Vol-3194/paper43
Wolfgang Fahl
Paper
| Paper | |
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 edit
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| description | |
| id | Vol-3194/paper43 |
| wikidataid | Q117344894→Q117344894 |
| title | Multiple Instance Learning for viral pneumonia chest X-ray Classification |
| pdfUrl | https://ceur-ws.org/Vol-3194/paper43.pdf |
| dblpUrl | https://dblp.org/rec/conf/sebd/AvolioFVZ22 |
| volume | Vol-3194→Vol-3194 |
| session | → |
Paper[edit]
| Paper | |
|---|---|
| edit
| |
| description | |
| id | Vol-3194/paper43 |
| wikidataid | Q117344894→Q117344894 |
| title | Multiple Instance Learning for viral pneumonia chest X-ray Classification |
| pdfUrl | https://ceur-ws.org/Vol-3194/paper43.pdf |
| dblpUrl | https://dblp.org/rec/conf/sebd/AvolioFVZ22 |
| volume | Vol-3194→Vol-3194 |
| session | → |
Multiple Instance Learning for viral pneumonia chest X-ray Classification[edit]
Multiple Instance Learning for Viral Pneumonia Chest
X-ray Classification
(Discussion Paper)
Matteo Avolio1,3 , Antonio Fuduli1,3 , Eugenio Vocaturo2,3 and Ester Zumpano2,3
1
Department of Mathematics and Computer Science - University of Calabria, Rende, Italy
2
Department of Computer Engineering, Modeling, Electronics, and Systems Sciences - University of Calabria, Rende, Italy
3
CNR-NANOTEC National Research Council, Rende, Italy
Abstract
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 different 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.
Keywords
Pneumonia imaging Classification, Multiple Instance Learning, Machine Learning
1. Introduction
The world is coping with the COVID-19 pandemic. COVID-19 is caused by a Severe Acute
Respiratory Sindrome Coronavirus (SARS-CoV-2) and its common symptoms are: fever, dry
cough, fatique, short breathing, vanishing of taste, loss of smell. The most effective way to limit
the spread of COVID-19 and the number of deaths is to identify infected persons at an early
stage of the disease and many different proposals have been investigated for the development
of automatic screening of COVID-19 from medical images analysis. COVID-19 has interstitial
pneumonia as the predominant clinical manifestation. Radiological imaging is able to highlight
any pneumonia: in the case of Coronavirus (Sars-Cov2) infection, it is possible to see an opacity
on the radiograph, called thickening and a greater extension of the pulmonary thickening [1].
Therefore, while huge challenges need to be faced, medical imaging analysis arises as a key
factor in the screening of viral pneumonia from bacteria pneumonia. In reasoning on the
SEBD 2022: The 30th Italian Symposium on Advanced Database Systems, June 19-22, 2022, Tirrenia (PI), Italy
" matteo.avolio@unical.it (M. Avolio); antonio.fuduli@unical.it (A. Fuduli); e.vocaturo@dimes.unical.it
(E. Vocaturo); e.zumpano@dimes.unical.it (E. Zumpano)
© 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073 CEUR Workshop Proceedings (CEUR-WS.org)
�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 affected 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].
2. Multiple Instance Learning
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
difference 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.
3. The MIL-RL algorithm
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
△
𝐻(𝑤, 𝑏) = {𝑥 ∈ R𝑛 | 𝑤𝑇 𝑥 + 𝑏 = 0}, (1)
�is the following:
⎧
𝑚 ∑︁ 𝑘 ∑︁
⎪ 1 2
∑︁ ∑︁
‖𝑤‖ + 𝐶
⎪
⎪
⎪ min 𝜉𝑗 + 𝐶 𝜉𝑗
⎪ 𝑦,𝑤,𝑏,𝜉 2
⎪
⎪
⎪ 𝑖=1 𝑗∈𝐽 + 𝑖=1 𝑗∈𝐽 −
⎪
⎪ 𝑖 𝑖
⎪
⎪
⎪
⎪
𝜉𝑗 ≥ 1 − 𝑦𝑗 (𝑤𝑇 𝑥𝑗 + 𝑏) 𝑗 ∈ 𝐽𝑖+ , 𝑖 = 1, . . . , 𝑚
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
𝜉𝑗 ≥ 1 + (𝑤𝑇 𝑥𝑗 + 𝑏) 𝑗 ∈ 𝐽𝑖− , 𝑖 = 1, . . . , 𝑘
⎪
⎪
⎪
⎪
⎪
⎪
⎨
∑︁ 𝑦𝑗 + 1 (2)
⎪ ≥ 1 𝑖 = 1, . . . , 𝑚
⎪
⎪
⎪ +
2
⎪
⎪
⎪ 𝑗∈𝐽𝑖
⎪
⎪
⎪
⎪
𝑦𝑗 ∈ {−1, +1} 𝑗 ∈ 𝐽𝑖+ , 𝑖 = 1, . . . , 𝑚
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
𝜉𝑗 ≥ 0 𝑗 ∈ 𝐽𝑖+ , 𝑖 = 1, . . . , 𝑚
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
𝜉𝑗 ≥ 0 𝑗 ∈ 𝐽𝑖− , 𝑖 = 1, . . . , 𝑘,
⎪
⎩
where: 𝑚 is the number of positive bags; 𝑘 is the number of negative bags; 𝑥𝑗 is the 𝑗-th
instance belonging to a bag; 𝐽𝑖+ is the index set corresponding to the instances of the 𝑖-th
positive bag; 𝐽𝑖− is the index set corresponding to the instances of the 𝑖-th negative bag.
