Attempts to incorporate topological information in supervised learning tasks have resulted in the creation of several techniques for vectorizing persistent homology barcodes. In this paper, we study thirteen such methods. Besides describing an organizational framework for these methods, we comprehensively benchmark them against three well-known classification tasks. Surprisingly, we discover that the best-performing method is a simple vectorization, which consists only of a few elementary summary statistics. Finally, we provide a convenient web application which has been designed to facilitate exploration and experimentation with various vectorization methods.

Covid-19 first occurred in Wuhan, China in December 2019. Subsequently, the virus spread throughout the world and as of June 2020 the total number of confirmed cases are above 4.7 million with over 315,000 deaths. Machine learning algorithms built on radiography images can be used as a decision support mechanism to aid radiologists to speed up the diagnostic process. The aim of this work is to conduct a critical analysis to investigate the applicability of convolutional neural networks (CNNs) for the purpose of COVID-19 detection in chest X-ray images and highlight the issues of using CNN directly on the whole image. To accomplish this task, we use 12-off-the-shelf CNN architectures in transfer learning mode on 3 publicly available chest X-ray databases together with proposing a shallow CNN architecture in which we train it from scratch. Chest X-ray images are fed into CNN models without any preprocessing to replicate researches used chest X-rays in this manner. Then a qualitative investigation performed to inspect the decisions made by CNNs using a technique known as class activation maps (CAM). Using CAMs, one can map the activations contributed to the decision of CNNs back to the original image to visualize the most discriminating region(s) on the input image. We conclude that CNN decisions should not be taken into consideration, despite their high classification accuracy, until clinicians can visually inspect and approve the region(s) of the input image used by CNNs that lead to its prediction.

An important tool in the field of topological data analysis is persistent homology (PH), which is used to encode abstract representations of the homology of data at different resolutions in the form of persistence barcode (PB). Normally, one will obtain one PB from a digital image when using a sublevel-set filtration method. In this work, we built more than one PB representation of a single image based on a landmark selection method, known as local binary patterns (LBP), which encode different types of local texture from a digital image. Starting from the top-left corner of any 3-by-3 patch selected from an input image, the LBP process starts by subtracting the central pixel value from its eight neighboring pixel values. Then, each cell is assigned with 1 if the subtraction outcome is positive, and 0 otherwise, to obtain an 8-bit binary representation. This process will identify a set of landmark pixels to represent 0-simplices and use Vietoris–Rips filtration to obtain its corresponding PB. Using LBP, we can construct up to 56 PBs from a single image if we restrict to only using the binary codes that have two circular transitions between 1 and 0. The information within these 56 PBs contain detailed local and global topological and geometrical information, which can be used to design effective machine learning models. We used four different PB vectorizations, namely, persistence landscapes, persistence images, Betti curves (barcode binning), and PB statistics. We tested the effectiveness of the proposed landmark-based PH on two publicly available breast abnormality detection datasets using mammogram scans. The sensitivity and specificity of the landmark-based PH obtained was over 90% and 85%, respectively, in both datasets for the detection of abnormal breast scans. Finally, the experimental results provide new insights on using different PB vectorizations with sublevel set filtrations and landmark-based Vietoris–Rips filtration from digital mammogram scans.

The Covid-19 first occurs in Wuhan, China in December 2019. After that the virus spread all around the world and at the time of writing this paper the total number of confirmed cases are above 4.7 million with over 315000 deaths. Machine learning algorithms built on radiography images can be used as a decision support mechanism to aid radiologists to speed up the diagnostic process. The aim of this work is to conduct a critical analysis to investigate the applicability of convolutional neural networks (CNNs) for the purpose of COVID-19 detection in chest X-ray images and highlight the issues of using CNN directly on the whole image. To achieve this task, we first use 12-off-the-shelf CNN architectures in transfer learning mode on 3 publicly available chest X-ray databases together with proposing a shallow CNN architecture in which we train it from scratch. Chest X-ray images fed into CNN models without any preprocessing to follow the many of researches using chest X-rays in this manner. Next, a qualitative investigation performed to inspect the decisions made by CNNs using a technique known as class activation maps (CAM). Using CAMs, one can map the activations contributed most to the decision of CNNs back to the original image to visualize the most discriminating regions on the input image. We conclude that CNN decisions should not be taken into consideration, despite their high classification accuracy, until clinicians can visually inspect, and approve, the region(s) of the input image used by CNNs that lead to its prediction.