR) gain. Graphical user interface (GUI) has been developed for analyzing the normal and abnormal patients in detail. Meanwhile, mobile application has been developed as a decision-making tool to classify that the patients is either normal or abnormal.

EVAL Cane: Nonintrusive Monitoring Platform With a Novel Gait-Based User-Identification Scheme

Considering the particularity of fragile people with reduced mobility, we design a nonintrusive platform called EVAL cane to assist and monitor the user’s walking. On the one hand, it has important walking-assistance functions, such as obstacle warning and fall detection. On the other hand, it collects the user’s long-term walking data in the background, which may be the potential physical-health-assessment data. Compared with an ordinary cane, the above two functions are implemented without any burden on the user’s life. In addition, we have considered the authentication security for that the walking data are private. To this end, we propose a novel user-identification scheme, leveraging the user walking gait data collected by EVAL cane. To the best of our knowledge, it is the first time that the gait information collected by cane is used for reinforcing monitoring system security. This scheme does not require the user to remember and enter any identity (such as a password), which is user-friendly for fragile people. In the scheme, a statistics-based rough gait feature-extraction method is put forward at first. Then, in order to improve the identification precision, we design a performance-based feature-deletion (PFD) algorithm to remove the bad features. Finally, a minimum Mahalanobis distance classifier is used. Experimental results show that the user-identification rate without the PFD algorithm can reach as high as 90.48%. In addition, the PFD algorithm further improves the performance by about 6%, reaching an excellent result of 96.43%.

PERBANDINGAN ALGORITMA PADA METODE KLASIFIKASI SUPERVISED BERBASIS CITRA ALOS AVNIR-2 UNTUK PEMETAAN MANGROVE

The goal of this research was to provide an appropriate algorithm for mapping the mangrove area in Anday. Supervised classification method applied that consisted of several algorithmic alternatives such as parallel piped, minimum distance algorithm, mahalanobis distance, maximum likelihood, and spectral angle mapper. In addition, this study was conducted by applying the image process of a near-infrared band of ALOS AVNIR-2 and then analysis was carried out to leverage the accuracy of the range of spectral values through field survey and to test the accuracy of mangrove zonation maps which was based the supervised classification method. The results revealed that the overall accuracy of parallelepiped was 29%, and 41.18% for minimum distance algorithm, mahalanobis distance was 58.82%, the maximum likelihood was 50%, and spectral angle mapper was 58.82%.

Идентификация таксонов морских рыб методом линейного дискриминантного анализа спектров отражения в ближней инфракрасной области

Introduction. Near-infrared (NIR) spectroscopy is a modern instrumental method for the quantitative and qualitative analysis of various objects. The method for analyzing the NIR spectra of diffuse reflection was successfully used to identify plant and animal species, drugs, etc. The issue of identifying objects of marine fishery is currently extremely important for modern fisheries, environmental monitoring, and identifying counterfeit products. The research objective was to identify the fish taxa using the discriminant analysis of reflection in the NIR region. Study objects and methods. The research featured 25 dried and defatted muscle tissue samples taken from different species of marine fish caught in the North Fishing Basin. The spectra were measured using a Fourier IR-spectrophotometer Shimadzu IRTracer-100 with a diffuse reflection measuring instrument. Measurements were carried out in the range from 700 to 7,000 cm–1. Mathematical processing of the spectra was performed using the MagicPlot Pro program ver. 2.9 (Magicplot Systems, LLC), while the statistical program IBM SPSS Statistics ver. 25 (IBM Corp., USA) was exploited to perform the linear discriminant analysis. Results and discussion. The spectra of diffuse reflection of NIR radiation were measured for 25 samples of marine fish species of different taxa caught in the North Fishing Basin. The range of 3,700 to 6,700 cm–1 was selected to assess the proximity of spectra in linear discriminant analysis. In this range, the team identified 19 spectral peaks, which made a significant contribution to canonical discriminatory functions. The resulting canonical discriminatory functions made it possible to divide the objects into eight nonoverlapping groups corresponding to each biological group of the fish. The analysis was based on a comparison of Mahalanobis distance between the group centroids and the NIR spectra of each studied fish species. The minimum Mahalanobis distance between the nearest groups was statistically significant. Conclusion. The research proved the possibility of taxonomic identification of marine fish based on measuring the spectral characteristics of their muscle tissue proteins in the range of 3,700 to 6,700 cm–1 of near-infrared region and classification by linear discriminant analysis.

