Domain Generalization for Medical Image Analysis: A Survey

Medical Image Analysis (MedIA) has become an essential tool in medicine and healthcare, aiding in disease diagnosis, prognosis, and treatment planning, and recent successes in deep learning (DL) have made significant contributions to its advances. However, DL models for MedIA remain challenging to deploy in real-world situations, failing for generalization under the distributional gap between training and testing samples, known as a distribution shift problem. Researchers have dedicated their efforts to developing various DL methods to adapt and perform robustly on unknown and out-of-distribution data distributions. This paper comprehensively reviews domain generalization studies specifically tailored for MedIA. We provide a holistic view of how domain generalization techniques interact within the broader MedIA system, going beyond methodologies to consider the operational implications on the entire MedIA workflow. Specifically, we categorize domain generalization methods into data-level, feature-level, model-level, and analysis-level methods. We show how those methods can be used in various stages of the MedIA workflow with DL equipped from data acquisition to model prediction and analysis. Furthermore, we include benchmark datasets and applications used to evaluate these approaches and analyze the strengths and weaknesses of various methods, unveiling future research opportunities

Data Visualization, Dimensionality Reduction, and Data Alignment via Manifold Learning

The high dimensionality of modern data introduces significant challenges in descriptive and exploratory data analysis. These challenges gave rise to extensive work on dimensionality reduction and manifold learning aiming to provide low dimensional representations that preserve or uncover intrinsic patterns and structures in the data. In this thesis, we expand the current literature in manifold learning developing two methods called DIG (Dynamical Information Geometry) and GRAE (Geometry Regularized Autoencoders). DIG is a method capable of finding low-dimensional representations of high-frequency multivariate time series data, especially suited for visualization. GRAE is a general framework which splices the well-established machinery from kernel manifold learning methods to recover a sensitive geometry, alongside the parametric structure of autoencoders. Manifold learning can also be useful to study data collected from different measurement instruments, conditions, or protocols of the same underlying system. In such cases the data is acquired in a multi-domain representation. The last two Chapters of this thesis are devoted to two new methods capable of aligning multi-domain data, leveraging their geometric structure alongside limited common information. First, we present DTA (Diffusion Transport Alignment), a semi-supervised manifold alignment method that exploits prior one-to-one correspondence knowledge between distinct data views and finds an aligned common representation. And finally, we introduce MALI (Manifold Alignment with Label Information). Here we drop the one-to-one prior correspondences assumption, since in many scenarios such information can not be provided, either due to the nature of the experimental design, or it becomes extremely costly. Instead, MALI only needs side-information in the form of discrete labels/classes present in both domains

Support matrix machine: A review

Support vector machine (SVM) is one of the most studied paradigms in the realm of machine learning for classification and regression problems. It relies on vectorized input data. However, a significant portion of the real-world data exists in matrix format, which is given as input to SVM by reshaping the matrices into vectors. The process of reshaping disrupts the spatial correlations inherent in the matrix data. Also, converting matrices into vectors results in input data with a high dimensionality, which introduces significant computational complexity. To overcome these issues in classifying matrix input data, support matrix machine (SMM) is proposed. It represents one of the emerging methodologies tailored for handling matrix input data. The SMM method preserves the structural information of the matrix data by using the spectral elastic net property which is a combination of the nuclear norm and Frobenius norm. This article provides the first in-depth analysis of the development of the SMM model, which can be used as a thorough summary by both novices and experts. We discuss numerous SMM variants, such as robust, sparse, class imbalance, and multi-class classification models. We also analyze the applications of the SMM model and conclude the article by outlining potential future research avenues and possibilities that may motivate academics to advance the SMM algorithm

Learning Graphical Models of Multivariate Functional Data with Applications to Neuroimaging

This dissertation investigates the functional graphical models that infer the functional connectivity based on neuroimaging data, which is noisy, high dimensional and has limited samples. The dissertation provides two recipes to infer the functional graphical model: 1) a fully Bayesian framework 2) an end-to-end deep model. We first propose a fully Bayesian regularization scheme to estimate functional graphical models. We consider a direct Bayesian analog of the functional graphical lasso proposed by Qiao et al. (2019).. We then propose a regularization strategy via the graphical horseshoe. We compare both Bayesian approaches to the frequentist functional graphical lasso, and compare the Bayesian functional graphical lasso to the functional graphical horseshoe. We applied the proposed methods with electroencephalography (EEG) data and diffusion tensor imaging (DTI) data. We find that the Bayesian methods tend to outperform the standard functional graphical lasso, and that the functional graphical horseshoe performs best overall, a procedure for which there is no direct frequentist analog. Then we consider a deep neural network architecture to estimate functional graphical models, by combining two simple off-the-shelf algorithms: adaptive functional principal components analysis (FPCA) Yao et al., 2021a) and convolutional graph estimator (Belilovsky et al., 2016). We train our proposed model with synthetic data which emulate the real world observations and prior knowledge. Based on synthetic data generation process, our model convert an inference problem as a supervised learning problem. Compared with other framework, our proposed deep model which offers a general recipe to infer the functional graphical model based on data-driven approach, take the raw functional dataset as input and avoid deriving sophisticated closed-form. Through simulation studies, we find that our deep functional graph model trained on synthetic data generalizes well and outperform other popular baselines marginally. In addition, we apply deep functional graphical model in the real world EEG data, and our proposed model discover meaningful brain connectivity. Finally, we are interested in estimating casual graph with functional input. In order to process functional covariates in causal estimation, we leverage the similar strategy as our deep functional graphical model. We extend popular deep causal models to infer causal effects with functional confoundings within the potential outcomes framework. Our method is simple yet effective, where we validate our proposed architecture in variety of simulation settings. Our work offers an alternative way to do causal inference with functional data

Graph analysis of functional brain networks: practical issues in translational neuroscience

The brain can be regarded as a network: a connected system where nodes, or units, represent different specialized regions and links, or connections, represent communication pathways. From a functional perspective communication is coded by temporal dependence between the activities of different brain areas. In the last decade, the abstract representation of the brain as a graph has allowed to visualize functional brain networks and describe their non-trivial topological properties in a compact and objective way. Nowadays, the use of graph analysis in translational neuroscience has become essential to quantify brain dysfunctions in terms of aberrant reconfiguration of functional brain networks. Despite its evident impact, graph analysis of functional brain networks is not a simple toolbox that can be blindly applied to brain signals. On the one hand, it requires a know-how of all the methodological steps of the processing pipeline that manipulates the input brain signals and extract the functional network properties. On the other hand, a knowledge of the neural phenomenon under study is required to perform physiological-relevant analysis. The aim of this review is to provide practical indications to make sense of brain network analysis and contrast counterproductive attitudes