Acute sinusitis classification using support and fuzzy support vector machines

The medical sector is currently in need of a method to aid in the classification of diseases, which contemporarily progresses into varying types. Therefore, the role of technology is highly relevant in the process of overcoming this challenge. This report discusses acute sinusitis, which is one of the most common forms of sinusitis, possibly caused by viruses, bacteria, fungi, pollutants, allergies, and also autoimmune reactions. Furthermore, the Support Vector Machines (SVM) and Fuzzy Support Vector Machines (FSVM) are used as a classification method to diagnose a person of acute sinusitis, therefore, this research aims to compare how both work, using Radial Basis Function (RBF) and Polynomial Kernel. Data of CT scan from Cipto Mangunkusumo Hospital, Indonesia was used to evaluate acute sinusitis, in terms of Accuracy, Sensitivity, Precision, and F1-Score. Thus, the final results indicate a better performance for FSVM than SVM in all perspectives, especially using the RBF kernel.


Introduction
Acute sinusitis is a major manifestation of sinusitis, which causes inflammation and swelling of spaces inside the nose [1]. Therefore, a sufferer possesses the tendency of difficulty in breathing [1], and also presents with other symptoms, including facial pain or a headache and also swelling in areas around the eyes or face [1].
This is most often caused by the common cold, a viral infection [1], although there are other infrequent reasons, which include cystic fibrosis, neoplasia, and mechanical ventilation [2]. Moreover, individuals with sinusitis exhibit numerous symptoms or signs, encompassing fever, cough, hyposmia, nasal congestion, nasal drainage, fatigue, maxillary dental pain, postnasal drip, facial pain, and ear pressure [2].
The methods used in diagnosis comprises of nasal endoscopy, Computed Tomograph Scanning (CT scan), Magnetic Resonance Imaging (MRI), nasal and sinus cultures, and allergy test [3]. These provide detailed description of the condition [3], and antibiotics are often required on instances where it is caused by bacterial infection, in order to prevent the disease proliferation [3].
This research uses the Support Vector Machines and the Fuzzy variety, which is an extended technique, as methods of diagnosing a patient of acute sinusitis. Therefore, they are conducted with the

Support Vector Machines
Support Vector Machines (SVM) is a method that is good at prediction, due to the fact that it provides data with high accuracy, through the use of Structural Risk Minimization (SRM) principle. In addition, the idea is based on identification of the best discriminant boundaries of two classes, with a measuring margin, termed hyperplane, given a sample of training dataset ᵢ ∈ ℜ N , while each label is notated yi ∈ {0,1} for i = 1,2,…, , where N is equivalent to the amount of data. Therefore, a separator is formulated as Equation (1) .  [24]. Identify the minimum point in Equation (2), and abstract it into Equation (3), creating a formulation called Quadratic Programming (QP) problem.

Support Vector Machines with Soft Margin
With constraint It is possible to resolve this challenge by various computational techniques, including Lagrange Multiplier which is showed in Equation (4).
Subtitute them into Equation (4) and it will get a result as in Equation (18) ( , , , , So, the problems above can be written as Equation (19) below: ) (19) with constraint in Equation (20) and (21) A kernel function was used to support the method in coping with non-linear separable data. This was, however, defined as ( ᵢ, ᵣ) = ( ᵢ). ( j), and through its substitution, the following was obtained in Equation (22): with constraint in Equation (23) and (24) Satisfactory results and outperform conventional classifiers are obtained by a polynomial or RBF kernel, which is stated in [25], both of which are applied in the Equation (25) and (26) below: The solution of the problem is shown in Equation (27)

Fuzzy Support Vector Machine
The Fuzzy variety is an extension of Support Vector Machines method, via a fuzzy membership, which is associated with each training point xi [26]. Therefore, it is possible to check all the training points in the class treated uniformly, although the effects are different in numerous real applications. Therefore, Z Rustam has developed a formulation of fuzzy membership, as seen in Equation (32) and (33) [27]: where A is a training dataset and B is a testing dataset [27]. The main purpose of Fuzzy Support Vector Machines is doing a preprocessing data. It will produce a new data that is ready to be processed by Support Vector Machines method. Basically, the step in the Fuzzy Support Vector Machines as same as Support Vector Machines, but a data has to be transformed into a new data ′ which is shown in Equation (34) and (35) below [27]:

Experimental Results
The Support Vector Machines and the Fuzzy variety are evaluated with RBF Kernel, and Polynomial, and subsequently a confusion matrix is created. : Number of samples having acute sinusitis diagnosed correctly : Sum of healthy people that were incorrectly identified to have acute sinusitis : Number of healthy individuals correctly spotted : The amount of samples with acute sinusitis that were incorrectly classified as healthy Accuracy explains how a data is being classified, while the second indicates sensitivity, which measures the proportion of actual positive cases that were predicted as such or true. In addition, the third is precision, which is the positive predictive value, while the last was denoted as F1-Score, used to deterrmine the balance between sensitivity and precision.
The graphs below show a comparison between Accuracy, Sensitivity, Precision, and F1-Score for each method.  Figure 1. Graph of Acute Sinusitis Classification for its Accuracy, Sensitivity, Precision, and F1-Score Based on Figure 1, the best method at accuracy, sensitivity, precision, and f1-score in Acute Sinusitis Classification are known. In addition, the accuracy, sensitivity, precision, and f1-score in FSVM Polynomial and RBF Kernel were recorded as methods that possessed the highest rate, while that of SVM was the lowest. Hence, based on the entire graph, the advantage observed was due to the fact that it is the extended form, hence, determining each data point with a fuzzy membership.

Conclusion
Based on the result and discussion, it is possible to conclude that Fuzzy Support Vector Machines are better at classifying acute sinusitis data, in contrast with the Support Vector Machines, and its usefulness, especially based on accuracy is illustrated with rate. The accuracy of Fuzzy Support Vector Machines with RBF Kernel reach a highest rate at 98.99% while Support Vector Machines with Polynomial Kernel reach a lowest rate at 97.35%. Furthermore, there are expectations that this method enables medical staffs to easily classify a disease or other medical problems. Moreover, subsequent investigations ought to identify other methods, using larger dataset, in order to create models that are more optimal, for the purpose of resolving classification problem.