An Efficient Motion Vector Recovery and Reconstruction Method for Spatiotemporal Video Error Concealment

In this article, an efficient spatiotemporal video error concealment (EC) based on motion vector (MV) recovery and a pixel reconstruction (PR) method is proposed. The pixel-based motion vector with partition (PMVP) is modified by using Mahalanobis distance (MD) rather than Euclidean distance (ED) for recovering MVs, as MD uses standard deviation and covariance of available pixels. Further, the MD gives more accuracy for non-square cluster compared to ED. This modified pixel-based motion vector with partition (MPMVP) algorithm is further upgrade by two different strategies. First, by using voting priority of available MVs based on the probabilities of similar directions. Second, by considering separate horizontal and vertical directions of available MVs in voting priority. For pixel reconstruction, modified spiral pixel reconstruction (MSPR) algorithm based on directional edge recovery method using minimum and maximum Mahalanobis distance from available pixels of surrounding MBs is proposed. Mahalanobis distance approach is most optimized similarity measure technique compared to other distance measurement approach to obtained lost motion vectors. These proposed EC techniques are compared with existing EC techniques like, SPR EC using ED, PMVP based EC with ED, and MV Interpolation by Zhou's method for various packet loss rates (PLRs) as 3%, 7%, 16%, 20% and quantization parameters (QPs) as 20, 24, 28, 32, 36. For total average in PLR of 3%, 7%, 16% and 20%, MSPR is having better PSNR compared to PMVP by 2.516, 2.29, 2.06 and 2.02 dB, respectively; and compared to SPR by 0.796, 0.718, 0.643 and 0.631 dB, respectively.

A Quantitative Ultrasound-Based Multi-Parameter Classifier for Breast Masses

This manuscript reports preliminary results obtained by combining estimates of two or three (among seven) quantitative ultrasound (QUS) parameters in a model-free, multi-parameter classifier to differentiate breast carcinomas from fibroadenomas (the most common benign solid tumor). Forty-three patients scheduled for core biopsy of a suspicious breast mass were recruited. Radiofrequency echo signal data were acquired using clinical breast ultrasound systems equipped with linear array transducers. The reference phantom method was used to obtain system-independent estimates of the specific attenuation (ATT), the average backscatter coefficients, the effective scatterer diameter (ESD) and an effective scatterer diameter heterogeneity index (ESDHI) over regions of interest within each mass. In addition, the envelope amplitude signal-to-noise ratio (SNR), the Nakagami shape parameter, m, and the maximum collapsed average (maxCA) of the generalized spectrum were also computed. Classification was performed using the minimum Mahalanobis distance to the centroids of the training classes and tested against biopsy results. Classification performance was evaluated with the area under the receiver operating characteristic (ROC) curve. The best performance with a two-parameter classifier used the ESD and ESDHI and resulted in an area under the ROC curve of 0.98 (95% confidence interval [CI]: 0.95-1.00). Classification performance improved with three parameters (ATT, ESD and ESDHI) yielding an area under the ROC curve of 0.999 (0.995-1.000). These results suggest that system-independent QUS parameters, when combined in a model-free classifier, are a promising tool to characterize breast tumors. A larger study is needed to further test this idea.

Partial Discharge Spectral Characterization in HF, VHF and UHF Bands Using Particle Swarm Optimization.

The measurement of partial discharge (PD) signals in the radio frequency (RF) range has gained popularity among utilities and specialized monitoring companies in recent years. Unfortunately, in most of the occasions the data are hidden by noise and coupled interferences that hinder their interpretation and renders them useless especially in acquisition systems in the ultra high frequency (UHF) band where the signals of interest are weak. This paper is focused on a method that uses a selective spectral signal characterization to feature each signal, type of partial discharge or interferences/noise, with the power contained in the most representative frequency bands. The technique can be considered as a dimensionality reduction problem where all the energy information contained in the frequency components is condensed in a reduced number of UHF or high frequency (HF) and very high frequency (VHF) bands. In general, dimensionality reduction methods make the interpretation of results a difficult task because the inherent physical nature of the signal is lost in the process. The proposed selective spectral characterization is a preprocessing tool that facilitates further main processing. The starting point is a clustering of signals that could form the core of a PD monitoring system. Therefore, the dimensionality reduction technique should discover the best frequency bands to enhance the affinity between signals in the same cluster and the differences between signals in different clusters. This is done maximizing the minimum Mahalanobis distance between clusters using particle swarm optimization (PSO). The tool is tested with three sets of experimental signals to demonstrate its capabilities in separating noise and PDs with low signal-to-noise ratio and separating different types of partial discharges measured in the UHF and HF/VHF bands.

