Anomaly detection (AD) in images, identifying significant deviations from normality, is a critical issue in computer vision. This paper introduces a novel approach to dimensionality reduction for AD using pre-trained convolutional neural network (CNN) that incorporate EfficientNet models. We investigate the importance of component selection and propose two types of tree search approaches, both employing a greedy strategy, for optimal eigencomponent selection. Our study conducts three main experiments to evaluate the effectiveness of our approach. The first experiment explores the influence of test set performance on component choice, the second experiment examines the performance when we train on one anomaly type and evaluate on all other types, and the third experiment investigates the impact of using a minimum number of images for training and selecting them based on anomaly types. Our approach aims to find the optimal subset of components that deliver the highest performance score, instead of focusing solely on the proportion of variance explained by each component and also understand the components behaviour in different settings. Our results indicate that the proposed method surpasses both Principal Component Analysis (PCA) and Negated Principal Component Analysis (NPCA) in terms of detection accuracy, even when using fewer components. Thus, our approach provides a promising alternative to conventional dimensionality reduction techniques in AD, and holds potential to enhance the efficiency and effectiveness of AD systems.

Dimension reduction is crucial in functional data analysis (FDA). The key tool to reduce the dimension of the data is functional principal component analysis. Existing approaches for functional principal component analysis usually involve the diagonalization of the covariance operator. With the increasing size and complexity of functional datasets, estimating the covariance operator has become more challenging. Therefore, there is a growing need for efficient methodologies to estimate the eigencomponents. Using the duality of the space of observations and the space of functional features, we propose to use the inner-product between the curves to estimate the eigenelements of multivariate and multidimensional functional datasets. The relationship between the eigenelements of the covariance operator and those of the inner-product matrix is established. We explore the application of these methodologies in several FDA settings and provide general guidance on their usability.

Gaussian Graphical models (GGM) are widely used to estimate the network structures in many applications ranging from biology to finance. In practice, data is often corrupted by latent confounders which biases inference of the underlying true graphical structure. In this paper, we compare and contrast two strategies for inference in graphical models with latent confounders: Gaussian graphical models with latent variables (LVGGM) and PCA-based removal of confounding (PCA+GGM). While these two approaches have similar goals, they are motivated by different assumptions about confounding. In this paper, we explore the connection between these two approaches and propose a new method, which combines the strengths of these two approaches. We prove the consistency and convergence rate for the PCA-based method and use these results to provide guidance about when to use each method. We demonstrate the effectiveness of our methodology using both simulations and in two real-world applications.