Variables 𝑏 and 𝑤 correspond respectively to the bias and normal to the hyperplane, variable
𝜉𝑗 gives a measure of the misclassification error of the instance 𝑥𝑗 , while 𝑦𝑗 is the class label to
be assigned to the instances of the positive bags. The positive parameter 𝐶 tunes the weight
between the maximization of the margin, obtained by minimizing the Euclidean norm of 𝑤,
and the minimization of the misclassification errors of the instances. Finally, the constraints
∑︁ 𝑦𝑗 + 1
≥ 1 𝑖 = 1, . . . , 𝑚 (3)
+
2
𝑗∈𝐽𝑖
impose that, for each positive bag, at least one instance should be positive (i.e. with label equal
to +1). Note that, when 𝑚 = 𝑘 = 1 and 𝑦𝑗 = +1 for any 𝑗, problem (2) reduces to the classical
SVM quadratic program. The core of MIL-RL is to solve, at each iteration, the Lagrangian
relaxation of problem (2), obtained by relaxing constraints (3):
⎧ ⎛ ⎞
𝑚 ∑︁ 𝑘 ∑︁ 𝑚
⎪ 1 ∑︁ ∑︁ ∑︁ ∑︁ 𝑦𝑗 + 1
‖𝑤‖2 + 𝐶 𝜆𝑖 ⎝1 −
⎪
⎪ min
⎪ 𝜉𝑗 + 𝐶 𝜉𝑗 + ⎠
⎪
⎪ 𝑦,𝑤,𝑏,𝜉 2 𝑖=1 + 𝑖=1 − 𝑖=1 +
2
𝑗∈𝐽𝑖 𝑗∈𝐽𝑖 𝑗∈𝐽𝑖
⎪
⎪
⎪
⎪
⎪
⎪
𝜉𝑗 ≥ 1 − 𝑦𝑗 (𝑤𝑇 𝑥𝑗 + 𝑏) 𝑗 ∈ 𝐽𝑖+ , 𝑖 = 1, . . . , 𝑚
⎪
⎪
⎪
⎪
⎪
⎪
⎨
𝜉𝑗 ≥ 1 + (𝑤𝑇 𝑥𝑗 + 𝑏) 𝑗 ∈ 𝐽𝑖− , 𝑖 = 1, . . . , 𝑘 (4)
⎪
⎪
⎪
𝑦𝑗 ∈ {−1, +1} 𝑗 ∈ 𝐽𝑖+ , 𝑖 = 1, . . . , 𝑚
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
𝜉𝑗 ≥ 0 𝑗 ∈ 𝐽𝑖+ , 𝑖 = 1, . . . , 𝑚
⎪
⎪
⎪
⎪
⎪
⎪
⎪
−
𝜉𝑗 ≥ 0 𝑗 ∈ 𝐽𝑖 , 𝑖 = 1, . . . , 𝑘,
⎩
�where 𝜆𝑖 ≥ 0 is the 𝑖-th Lagrangian multiplier associated to the 𝑖-th constraint of the type (3).
[12] shows that, considering the Lagrangian dual of the primal problem (2), in correspondence
to the optimal solution there is no dual gap between the primal and dual objective functions.
4. The mi-SPSVM algorithm
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 efficiency. It computes a separating
hyperplane of the type (1) by solving, at each iteration, the following quadratic problem:
⎧ ⃦ ⃦2
⃦ 𝑤 ⃦ +𝐶
1⃦ ⃦ ∑︁
2
∑︁
min 𝜉 + 𝐶 𝜉𝑗
⎪
⎪ 𝑗
2⃦ 𝑏 ⃦ 2
⎪
⎪
⎪ 𝑤,𝑏,𝜉
⎪
⎪ + 𝑗∈𝐽 − 𝑗∈𝐽
⎪
⎪
⎪
⎪
⎨
𝜉𝑗 = 1 − (𝑤𝑇 𝑥𝑗 + 𝑏) 𝑗 ∈ 𝐽+ (5)
⎪
⎪
⎪
𝜉𝑗 ≥ 1 + (𝑤𝑇 𝑥𝑗 + 𝑏) 𝑗 ∈ 𝐽−
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
𝑗 ∈ 𝐽 −,
⎩
𝜉𝑗 ≥ 0
by varying of the sets 𝐽 + and 𝐽 − , which contain the indexes of the instances currently
considered positive and negative, respectively. At the initialization step, 𝐽 + contains the
indexes of all the instances of the positive bags, while 𝐽 − contains the indexes of all the
instances of the negative bags. Once an optimal solution, say (𝑤* , 𝑏* , 𝜉 * ), to problem (5) has
been computed, the two sets 𝐽 + and 𝐽 − are updated in the following way:
𝐽 + := 𝐽 + ∖ 𝐽¯ and 𝐽 − := 𝐽 − ∪ 𝐽¯
where 𝐽¯ = {𝑗 ∈ 𝐽 + ∖ 𝐽 * | 𝑤*𝑇 𝑥𝑗 + 𝑏* ≤ −1},
△
with 𝐽 * = {𝑗𝑖* , 𝑖 = 1, . . . , 𝑚 | 𝑤*𝑇 𝑥𝑗𝑖* +𝑏* ≤ −1} and 𝑗𝑖* = arg max𝑗∈(𝐽 + ∩𝐽 + ) {𝑤*𝑇 𝑥𝑗 +𝑏* }.