The utility of empirically assigning ancestry groups in cross-population genetic studies of addiction.

Given moderate heritability and significant heterogeneity among addiction phenotypes, successful genome-wide association studies (GWAS) are expected to need very large samples. As sample sizes grow, so can genetic diversity leading to challenges in analyzing these data. Methods for empirically assigning individuals to genetically informed ancestry groups are needed. We describe a strategy for empirically assigning ancestry groups in ethnically diverse GWAS data including extensions of principal component analysis (PCA) and population matching through minimum Mahalanobis distance. We apply these methods to data from Spit for Science (S4S): the University Student Survey, a study following college students longitudinally that includes genetic and environmental data on substance use and mental health (n = 7,603). The genetic-based population assignments for S4S were 48.7% European, 22.5% African, 10.4% Americas, 9.2% East Asian, and 9.2% South Asian descent. Self-reported census categories "More than one race" and "Unknown"as well as "Hawaiian/Pacific Islander" and "American-Indian/Native Alaskan" were empirically assigned representing a +9% sample retention over conventional methods. Although there was high concordance between self-reported race and empirical population-match (+.924), there was reduction in variance for most ancestry PCs for genetic-based population assignments. We were able to create more genetically homogenous groups and reduce sample and marker loss through cross-ancestry meta-analysis, potentially increasing power to detect etiologically relevant variation. Our approach provides a framework for empirically assigning genetic ancestry groups which can be applied to other ethnically diverse genetic studies. Given the important public health impact and demonstrable gains in statistical power from studying diverse populations, empirically sound practices for genetic studies are needed. (Am J Addict 2017;26:494-501).

An Iterative Method for Determining the Most Probable Bifurcation in Large Scale Power Systems

An iterative method is presented to determine the most probable voltage stability limit by identifying the closest saddle node bifurcation in a probability-loading space starting at the expected initial system state. The iterative method is applied to the probability space to identify the closest saddle node bifurcation by means of the Mahalanobis distance. Further the method provides an ellipsoidal load subspace corresponding to the most probable bifurcation. This ellipsoid is a lower bound for the probability of bifurcation. To verify the proposed methodology examples are given and the minimum Mahalanobis distance, for dependent and independent load patterns, is compared with the minimum Euclidian distance.

Detecting destabilizing wheelchair conditions for maintaining seated posture

Purpose: The purpose of this study was to detect and classify potentially destabilizing conditions encountered by manual wheelchair users with spinal cord injuries (SCI) to dynamically increase stability and prevent falls.Methods: A volunteer with motor complete T11 paraplegia repeatedly propelled his manual wheelchair over level ground and simulated destabilizing conditions including sudden stops, bumps and rough terrain. Wireless inertial measurement units attached to the wheelchair frame and his sternum recorded associated accelerations and angular velocities. Algorithms based on mean, standard deviation and minimum Mahalanobis distance between conditions were constructed and applied to the data off-line to discriminate between events. Classification accuracy was computed to assess effects of sensor position and potential for automatically selecting a dynamic intervention to best stabilize the wheelchair user.Results: The decision algorithm based on acceleration signals successfully differentiated destabilizing conditions and level over-ground propulsion with classification accuracies of 95.8, 58.3 and 91.7% for the chest, wheelchair and both sensors, respectively.Conclusion: Mahalanobis distance classification based on trunk accelerations is a feasible method for detecting destabilizing events encountered by wheelchair users and may serve as an effective trigger for protective interventions. Incorporating data from wheelchair-mounted sensors decreases the false negative rate.Implications for RehabilitationSCI has a significant impact on quality of life, compromising the ability to participate in social or leisure activities, and complete other activities of daily living for an independent lifestyle.Using inertial measurement units to build an event classifier for control the actions of a neuroprosthetic device for maintaining seated posture in wheelchair users.Varying muscle activation increases user stability reducing the risk of injury.

