Linear optimal transport subspaces for point set classification

Learning from point sets is an essential component in many computer vision and machine learning applications. Native, unordered, and permutation invariant set structure space is challenging to model, particularly for point set classification under spatial deformations. Here we propose a framework for classifying point sets experiencing certain types of spatial deformations, with a particular emphasis on datasets featuring affine deformations. Our approach employs the Linear Optimal Transport (LOT) transform to obtain a linear embedding of set-structured data. Utilizing the mathematical properties of the LOT transform, we demonstrate its capacity to accommodate variations in point sets by constructing a convex data space, effectively simplifying point set classification problems. Our method, which employs a nearest-subspace algorithm in the LOT space, demonstrates label efficiency, non-iterative behavior, and requires no hyper-parameter tuning. It achieves competitive accuracies compared to state-of-the-art methods across various point set classification tasks. Furthermore, our approach exhibits robustness in out-of-distribution scenarios where training and test distributions vary in terms of deformation magnitudes.

End-to-End Signal Classification in Signed Cumulative Distribution Transform Space

This paper presents a new end-to-end signal classification method using the signed cumulative distribution transform (SCDT). We adopt a transport generative model to define the classification problem. We then make use of mathematical properties of the SCDT to render the problem easier in transform domain, and solve for the class of an unknown sample using a nearest local subspace (NLS) search algorithm in SCDT domain. Experiments show that the proposed method provides high accuracy classification results while being computationally cheap, data efficient, and robust to out-of-distribution samples with respect to the existing end-to-end classification methods. The implementation of the proposed method in Python language is integrated as a part of the software package PyTransKit.

Invariance encoding in sliced-Wasserstein space for image classification with limited training data

Deep convolutional neural networks (CNNs) are broadly considered to be state-of-the-art generic end-to-end image classification systems. However, they are known to underperform when training data are limited and thus require data augmentation strategies that render the method computationally expensive and not always effective. Rather than using a data augmentation strategy to encode invariances as typically done in machine learning, here we propose to mathematically augment a nearest subspace classification model in sliced-Wasserstein space by exploiting certain mathematical properties of the Radon Cumulative Distribution Transform (R-CDT), a recently introduced image transform. We demonstrate that for a particular type of learning problem, our mathematical solution has advantages over data augmentation with deep CNNs in terms of classification accuracy and computational complexity, and is particularly effective under a limited training data setting. The method is simple, effective, computationally efficient, non-iterative, and requires no parameters to be tuned. Python code implementing our method is available at https://github.com/rohdelab/mathematical augmentation. Our method is integrated as a part of the software package PyTransKit, which is available at https://github.com/rohdelab/PyTransKit.

Real-time intelligent classification of COVID-19 and thrombosis via massive image-based analysis of platelet aggregates

Microvascular thrombosis is a typical symptom of COVID-19 and shows similarities to thrombosis. Using a microfluidic imaging flow cytometer, we measured the blood of 181 COVID-19 samples and 101 non-COVID-19 thrombosis samples, resulting in a total of 6.3 million bright-field images. We trained a convolutional neural network to distinguish single platelets, platelet aggregates, and white blood cells and performed classical image analysis for each subpopulation individually. Based on derived single-cell features for each population, we trained machine learning models for classification between COVID-19 and non-COVID-19 thrombosis, resulting in a patient testing accuracy of 75%. This result indicates that platelet formation differs between COVID-19 and non-COVID-19 thrombosis. All analysis steps were optimized for efficiency and implemented in an easy-to-use plugin for the image viewer napari, allowing the entire analysis to be performed within seconds on mid-range computers, which could be used for real-time diagnosis.

Massive image-based single-cell profiling reveals high levels of circulating platelet aggregates in patients with COVID-19

A characteristic clinical feature of COVID-19 is the frequent incidence of microvascular thrombosis. In fact, COVID-19 autopsy reports have shown widespread thrombotic microangiopathy characterized by extensive diffuse microthrombi within peripheral capillaries and arterioles in lungs, hearts, and other organs, resulting in multiorgan failure. However, the underlying process of COVID-19-associated microvascular thrombosis remains elusive due to the lack of tools to statistically examine platelet aggregation (i.e., the initiation of microthrombus formation) in detail. Here we report the landscape of circulating platelet aggregates in COVID-19 obtained by massive single-cell image-based profiling and temporal monitoring of the blood of COVID-19 patients (n = 110). Surprisingly, our analysis of the big image data shows the anomalous presence of excessive platelet aggregates in nearly 90% of all COVID-19 patients. Furthermore, results indicate strong links between the concentration of platelet aggregates and the severity, mortality, respiratory condition, and vascular endothelial dysfunction level of COVID-19 patients.

Radon Cumulative Distribution Transform Subspace Modeling for Image Classification

We present a new supervised image classification method applicable to a broad class of image deformation models. The method makes use of the previously described Radon Cumulative Distribution Transform (R-CDT) for image data, whose mathematical properties are exploited to express the image data in a form that is more suitable for machine learning. While certain operations such as translation, scaling, and higher-order transformations are challenging to model in native image space, we show the R-CDT can capture some of these variations and thus render the associated image classification problems easier to solve. The method - utilizing a nearest-subspace algorithm in the R-CDT space - is simple to implement, non-iterative, has no hyper-parameters to tune, is computationally efficient, label efficient, and provides competitive accuracies to state-of-the-art neural networks for many types of classification problems. In addition to the test accuracy performances, we show improvements (with respect to neural network-based methods) in terms of computational efficiency (it can be implemented without the use of GPUs), number of training samples needed for training, as well as out-of-distribution generalization. The Python code for reproducing our results is available at [1].

Cell Image Classification: A Comparative Overview

Cell image classification methods are currently being used in numerous applications in cell biology and medicine. Applications include understanding the effects of genes and drugs in screening experiments, understanding the role and subcellular localization of different proteins, as well as diagnosis and prognosis of cancer from images acquired using cytological and histological techniques. The article also reviews three main approaches for cell image classification most often used: numerical feature extraction, end-to-end classification with neural networks (NNs), and transport-based morphometry (TBM). In addition, we provide comparisons on four different cell imaging datasets to highlight the relative strength of each method. The results computed using four publicly available datasets show that numerical features tend to carry the best discriminative information for most of the classification tasks. Results also show that NN-based methods produce state-of-the-art results in the dataset that contains a relatively large number of training samples. Data augmentation or the choice of a more recently reported architecture does not necessarily improve the classification performance of NNs in the datasets with limited number of training samples. If understanding and visualization are desired aspects, TBM methods can offer the ability to invert classification functions, and thus can aid in the interpretation of results. These and other comparison outcomes are discussed with the aim of clarifying the advantages and disadvantages of each method. © 2020 International Society for Advancement of Cytometry.