𝑖
Some comments on the updating of the sets 𝐽 + and 𝐽 − are in order. A particular role in the
definition of the set 𝐽¯ is played by the set 𝐽 * , introduced for taking into account constraints (3).
We recall that such constraints impose the satisfaction of the standard MIL assumption, stating
that, for each positive bag, at least one instance must be positive. At the current iteration, the set
𝐽 * is the index set (subset of 𝐽 + ) corresponding to the instances closest, for each positive bag, to
the current hyperplane 𝐻(𝑤* , 𝑏* ) and strictly lying in the negative side with respect to it. If an
index, say 𝑗𝑖* ∈ 𝐽 * , corresponding to one of such instances entered the set 𝐽 − , all the instances
of the 𝑖-th positive bag would be considered negative by problem (5), favouring the violation
of the standard MIL assumption. This is the reason why the indexes of 𝐽 * are prevented from
entering the set 𝐽 − : in this way, for each positive bag, at least an index corresponding to one of
its instances is guaranteed to be inside 𝐽 + .
�Figure 1: Examples of X-ray chest images of healthy people
Figure 2: Examples of X-ray chest images of people with bacterial pneumonia
Figure 3: Examples of X-ray chest images of people with viral pneumonia
5. Numerical results
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 differences 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 differences 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 different sizes of the testing and training sets, we have
used three different validation protocols: the 5-fold cross-validation (5-CV), the 10-fold cross-
validation (10-CV) and the Leave-One-Out validation. As for the optimal computation of the
tuning parameter C characterizing the models (2) and (5), in both the cases we have adopted a
be-level approach of the type used in [18] and in [11].
� 5-CV 10-CV Leave-One-Out
MIL-RL mi-SPSVM MIL-RL mi-SPSVM MIL-RL mi-SPSVM
Correctness (%) 88.00 91.00 89.00 91.00 90.00 91.00
Sensitivity (%) 94.70 94.70 93.83 93.83 94.00 94.00
Specificity (%) 82.50 87.50 83.38 86.81 86.00 88.00
F-score (%) 88.73 91.68 88.89 90.74 90.38 91.26
CPU time (secs) 0.24 0.04 0.32 0.06 0.59 0.14
Table 1
X-ray chest images: average testing values relating 50 normal vs 50 with bacterial pneumonia
5-CV 10-CV Leave-One-Out
MIL-RL mi-SPSVM MIL-RL mi-SPSVM MIL-RL mi-SPSVM
Correctness (%) 87.00 88.00 84.00 87.00 86.00 89.00
Sensitivity (%) 86.36 93.18 90.71 90.71 88.00 94.00
Specificity (%) 88.61 83.89 77.38 83.05 84.00 84.00
F-score (%) 86.53 88.63 84.85 87.36 86.27 89.52
CPU time (secs) 0.35 0.05 0.56 0.06 0.58 0.07
Table 2
X-ray chest images: average testing values relating 50 normal vs 50 with viral pneumonia
5-CV 10-CV Leave-One-Out
MIL-RL mi-SPSVM MIL-RL mi-SPSVM MIL-RL mi-SPSVM
Correctness (%) 72.00 67.00 75.00 74.00 71.00 74.00
Sensitivity (%) 71.74 80.23 73.98 80.83 68.00 82.00
Specificity (%) 70.83 54.44 74.86 63.10 74.00 66.00
F-score (%) 70.46 69.99 73.06 73.69 70.10 75.93
CPU time (secs) 0.36 0.06 0.89 0.06 0.93 0.15
Table 3
X-ray chest images: average testing values relating 50 with bacterial vs 50 with viral pneumonia
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%).
6. Conclusions and future work
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
efficiency, 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].
References
[1] H. X. Bai, et al., Performance of radiologists in differentiating covid-19 from non-covid-19
viral pneumonia at chest ct, Radiology 296 (2020) E46–E54.
[2] E. Zumpano, A. Fuduli, E. Vocaturo, M. Avolio, Viral pneumonia images classification by
multiple instance learning: preliminary results, in: IDEAS 2021, ACM, 2021, pp. 292–296.
