Malaria is an infectious disease caused by parasitic protozoans of the Plasmodium family. These parasites are transmitted by mosquitos which are common in certain parts of the world. Based on their specific climates, these regions have been classified as low and high risk regions using a backpropagation neural network (BPNN). However, this approach yielded low performance and stability necessitating development of a more robust model. We hypothesized that by spiking neuron models in simulating the characteristics of a neuron, which when embedded with a BPNN, could improve the performance for the assessment of malaria prone regions. To this end, we created an inter-spike interval (ISI)-based BPNN (ISI-BPNN) architecture that uses a single-pass spiking learning strategy and has a parallel structure that is useful for non-linear regression tasks. Existing malaria dataset comprised of 1296 records, that met these attributes, were used. ISI-BPNN showed superior performance, and a high accuracy. The benchmarking results showed reliability and stability and an improvement of 11.9% against a multilayer perceptron and 9.19% against integrate-and-fire neuron models. The ISI-BPNN model is well suited for deciphering the risk of acquiring malaria as well as other diseases in prone regions of the world.
Malaria is a life threatening mosquito-borne infectious disease that exists in almost all nations. Almost half of the world’s population is at risk of malaria (1). The epidemiological patterns of malaria have been changing globally. The World Health Organization (WHO)’s world malaria report of 2018 stated that there were 219 million malaria cases worldwide and a total of 435,000 estimated deaths in 2017 (2). Southern Africa has the highest share of global malaria, with 194 million malaria cases and 407,000 deaths. High rates were also seen in the Asia Pacific region: Myanmar had 962,000 malaria cases with 2880 deaths, India 105,000 malaria cases and 690 deaths, and Indonesia 105,000 malaria cases and 1230 deaths as shown in Table 1. Ashwani et al. (3) reported on the malaria statistics in India, finding 4,481 confirmed deaths (medically certified) and an estimated 49,796 deaths (unconfirmed death reports). The authors gave statistics for Orissa (a state in the west of India) with almost 96,000 malaria cases and 1,793 deaths; for Madhya Pradesh (central India), these Figures were 50,000 malaria cases with 890 deaths, and in Karnataka (southern India) 82,000 malaria cases with 407 deaths. The authors further stated that adult and child cases gave rise to 2,681 malaria deaths; 90% were in rural areas, and 86% were due to a lack of medical facilities. Walther et al. (4) presented a survey of quantitative epidemiology methods and addressed global challenges to the worldwide elimination of malaria. Darkoh et al. (5) developed a water-based prediction model for the prediction of malaria prevalence in Ameni, in the west of Ghana.
|Global burden (2016-2017)|
|2||South-East Asia||14.6 million||27000|
|3||Eastern Mediterranean||4.3 million||8200|
Malaria is caused by a family of parasitic protozoans of the Plasmodium family. The Plasmodium parasite has several different species, but only five are responsible for malaria infection: Falciparum, Vivax, Malariae, Ovale, and Knowlesi. In India, the first two of these species cause malaria in humans. The dominant infecting species is Vivax; however, there was a reduction in its prevalence in 1985, which brought the ratio of Falciparum to Vivax to 0.41. In 1995, the ratio increased to 0.60 and this had changed to 1.01 by 2010 (6). The WHO launched a project of prevention and control of malaria disease in India, and the current work was carried out under their aegis (1). Certain geographical regions are more affected than others by the number of patients and by climatic conditions, which are dependent on attributes such as temperature, humidity and rainfall, it is therefore necessary to classify these regions into low or high-risk areas for malaria. By classifying malaria-prone zones, we can obtain information about high-risk areas, which can then be reported to the municipal authorities and other local bodies. These organizations can use this information to prevent this disease by initiating early fogging and other control measures to stop the breeding of malaria species. Our objective is therefore to classify regions of high or low proneness to malaria, based on climatic conditions and their changes. This study is focused on the identification of malaria-prone zones and on the triggers for the occurrence of malaria in a specific geographic location in Goa, India.
