At the end of 2019 anew coronavirus, SARS-CoV-2, was identified as responsible for the lung infection, now called COVID-19 (coronavirus disease 2019). Since then there has been an exponential growth of infections and at the beginning of March 2020 the WHO declared the epidemic a global emergency. An early diagnosis of those carrying the virus becomes crucial to contain the spread, morbidity and mortality of the pandemic. The definitive diagnosis is made through specific tests, among which imaging tests play an important role in the care path of the patient with suspected or confirmed COVID-19. Patients with serious COVID-19 typically experience viral pneumonia. This paper uses the Multiple Instance Learning paradigm to classify pneumonia X-ray images, considering three diferent classes: radiographies of healthy people, radiographies of people with bacterial pneumonia and of people with viral pneumonia. The proposed algorithms, which are very fast in practice, appear promising especially if we take into account that no preprocessing technique has been used.
assessment of COVID-19 chest radiography (CXR) and computed tomography (CT) are used. CT imaging shows high sensitivity, but X-ray imaging is cheaper, easier to perform and in addition (portable) X-ray machines are much more available also in poor and developing countries [2, 3]. The idea underlying this work arises within the described scenario, characterized by an intense activity of scientific research, aimed at supporting fast solutions for diagnostics on COVID-19, which is a special case of viral pneumonia. Considering that there are recurring features that characterize the radiographs of patients afected by viral pneumonia, we propose a chest X-ray classification technique based on the Multiple Instance Learning (MIL) approach.
We have considered a subset of images taken from the public Kaggle chest X-ray dataset [4] from which we have randomly extracted 50 images related to radiography of healthy people, 50 of people with bacterial pneumonia and 50 of people with viral pneumonia. This data set is widely used in the literature in connection with specific COVID-19 data sets, as reported in [ 5].
Multiple Instance Learning [6] is a classification technique consisting in the separation of point sets: such sets are called bags and the points inside the sets are called instances. The main diference of a MIL approach with respect to the classical supervised classification is that in the learning phase only the class labels of the bags are known, while the class labels of the instances remain unknown. A particular role played by MIL is in medical image and video analysis, as shown in [7]. Diagnostics by means of image analysis is an important field in order to support physicians to have early diagnoses [8, 9, 10]. We focus on binary MIL classification with two classes of instances, on the basis of the the so-called standard MIL assumption, which considers positive a bag containing at least a positive instance and negative a bag containing only negative instances. Such assumption fits very well with diagnostics by images: in fact a patient is non-healthy (i.e. is positive) if his/her medical scan (bag) contains at least an abnormal subregion and is healthy if all the subregions forming his/her medical scan are normal. In [11] a MIL approach has been used for melanoma detection on color dermoscopic images, with the aim to discriminate between melanomas (positive images) and common nevi (negative images). The obtained results encourage to investigate possible use of MIL techniques also in viral pneumonia detection by means of chest X-rays images. In particular, using binary MIL classification techniques, our aim is to discriminate between X-rays images of healthy patients versus patients with bacteria pneumonia, healthy patients versus patients with viral pneumonia and patients with bacteria pneumonia versus patients with viral pneumonia.
MIL-RL algorithm [12] is an instance-level technique based on solving, by Lagrangian relaxation
[13], the Support Vector Machine (SVM) type model proposed by Andrews et al. in [14]. Such
model, providing an SVM separating hyperplane of the type
(, ) =△ { ∈ R | + = 0},
(
Variables and correspond respectively to the bias and normal to the hyperplane, variable gives a measure of the misclassification error of the instance , while is the class label to be assigned to the instances of the positive bags. The positive parameter tunes the weight between the maximization of the margin, obtained by minimizing the Euclidean norm of , and the minimization of the misclassification errors of the instances. Finally, the constraints ∈+ ∑︁ + 1 ≥ 1 = 1, . . . ,
2
impose that, for each positive bag, at least one instance should be positive (i.e. with label equal
to +1). Note that, when = = 1 and = +1 for any , problem (
Algorithm mi-SPSVM has been introduced in [15] and it exploits the good properties exhibited
for supervised classification by the SVM technique in terms of accuracy and by the PSVM
(Proximal Support Vector Machine) approach [16] in terms of eficiency. It computes a separating
hyperplane of the type (
∈−
= 1 − ( + ) ∈ +
≥ 1 + ( + ) ∈ −
≥ 0 ∈ − ,
(
¯ + := + ∖
¯ − := − ∪ and 1}, where ¯ = { ∈ + ∖ * | * + * ≤ − with * = {* , = 1, . . . , | * * + * ≤ − 1} and * =△ arg max∈(+∩+){* + * }.