[3] E. Vocaturo, E. Zumpano, L. Caroprese, Convolutional neural network techniques on x-ray
images for covid-19 classification, in: BIBM, IEEE, 2021, pp. 3113–3115.
[4] P. Mooney, Chest X-ray images (pneumonia), 2021. URL: https://www.kaggle.com/
paultimothymooney/chest-xray-pneumonia, available on line.
[5] H. S. Alghamdi, G. Amoudi, S. Elhag, K. Saeedi, J. Nasser, Deep learning approaches for
detecting COVID-19 from chest X-ray images: A survey, IEEE Access 9 (2021) 20235–20254.
[6] F. Herrera, et al., Multiple instance learning: Foundations and algorithms, Springer Inter-
national Publishing, 2016.
[7] G. Quellec, G. Cazuguel, B. Cochener, M. Lamard, Multiple-instance learning for medical
image and video analysis, IEEE Reviews in Biomedical Engineering 10 (2017) 213–234.
[8] E. Vocaturo, E. Zumpano, Supporting the diagnosis of dysplastic nevi syndrome via
multiple instance learning approaches, in: AI4H@ECAI, volume 2820, 2020, pp. 39–44.
[9] E. Vocaturo, E. Zumpano, Diabetic retinopathy images classification via multiple instance
learning, in: CHASE, IEEE, 2021, pp. 143–148.
[10] E. Vocaturo, E. Zumpano, Multiple instance learning approaches for melanoma and
dysplastic nevi images classification, in: ICMLA, IEEE, 2020, pp. 1396–1401.
[11] A. Astorino, A. Fuduli, P. Veltri, E. Vocaturo, Melanoma detection by means of multiple
instance learning, Interdisciplinary Sciences: Computational Life Sciences 12 (2020) 24–31.
[12] A. Astorino, A. Fuduli, M. Gaudioso, A Lagrangian relaxation approach for binary multiple
� instance classification, IEEE Transactions on Neural Networks and Learning Systems 30
(2019) 2662 – 2671.
[13] M. Guignard, Lagrangean relaxation, Top 11 (2003) 151–200.
[14] S. Andrews, I. Tsochantaridis, T. Hofmann, Support vector machines for multiple-instance
learning, in: S. Becker, S. Thrun, K. Obermayer (Eds.), Advances in Neural Information
Processing Systems, MIT Press, Cambridge, 2003, pp. 561–568.
[15] M. Avolio, A. Fuduli, A semiproximal support vector machine approach for binary multiple
instance learning, IEEE Transactions on Neural Networks and Learning Systems, 32(8), pp.
3566-3577 (2021).
[16] G. Fung, O. Mangasarian, Proximal support vector machine classifiers, in: Proceedings
KDD-2001: Knowledge discovery and data mining, ACM, 2001, pp. 77–86.
[17] A. Astorino, A. Fuduli, P. Veltri, E. Vocaturo, On a recent algorithm for multiple instance
learning. preliminary applications in image classification, in: BIBM, 2017, pp. 1615–1619.
[18] A. Astorino, A. Fuduli, The proximal trajectory algorithm in SVM cross validation, IEEE
Transactions on Neural Networks and Learning Systems 27 (2016) 966–977.
[19] P. Kukic, C. Mirabello, G. Tradigo, I. Walsh, P. Veltri, G. Pollastri, Toward an accurate
prediction of inter-residue distances in proteins using 2d recursive neural networks, BMC
Bioinformatics 15 (2014).
[20] G. Tradigo, S. De Rosa, P. Vizza, G. Fragomeni, P. H. Guzzi, C. Indolfi, P. Veltri, Calculation
of intracoronary pressure-based indexes with jlabchart, Applied Sciences 12 (2022).
[21] N. Cassavia, S. Flesca, M. Ianni, E. Masciari, C. Pulice, Distributed computing by leveraging
and rewarding idling user resources from p2p networks, Journal of Parallel and Distributed
Computing 122 (2018) 81–94.
[22] E. Zumpano, P. Iaquinta, L. Caroprese, F. Dattola, G. Tradigo, P. Veltri, E. Vocaturo, Sim-
patico 3d mobile for diagnostic procedures, ACM, 2019.
[23] L. Caroprese, E. Zumpano, Handling preferences in P2P systems, in: FOIKS, volume 7153,
Springer, 2012, pp. 91–106.
[24] L. Caroprese, E. Zumpano, Aggregates and priorities in P2P data management systems, in:
IDEAS, ACM, 2011, pp. 1–7.
[25] L. Caroprese, E. Zumpano, A logic framework for P2P deductive databases, Theory Pract.
Log. Program. 20 (2020) 1–43.
[26] L. Caroprese, E. Zumpano, Declarative semantics for P2P data management system, J.
Data Semant. 9 (2020) 101–122.
[27] A. Guzzo, A. Rullo, E. Vocaturo, Process mining applications in the healthcare domain:
A comprehensive review, Wiley Interdisciplinary Reviews: Data Mining and Knowledge
Discovery 12 (2022) e1442.
