Mahalanobis distance

About: Mahalanobis distance is a research topic. Over the lifetime, 4616 publications have been published within this topic receiving 95294 citations.

Modeling the Distribution of Normal Data in Pre-Trained Deep Features for Anomaly Detection

Abstract: Anomaly Detection (AD) in images is a fundamental computer vision problem and refers to identifying images and/or image substructures that deviate significantly from the norm. Popular AD algorithms commonly try to learn a model of normality from scratch using task specific datasets, but are limited to semi-supervised approaches employing mostly normal data due to the inaccessibility of anomalies on a large scale combined with the ambiguous nature of anomaly appearance. We follow an alternative approach and demonstrate that deep feature representations learned by discriminative models on large natural image datasets are well suited to describe normality and detect even subtle anomalies in a transfer learning setting. Our model of normality is established by fitting a multivariate Gaussian (MVG) to deep feature representations of classification networks trained on ImageNet using normal data only. By subsequently applying the Mahalanobis distance as the anomaly score we outperform the current state of the art on the public MVTec AD dataset, achieving an Area Under the Receiver Operating Characteristic curve of 95.8 ± 1.2% (mean ± SEM) over all 15 classes. We further investigate why the learned representations are discriminative to the AD task using Principal Component Analysis. We find that the principal components containing little variance in normal data are the ones crucial for discriminating between normal and anomalous instances. This gives a possible explanation to the often subpar performance of AD approaches trained from scratch using normal data only. By selectively fitting a MVG to these most relevant components only, we are able to further reduce model complexity while retaining AD performance. We also investigate setting the working point by selecting acceptable False Positive Rate thresholds based on the MVG assumption. Code is publicly available at https://github.com/ORippler/gaussian-ad-mvtec.

Improving Reconstruction Autoencoder Out-of-distribution Detection with Mahalanobis Distance.

Abstract: There is an increasingly apparent need for validating the classifications made by deep learning systems in safety-critical applications like autonomous vehicle systems. A number of recent papers have proposed methods for detecting anomalous image data that appear different from known inlier data samples, including reconstruction-based autoencoders. Autoencoders optimize the compression of input data to a latent space of a dimensionality smaller than the original input and attempt to accurately reconstruct the input using that compressed representation. Since the latent vector is optimized to capture the salient features from the inlier class only, it is commonly assumed that images of objects from outside of the training class cannot effectively be compressed and reconstructed. Some thus consider reconstruction error as a kind of novelty measure. Here we suggest that reconstruction-based approaches fail to capture particular anomalies that lie far from known inlier samples in latent space but near the latent dimension manifold defined by the parameters of the model. We propose incorporating the Mahalanobis distance in latent space to better capture these out-of-distribution samples and our results show that this method often improves performance over the baseline approach.

Modeling hyperspectral imaging data

Abstract: Developing proper models for hyperspectral imaging (HSI) data allows for useful and reliable algorithms for data exploitation. These models provide the foundation for development and evaluation of detection, classification, clustering, and estimation algorithms. To date, real world HSI data has been modeled as a single multivariate Gaussian, however it is well known that real data often exhibits non-Gaussian behavior with multi-modal distributions. Instead of the single multivariate Gaussian distribution, HSI data can be model as a finite mixture model, where each of the mixture components need not be Gaussian. This paper will focus on techniques used to segment HSI data into homogenous clusters. Once the data has been segmented, each individual cluster can be modeled, and the benefits provided by the homogeneous clustering of the data versus non-clustering explored. One of the promising techniques uses the Expectation-Maximization (EM) algorithm to cluster the data into Elliptically Contoured Distributions (ECDs). A larger family of distributions, the family of ECDs includes the mutlivariate Gaussian distribution and exhibits most of its properties. ECDs are uniquely defined by their multivariate mean, covariance and the distribution of its Mahalanobis (or quadratic) distance metric. This metric lets multivariate data be identified using a univariate statistic and can be adjusted to more closely match the longer tailed distributions of real data. This paper will focus on three issues. First, the definition of the multivariate Elliptically Contoured Distribution mixture model will be developed. Second, various techniques will be described that segment the mixed data into homogeneous clusters. Most of this work will focus on the EM algorithm and the multivariate t-distribution, which is a member of the family of ECDs and provides longer tailed distributions than the Gaussian. Lastly, results using HSI data from the AVIRIS sensor will be shown, and the benefits of clustered data will be presented.

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

Abstract: 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.