Some comments on the updating of the sets + and − are in order. A particular role in the
definition of the set ¯ is played by the set * , introduced for taking into account constraints (
No pre-processing step is performed in this paper. This assumption allows us to attribute the results only to the performance of the applied algorithms and not to the goodness of the pre-processing phase. A balanced dataset extracted from from the public dataset ([4]) available at https://www.kaggle.com/paultimothymooney/chest-xray-pneumonia consists of 50 images of healthy people (Figure 1), 50 of people with bacterial pneumonia (Figure 2) and 50 of people with viral pneumonia (Figure 3) This proposal uses the Matlab implementation of MIL-RL in [11] and the Matlab implementation of mi-SPSVM in [15].
As for the segmentation process, we have adopted a procedure similar to that one used in [17]. In particular, we have reduced the resolution of each image to 128 × 128 pixels dimension and we have grouped the pixels in appropriate square subregions (blobs). In this way, each image is represented as a bag, while a blob corresponds to an instance of the bag. For each instance (blob), we have considered the following 10 features: the average and the variance of the grey-scale intensity of the blob: 2 features; the diferences between the average of the grey-scale intensity of the blob and that ones of the adjacent blobs (upper, lower, left, right): 4 features; the diferences between the variance of the grey-scale intensity of the blob and that ones of the adjacent blobs (upper, lower, left, right): 4 features.
The following X-ray chest images classification have been performed: (i) bacterial pneumonia (positive) images versus normal (negative) images (Table 1); (ii) viral pneumonia (positive) images versus normal (negative) images (Table 2); (iii) viral pneumonia (positive) images versus bacterial pneumonia (negative) images (Table 3).
In particular, in order to consider diferent sizes of the testing and training sets, we have
used three diferent validation protocols: the 5-fold cross-validation (5-CV), the 10-fold
crossvalidation (10-CV) and the Leave-One-Out validation. As for the optimal computation of the
tuning parameter C characterizing the models (
Correctness (%) Sensitivity (%) Specificity (%)
F-score (%) CPU time (secs)
Tables 1, 2 and 3 report the average values provided by MIL-RL and mi-SPSVM in terms of correctness (accuracy), sensitivity, specificity and F-score, computed on the testing set and the average CPU time spent by the classifier to determine the optimal separation hyperplane. Observe that mi-SPSVM is clearly faster than MIL-RL and, in general, it classifies better, even if the accuracy results provided by the two codes appear comparable. In classifying bacterial pneumonia (Table 1) and viral pneumonia (Table 2) against normal X-ray chest images we obtain high values of accuracy (about 90%) and sensitivity (about 94%). We recall that the sensitivity (also called true positive rate) is a very important parameter in diagnostics since it measures the proportion of positive patients correctly identified. On the other hand, when we discriminate between the viral pneumonia and the bacterial pneumonia images (Table 3), we obtain lower results with respect to those ones reported in Tables 1 and 2, as expected since the two classes are very similar. Nevertheless, these values appear reasonable, especially in terms of sensitivity (82% provided by mi-SPSVM) and of F-score (75.93%).
This work presented some preliminary numerical results obtained from classification of viral
pneumonia against bacterial pneumonia and normal X-ray chest images, by means of MIL
algorithms. Results appear promising, especially considering that no preprocessing phase has
been performed. Moreover our MIL techniques appear appealing also in terms of computational
eficiency, since the separation hyperplane is always obtained in less than one second. Future
research could consist in appropriately preprocessing the images and in considering additional
features [19, 20] to be exploited in the classification process, including also COVID-19 chest
X-ray images and distributing the classification algorithms [ 21]. Our aim goal is to create
a framework that can support the diagnostics of COVID-19, possibly by expanding one of
our solutions already implemented [22] in a distributed environment [23, 24, 25, 26] and also
including aspects of process management from a health perspective [27]. As for further future
research we plan to apply the MIL approach to other medical domains such as [28, 29, 30, 9].
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