[28] E. Vocaturo, E. Zumpano, AI for the detection of the diabetic retinopathy, in: Integrating
Artificial Intelligence and IoT for Advanced Health Informatics - Technology, Communica-
tions and Computing, Springer, 2022, pp. 129–140.
[29] E. Vocaturo, E. Zumpano, ECG analysis via machine learning techniques: News and
perspectives, in: BIBM1, IEEE, 2021, pp. 3106–3112.
[30] E. Vocaturo, E. Zumpano, Artificial intelligence approaches on ultrasound for breast cancer
diagnosis, in: BIBM, IEEE, 2021, pp. 3116–3121.
�
Multiple Instance Learning for viral pneumonia chest X-ray Classification[edit]
Multiple Instance Learning for Viral Pneumonia Chest
X-ray Classification
(Discussion Paper)
Matteo Avolio1,3 , Antonio Fuduli1,3 , Eugenio Vocaturo2,3 and Ester Zumpano2,3
1
Department of Mathematics and Computer Science - University of Calabria, Rende, Italy
2
Department of Computer Engineering, Modeling, Electronics, and Systems Sciences - University of Calabria, Rende, Italy
3
CNR-NANOTEC National Research Council, Rende, Italy
Abstract
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 different 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.
Keywords
Pneumonia imaging Classification, Multiple Instance Learning, Machine Learning
1. Introduction
The world is coping with the COVID-19 pandemic. COVID-19 is caused by a Severe Acute
Respiratory Sindrome Coronavirus (SARS-CoV-2) and its common symptoms are: fever, dry
cough, fatique, short breathing, vanishing of taste, loss of smell. The most effective way to limit
the spread of COVID-19 and the number of deaths is to identify infected persons at an early
stage of the disease and many different proposals have been investigated for the development
of automatic screening of COVID-19 from medical images analysis. COVID-19 has interstitial
pneumonia as the predominant clinical manifestation. Radiological imaging is able to highlight
any pneumonia: in the case of Coronavirus (Sars-Cov2) infection, it is possible to see an opacity
on the radiograph, called thickening and a greater extension of the pulmonary thickening [1].
Therefore, while huge challenges need to be faced, medical imaging analysis arises as a key
factor in the screening of viral pneumonia from bacteria pneumonia. In reasoning on the
SEBD 2022: The 30th Italian Symposium on Advanced Database Systems, June 19-22, 2022, Tirrenia (PI), Italy
" matteo.avolio@unical.it (M. Avolio); antonio.fuduli@unical.it (A. Fuduli); e.vocaturo@dimes.unical.it
(E. Vocaturo); e.zumpano@dimes.unical.it (E. Zumpano)
© 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073 CEUR Workshop Proceedings (CEUR-WS.org)
�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 affected 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].
2. Multiple Instance Learning
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
difference 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.
3. The MIL-RL algorithm
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
△
𝐻(𝑤, 𝑏) = {𝑥 ∈ R𝑛 | 𝑤𝑇 𝑥 + 𝑏 = 0}, (1)
�is the following:
⎧
𝑚 ∑︁ 𝑘 ∑︁
⎪ 1 2
∑︁ ∑︁
‖𝑤‖ + 𝐶
⎪
⎪
⎪ min 𝜉𝑗 + 𝐶 𝜉𝑗
⎪ 𝑦,𝑤,𝑏,𝜉 2
⎪
⎪
⎪ 𝑖=1 𝑗∈𝐽 + 𝑖=1 𝑗∈𝐽 −
⎪
⎪ 𝑖 𝑖
⎪
⎪
⎪
⎪
𝜉𝑗 ≥ 1 − 𝑦𝑗 (𝑤𝑇 𝑥𝑗 + 𝑏) 𝑗 ∈ 𝐽𝑖+ , 𝑖 = 1, . . . , 𝑚
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
𝜉𝑗 ≥ 1 + (𝑤𝑇 𝑥𝑗 + 𝑏) 𝑗 ∈ 𝐽𝑖− , 𝑖 = 1, . . . , 𝑘
⎪
⎪
⎪
⎪
⎪
⎪
⎨
∑︁ 𝑦𝑗 + 1 (2)
⎪ ≥ 1 𝑖 = 1, . . . , 𝑚
⎪
⎪
⎪ +
2
⎪
⎪
⎪ 𝑗∈𝐽𝑖
⎪
⎪
⎪
⎪
𝑦𝑗 ∈ {−1, +1} 𝑗 ∈ 𝐽𝑖+ , 𝑖 = 1, . . . , 𝑚
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
𝜉𝑗 ≥ 0 𝑗 ∈ 𝐽𝑖+ , 𝑖 = 1, . . . , 𝑚
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
𝜉𝑗 ≥ 0 𝑗 ∈ 𝐽𝑖− , 𝑖 = 1, . . . , 𝑘,
⎪
⎩
where: 𝑚 is the number of positive bags; 𝑘 is the number of negative bags; 𝑥𝑗 is the 𝑗-th
instance belonging to a bag; 𝐽𝑖+ is the index set corresponding to the instances of the 𝑖-th
positive bag; 𝐽𝑖− is the index set corresponding to the instances of the 𝑖-th negative bag.