Malaria is usually transmitted by a female mosquito (7)(8). Malaria is also communicable through the bite of the mosquito. When, an infected Anopheles mosquito bites, it introduces parasite to our blood. Also, when a mosquito bites an infected person, biting mosquito becomes infected and it transmits the parasite. The parasite, present in Anopheles saliva, enters the blood through the bite. Through the bloodstream, parasite reaches to the liver. Parasite matures and reproduces in the liver within 48 to 72 hours (9)(10). The matured parasite then travels through the bloodstream, and starts infecting the blood cells, usually RBC. Once parasite enters into RBC, it starts multiplying within two to three days, causing the burst of a cell, and as a result, this infection is transmitted to other cells in the blood. At synchronous time intervals, infected blood cells burst and it introduces more population of parasites in the blood. The bursting cycle of infected blood cells is 48-72 hours. Each time when cells are bursting, a person feels a bout of fever, sweating and chills. Malaria parasite infection cycle is shown in Figure 1. The parasites persuade separation of the infected hepatocyte takes place, enabling it to relocate to the liver sinusoid where sprouting of parasite-filled vesicles called merosomes (Figure 1: Label 1). The new merozoites rapidly divide within erythrocytes, sometimes synchronously in cycles with fever and chills (Figure 1: Label 2). Responding to an unconfirmed cue, few parasites separate into male and female gametocytes (Figure 1: Label 3), which are the forms that live inactively in the circulatory system for a week. When gametocyte enters the mosquito by means of blood, they quickly transit to become initiated male and female gametes (Figure 1: Label 4). The motile and fleeting diploid parasite frame, the ookinete, moves out of the blood (Figure 1: Label 5), over the peritrophic lattice to the mid-gut partition where an oocyst is shaped (Figure 1: Label 6). After a meiotic decrease in the chromosome, numbers of sporozoites are framed inside the oocyst (Figure 1: Label 7). Finally, the oocyst splits and sporozoites relocate to the salivary organ to anticipate exchange with vertebrate host. Malaria infection can grow to hypoglycemia, cerebral malaria or anemia as result the blood carrying capillaries are blocked due to the thickness of blood. This happens, when the parasite is drug resistant or there is a lack of availability in proper medicines. The cerebral malaria is a key factor of lifetime learning disabilities (11), it can cause coma and further may lead to death.
Malaria parasite life cycle.
There have been few studies in the field of regional classification of malaria-proneness. Recently, Santosh et al. (12) presented an artificial neural network (ANN) that uses a sigmoid function as an activation function in a prediction model for malaria using data engineering, for the southern regions of India, and addressed the problems of scalability and time complexity for traditional machine learning algorithms. For classification, a feedforward multilayer perceptron (MLP) is a widely used neuron model that uses backpropagation (BP) as a learning method with weight updating (13). Feedforward nets are efficient in terms of classification, but are time-consuming.
The first artificial neuron was proposed by McCulloch et al. (14), and was known as a linear threshold unit (LTU) or threshold logic unit (TLU). This model was a mathematical interpretation of a neuron. Sharp et al. (15) proposed an electrical model of an artificial neuron and explained the oscillation properties exhibited by this neuron. Izhikevich (16) introduced the concept of resonate and firing in neural activities, which exhibited biological properties. In recent years, spiking neuron models (third-generation ANNs) are used in classification and prediction problems and these have shown improvements over conventional neuron models. Abbott (17) introduced the concept of threshold values for spike generation, and stated that an integrate-and-fire neuron (IFN) exhibits almost all of the characteristics of pharmacological input neurons or natural neurons. Abbott et al. (18) developed a generalized non-linear IFN for electrical circuits. Stein et al. (19) developed a new model by introducing a leaky term into the IFN and it was added to the membrane potential, the model was termed a leaky IFN (LIFN), and this model was developed as a special case of the generalized IFM model. Nicolas et al. (20) proposed another special case called the quadratic IFN (QIFN), which was derived from the generalized IFN model. Fourcaud et al. (21) presented an exponential IFN (EIFN) neuron model which uses an input current in the form of an exponential or spiking current. A further description of spiking neural networks is presented in the Discussion section.