Generalized quadratic discriminant analysis

In linear discriminant analysis, the assumption of equality of the dispersion matrices of different classes leads to a classification rule based on minimum Mahalanobis distance from the class centres. However, without this assumption, the resulting quadratic discriminant classifier involves, in addition to the Mahalanobis distances, the ratio of the determinants of the dispersion matrices as a factor. In fact, it has been observed that, for discriminating between populations with underlying elliptically symmetric distributions, such classifiers also incorporate similar factors, apart from the Mahalanobis distances.In this paper, a nonparametric classification technique which generalizes discriminant analysis has been proposed. The method of cross-validation is used to make the technique adaptive to a given dataset. An extensive simulation study is presented to illustrate the potential of the method. Finally, through implementation on a number of real-life data sets, it has been demonstrated that the proposed generalized quadratic discriminant analysis (GQDA) compares very favourably with other nonparametric methods, and is computationally cost-effective.

Classification of in-tube boiling R134a data belonging to the smooth and corrugated tubes

Different types of tubes have been used to improve cooling systems regarding the performance, cost and compactness. Corrugated tubes are tubes with their inner surface enhanced in these systems. One of the applications of machine learning, named as pattern classification, is often used to separate the human faces, voices, finger prints etc. In this study, it is used to separate the R134a data taken in-tube boiling process in smooth and enhanced tubes automatically. In other words, the developed numerical algorithms enabled artificial intelligence to predict the type of tubes having equivalent diameters used in the experiments. Systematical experiments, including saturation temperatures of 10, 15 and 20°C, mass fluxes of 200, 300 and 400kgm−2s−1 and heat fluxes of 20, 25 and 30Wm−2, are carried out for the comparisons using smooth and 5 different types of corrugated tubes having various corrugation depths and helix angles. The boiling process in the test tubes has been measured with 300 data points, having 30 individual parameters (inputs) for varying tube types for the reduction process by the Linear Discriminant Analysis (LDA) and Principle Component Analysis (PCA). The classification success rates of the methods of Linear Discriminant Classifier (LDC), Quadratic Discriminant Classifier (QDC), Naive Bayes Classifier (NBC) and Minimum Mahalanobis Distance Classifier (MMDC) by each dimensional reduction and the total area occupying under receiver operating characteristic (ROC) curves are determined according to 3-fold cross validation method. NBC method has the highest classification success with the accuracy of 98.33% as a result of the reduction to 3 dimensions by LDA method. In addition to this, QDC method has the highest area under curve (AUC) with the value of 0.9994 according to the reduction to 3 dimensions by LDA method. Dependency analyses showed that the use of 8 dimensional experimental parameters as the most important input is enough to determine the type of test tubes with a high accuracy.

Band-Reweighed Gabor Kernel Embedding for Face Image Representation and Recognition.

Face recognition with illumination or pose variation is a challenging problem in image processing and pattern recognition. A novel algorithm using band-reweighed Gabor kernel embedding to deal with the problem is proposed in this paper. For a given image, it is first transformed by a group of Gabor filters, which output Gabor features using different orientation and scale parameters. Fisher scoring function is used to measure the importance of features in each band, and then, the features with the largest scores are preserved for saving memory requirements. The reduced bands are combined by a vector, which is determined by a weighted kernel discriminant criterion and solved by a constrained quadratic programming method, and then, the weighted sum of these nonlinear bands is defined as the similarity between two images. Compared with existing concatenation-based Gabor feature representation and the uniformly weighted similarity calculation approaches, our method provides a new way to use Gabor features for face recognition and presents a reasonable interpretation for highlighting discriminant orientations and scales. The minimum Mahalanobis distance considering the spatial correlations within the data is exploited for feature matching, and the graphical lasso is used therein for directly estimating the sparse inverse covariance matrix. Experiments using benchmark databases show that our new algorithm improves the recognition results and obtains competitive performance.

Human Detection by Quadratic Classification on Subspace of Extended Histogram of Gradients

This paper proposes a quadratic classification approach on the subspace of Extended Histogram of Gradients (ExHoG) for human detection. By investigating the limitations of Histogram of Gradients (HG) and Histogram of Oriented Gradients (HOG), ExHoG is proposed as a new feature for human detection. ExHoG alleviates the problem of discrimination between a dark object against a bright background and vice versa inherent in HG. It also resolves an issue of HOG whereby gradients of opposite directions in the same cell are mapped into the same histogram bin. We reduce the dimensionality of ExHoG using Asymmetric Principal Component Analysis (APCA) for improved quadratic classification. APCA also addresses the asymmetry issue in training sets of human detection where there are much fewer human samples than non-human samples. Our proposed approach is tested on three established benchmarking data sets--INRIA, Caltech, and Daimler--using a modified Minimum Mahalanobis distance classifier. Results indicate that the proposed approach outperforms current state-of-the-art human detection methods.