Variables 𝑏 and 𝑤 correspond respectively to the bias and normal to the hyperplane, variable
𝜉𝑗 gives a measure of the misclassification error of the instance 𝑥𝑗 , while 𝑦𝑗 is the class label to
be assigned to the instances of the positive bags. The positive parameter 𝐶 tunes the weight
between the maximization of the margin, obtained by minimizing the Euclidean norm of 𝑤,
and the minimization of the misclassification errors of the instances. Finally, the constraints
∑︁ 𝑦𝑗 + 1
≥ 1 𝑖 = 1, . . . , 𝑚 (3)
+
2
𝑗∈𝐽𝑖
impose that, for each positive bag, at least one instance should be positive (i.e. with label equal
to +1). Note that, when 𝑚 = 𝑘 = 1 and 𝑦𝑗 = +1 for any 𝑗, problem (2) reduces to the classical
SVM quadratic program. The core of MIL-RL is to solve, at each iteration, the Lagrangian
relaxation of problem (2), obtained by relaxing constraints (3):
⎧ ⎛ ⎞
𝑚 ∑︁ 𝑘 ∑︁ 𝑚
⎪ 1 ∑︁ ∑︁ ∑︁ ∑︁ 𝑦𝑗 + 1
‖𝑤‖2 + 𝐶 𝜆𝑖 ⎝1 −
⎪
⎪ min
⎪ 𝜉𝑗 + 𝐶 𝜉𝑗 + ⎠
⎪
⎪ 𝑦,𝑤,𝑏,𝜉 2 𝑖=1 + 𝑖=1 − 𝑖=1 +
2
𝑗∈𝐽𝑖 𝑗∈𝐽𝑖 𝑗∈𝐽𝑖
⎪
⎪
⎪
⎪
⎪
⎪
𝜉𝑗 ≥ 1 − 𝑦𝑗 (𝑤𝑇 𝑥𝑗 + 𝑏) 𝑗 ∈ 𝐽𝑖+ , 𝑖 = 1, . . . , 𝑚
⎪
⎪
⎪
⎪
⎪
⎪
⎨
𝜉𝑗 ≥ 1 + (𝑤𝑇 𝑥𝑗 + 𝑏) 𝑗 ∈ 𝐽𝑖− , 𝑖 = 1, . . . , 𝑘 (4)
⎪
⎪
⎪
𝑦𝑗 ∈ {−1, +1} 𝑗 ∈ 𝐽𝑖+ , 𝑖 = 1, . . . , 𝑚
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
𝜉𝑗 ≥ 0 𝑗 ∈ 𝐽𝑖+ , 𝑖 = 1, . . . , 𝑚
⎪
⎪
⎪
⎪
⎪
⎪
⎪
−
𝜉𝑗 ≥ 0 𝑗 ∈ 𝐽𝑖 , 𝑖 = 1, . . . , 𝑘,
⎩
�where 𝜆𝑖 ≥ 0 is the 𝑖-th Lagrangian multiplier associated to the 𝑖-th constraint of the type (3).
[12] shows that, considering the Lagrangian dual of the primal problem (2), in correspondence
to the optimal solution there is no dual gap between the primal and dual objective functions.
4. The mi-SPSVM algorithm
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 efficiency. It computes a separating
hyperplane of the type (1) by solving, at each iteration, the following quadratic problem:
⎧ ⃦ ⃦2
⃦ 𝑤 ⃦ +𝐶
1⃦ ⃦ ∑︁
2
∑︁
min 𝜉 + 𝐶 𝜉𝑗
⎪
⎪ 𝑗
2⃦ 𝑏 ⃦ 2
⎪
⎪
⎪ 𝑤,𝑏,𝜉
⎪
⎪ + 𝑗∈𝐽 − 𝑗∈𝐽
⎪
⎪
⎪
⎪
⎨
𝜉𝑗 = 1 − (𝑤𝑇 𝑥𝑗 + 𝑏) 𝑗 ∈ 𝐽+ (5)
⎪
⎪
⎪
𝜉𝑗 ≥ 1 + (𝑤𝑇 𝑥𝑗 + 𝑏) 𝑗 ∈ 𝐽−
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
𝑗 ∈ 𝐽 −,
⎩
𝜉𝑗 ≥ 0
by varying of the sets 𝐽 + and 𝐽 − , which contain the indexes of the instances currently
considered positive and negative, respectively. At the initialization step, 𝐽 + contains the
indexes of all the instances of the positive bags, while 𝐽 − contains the indexes of all the
instances of the negative bags. Once an optimal solution, say (𝑤* , 𝑏* , 𝜉 * ), to problem (5) has
been computed, the two sets 𝐽 + and 𝐽 − are updated in the following way:
𝐽 + := 𝐽 + ∖ 𝐽¯ and 𝐽 − := 𝐽 − ∪ 𝐽¯
where 𝐽¯ = {𝑗 ∈ 𝐽 + ∖ 𝐽 * | 𝑤*𝑇 𝑥𝑗 + 𝑏* ≤ −1},
△
with 𝐽 * = {𝑗𝑖* , 𝑖 = 1, . . . , 𝑚 | 𝑤*𝑇 𝑥𝑗𝑖* +𝑏* ≤ −1} and 𝑗𝑖* = arg max𝑗∈(𝐽 + ∩𝐽 + ) {𝑤*𝑇 𝑥𝑗 +𝑏* }.
𝑖
Some comments on the updating of the sets 𝐽 + and 𝐽 − are in order. A particular role in the
definition of the set 𝐽¯ is played by the set 𝐽 * , introduced for taking into account constraints (3).
We recall that such constraints impose the satisfaction of the standard MIL assumption, stating
that, for each positive bag, at least one instance must be positive. At the current iteration, the set
𝐽 * is the index set (subset of 𝐽 + ) corresponding to the instances closest, for each positive bag, to
the current hyperplane 𝐻(𝑤* , 𝑏* ) and strictly lying in the negative side with respect to it. If an
index, say 𝑗𝑖* ∈ 𝐽 * , corresponding to one of such instances entered the set 𝐽 − , all the instances
of the 𝑖-th positive bag would be considered negative by problem (5), favouring the violation
of the standard MIL assumption. This is the reason why the indexes of 𝐽 * are prevented from
entering the set 𝐽 − : in this way, for each positive bag, at least an index corresponding to one of
its instances is guaranteed to be inside 𝐽 + .
�Figure 1: Examples of X-ray chest images of healthy people
Figure 2: Examples of X-ray chest images of people with bacterial pneumonia
Figure 3: Examples of X-ray chest images of people with viral pneumonia
5. Numerical results
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 differences 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 differences 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 different sizes of the testing and training sets, we have
used three different validation protocols: the 5-fold cross-validation (5-CV), the 10-fold cross-
validation (10-CV) and the Leave-One-Out validation. As for the optimal computation of the
tuning parameter C characterizing the models (2) and (5), in both the cases we have adopted a
be-level approach of the type used in [18] and in [11].
� 5-CV 10-CV Leave-One-Out
MIL-RL mi-SPSVM MIL-RL mi-SPSVM MIL-RL mi-SPSVM
Correctness (%) 88.00 91.00 89.00 91.00 90.00 91.00
Sensitivity (%) 94.70 94.70 93.83 93.83 94.00 94.00
Specificity (%) 82.50 87.50 83.38 86.81 86.00 88.00
F-score (%) 88.73 91.68 88.89 90.74 90.38 91.26
CPU time (secs) 0.24 0.04 0.32 0.06 0.59 0.14
Table 1
X-ray chest images: average testing values relating 50 normal vs 50 with bacterial pneumonia
5-CV 10-CV Leave-One-Out
MIL-RL mi-SPSVM MIL-RL mi-SPSVM MIL-RL mi-SPSVM
Correctness (%) 87.00 88.00 84.00 87.00 86.00 89.00
Sensitivity (%) 86.36 93.18 90.71 90.71 88.00 94.00
Specificity (%) 88.61 83.89 77.38 83.05 84.00 84.00
F-score (%) 86.53 88.63 84.85 87.36 86.27 89.52
CPU time (secs) 0.35 0.05 0.56 0.06 0.58 0.07
Table 2
X-ray chest images: average testing values relating 50 normal vs 50 with viral pneumonia
5-CV 10-CV Leave-One-Out
MIL-RL mi-SPSVM MIL-RL mi-SPSVM MIL-RL mi-SPSVM
Correctness (%) 72.00 67.00 75.00 74.00 71.00 74.00
Sensitivity (%) 71.74 80.23 73.98 80.83 68.00 82.00
Specificity (%) 70.83 54.44 74.86 63.10 74.00 66.00
F-score (%) 70.46 69.99 73.06 73.69 70.10 75.93
CPU time (secs) 0.36 0.06 0.89 0.06 0.93 0.15
Table 3
X-ray chest images: average testing values relating 50 with bacterial vs 50 with viral pneumonia
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%).
6. Conclusions and future work
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
efficiency, 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].
References
[1] H. X. Bai, et al., Performance of radiologists in differentiating covid-19 from non-covid-19
viral pneumonia at chest ct, Radiology 296 (2020) E46–E54.
[2] E. Zumpano, A. Fuduli, E. Vocaturo, M. Avolio, Viral pneumonia images classification by
multiple instance learning: preliminary results, in: IDEAS 2021, ACM, 2021, pp. 292–296.
[3] E. Vocaturo, E. Zumpano, L. Caroprese, Convolutional neural network techniques on x-ray
images for covid-19 classification, in: BIBM, IEEE, 2021, pp. 3113–3115.
[4] P. Mooney, Chest X-ray images (pneumonia), 2021. URL: https://www.kaggle.com/
paultimothymooney/chest-xray-pneumonia, available on line.
[5] H. S. Alghamdi, G. Amoudi, S. Elhag, K. Saeedi, J. Nasser, Deep learning approaches for
detecting COVID-19 from chest X-ray images: A survey, IEEE Access 9 (2021) 20235–20254.
[6] F. Herrera, et al., Multiple instance learning: Foundations and algorithms, Springer Inter-
national Publishing, 2016.
[7] G. Quellec, G. Cazuguel, B. Cochener, M. Lamard, Multiple-instance learning for medical
image and video analysis, IEEE Reviews in Biomedical Engineering 10 (2017) 213–234.
[8] E. Vocaturo, E. Zumpano, Supporting the diagnosis of dysplastic nevi syndrome via
multiple instance learning approaches, in: AI4H@ECAI, volume 2820, 2020, pp. 39–44.
[9] E. Vocaturo, E. Zumpano, Diabetic retinopathy images classification via multiple instance
learning, in: CHASE, IEEE, 2021, pp. 143–148.
[10] E. Vocaturo, E. Zumpano, Multiple instance learning approaches for melanoma and
dysplastic nevi images classification, in: ICMLA, IEEE, 2020, pp. 1396–1401.
[11] A. Astorino, A. Fuduli, P. Veltri, E. Vocaturo, Melanoma detection by means of multiple
instance learning, Interdisciplinary Sciences: Computational Life Sciences 12 (2020) 24–31.
[12] A. Astorino, A. Fuduli, M. Gaudioso, A Lagrangian relaxation approach for binary multiple
� instance classification, IEEE Transactions on Neural Networks and Learning Systems 30
(2019) 2662 – 2671.
[13] M. Guignard, Lagrangean relaxation, Top 11 (2003) 151–200.
[14] S. Andrews, I. Tsochantaridis, T. Hofmann, Support vector machines for multiple-instance
learning, in: S. Becker, S. Thrun, K. Obermayer (Eds.), Advances in Neural Information
Processing Systems, MIT Press, Cambridge, 2003, pp. 561–568.
[15] M. Avolio, A. Fuduli, A semiproximal support vector machine approach for binary multiple
instance learning, IEEE Transactions on Neural Networks and Learning Systems, 32(8), pp.
3566-3577 (2021).
[16] G. Fung, O. Mangasarian, Proximal support vector machine classifiers, in: Proceedings
KDD-2001: Knowledge discovery and data mining, ACM, 2001, pp. 77–86.
[17] A. Astorino, A. Fuduli, P. Veltri, E. Vocaturo, On a recent algorithm for multiple instance
learning. preliminary applications in image classification, in: BIBM, 2017, pp. 1615–1619.
[18] A. Astorino, A. Fuduli, The proximal trajectory algorithm in SVM cross validation, IEEE
Transactions on Neural Networks and Learning Systems 27 (2016) 966–977.
[19] P. Kukic, C. Mirabello, G. Tradigo, I. Walsh, P. Veltri, G. Pollastri, Toward an accurate
prediction of inter-residue distances in proteins using 2d recursive neural networks, BMC
Bioinformatics 15 (2014).
[20] G. Tradigo, S. De Rosa, P. Vizza, G. Fragomeni, P. H. Guzzi, C. Indolfi, P. Veltri, Calculation
of intracoronary pressure-based indexes with jlabchart, Applied Sciences 12 (2022).
[21] N. Cassavia, S. Flesca, M. Ianni, E. Masciari, C. Pulice, Distributed computing by leveraging
and rewarding idling user resources from p2p networks, Journal of Parallel and Distributed
Computing 122 (2018) 81–94.
[22] E. Zumpano, P. Iaquinta, L. Caroprese, F. Dattola, G. Tradigo, P. Veltri, E. Vocaturo, Sim-
patico 3d mobile for diagnostic procedures, ACM, 2019.
[23] L. Caroprese, E. Zumpano, Handling preferences in P2P systems, in: FOIKS, volume 7153,
Springer, 2012, pp. 91–106.
[24] L. Caroprese, E. Zumpano, Aggregates and priorities in P2P data management systems, in:
IDEAS, ACM, 2011, pp. 1–7.
[25] L. Caroprese, E. Zumpano, A logic framework for P2P deductive databases, Theory Pract.
Log. Program. 20 (2020) 1–43.
[26] L. Caroprese, E. Zumpano, Declarative semantics for P2P data management system, J.
Data Semant. 9 (2020) 101–122.
[27] A. Guzzo, A. Rullo, E. Vocaturo, Process mining applications in the healthcare domain:
A comprehensive review, Wiley Interdisciplinary Reviews: Data Mining and Knowledge
Discovery 12 (2022) e1442.
[28] E. Vocaturo, E. Zumpano, AI for the detection of the diabetic retinopathy, in: Integrating
Artificial Intelligence and IoT for Advanced Health Informatics - Technology, Communica-
tions and Computing, Springer, 2022, pp. 129–140.
[29] E. Vocaturo, E. Zumpano, ECG analysis via machine learning techniques: News and
perspectives, in: BIBM1, IEEE, 2021, pp. 3106–3112.
[30] E. Vocaturo, E. Zumpano, Artificial intelligence approaches on ultrasound for breast cancer
diagnosis, in: BIBM, IEEE, 2021, pp. 3116–3121.
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