The interspike interval (ISI) is a key factor affecting the passing of information from one neuron to another. Yadav et al. (13) observed that ANNs are efficient in performing pattern classification when the biological properties of the neuron are included. The authors used an MLP with an ISI derived from IFN, and this yielded better accuracy and lower time complexity. We thus hypothesize that the ISI obtained from the proposed neuron model with a BPNN will yield a regional classifier for our objective solution. This neuron mimics the characteristics of natural neurons, and when embedded with BPNN, can provide a more robust solution. This study presents an ISI-based BPNN (ISI-BPNN) function in which the proposed architecture is a single-pass spiking learning strategy which is useful for nonlinear regression tasks.
Based on this approach, we implemented an architecture that leads to the following contributions: (i) the design of a new spiking function for a nonlinear IFN model (NLIFN) and its ISI; (ii) this ISI is then used as an aggregation function in a BNN, and is referred to as an ISI-BPNN. In addition, weight updating equations are derived and comparative studies are performed via experiment; (iii) real-world malaria data are used in a comparative performance evaluation of the proposed ISI-BPNN. The rest of the paper is organized as follows: Section 3 presents a mathematical model of the spiking function along with the ISI-BPNN architecture. Machine learning architecture is discussed in Section 4, and the experimental protocol involving a real-world malaria dataset is discussed in Section 5. The results of experiments using the proposed method are presented in Section 6. A performance evaluation of ISI-BPNN is conducted in Section 7, and Section 8 contains a scientific validation and statistical analysis. In Section 9, we summarize the paper and present a discussion of the proposed design, including benchmarking, special notes on the sigmoid function and neural networks and their strengths and weaknesses, and future work. Finally, the study is concluded in Section 10.
A spiking neuron model closely mimics and simulates the computational characteristics of a natural neuron. The IFN was the first model of a biological neuron, and was designed using a simple R-C circuit (11). In an IFN, action potentials are represented as an event, often termed a spike, and neurons communicate with each other based on spike time intervals.
The design of the proposed system is inspired by the generalized IFN model. We create a spiking function, and the aggregated output is used as input to the sigmoid function in the BP algorithm. We therefore call our approach ISI-BPNN. The global model is shown in Figure 2. The object process diagram illustrates the procedure of the model development, and contains three processes: the design of the spiking function, the design of the ISI and the integration of ISI with BPNN, as shown by three different ellipses. The spiking model (phase I) is designed using the generalized IFN model, retaining features such as robustness, constraints and a single-pass model (derived in the next section). Phase II uses constraints and an integration model to generate the aggregate function. Phase III uses this weighted aggregated sum to generate the ISI-BPNN, using the steepest descent paradigm. Following this, the input to the sigmoid function is constructed, and finally, the new classifier is obtained from the sigmoid function.
Object process model showing the aggregate sum used in the design of ISI-BPNN
An IFN is an efficient model that is capable of computing the characteristics of a biological neuron over time. In an IFN, the membrane potential is directly proportional to an externally injected current. When this current is injected, the voltage potential rises, and after a certain time settles down to a threshold value. Once the membrane potential reaches a desired threshold, it generates a spike and then resets the voltage immediately after this spike. Usually, a biological neuron has memory, an equivalence term called a leak term is added to an IFN, and this is known as an LIFN. This is the most representative model of an actual biological neuron. The memory term is included in an action potential that represents the diffusion of ions inside the membrane cell. Biologically, diffusion occurs when the membrane cell is in disequilibrium. The generalized nonlinear IFN (21) is represented as:
where is the membrane constant, is the membrane potential at time , is the leaky inductance of the membrane, represents the external input current, and and represent the generalized functions of the membrane potential. We can obtain the QIFN by substituting a specific function of second order () for the membrane potential () and can obtain the EIFN model by substituting an exponent term () as a specific function for the membrane potential in the general equation for a nonlinear IFN, as shown in Eq. (1).
A new spiking model for a nonlinear IFN is proposed in this work. The proposed spiking function has the form, where and are positive numerals and have the relation: ;, represents the membrane potential, and represent the membrane potential function at time t and the cubic power function of respectively and is the inductance of the membrane. If we substitute the values of and into Eq. (1), i.e. and the values of a and b are substituted, we obtain an updated equation as given in Eq. (2):
where, , , , , and are the membrane potential, leak potential, external current input, time, membrane time constant, and incremental time, respectively (the derivation of Eq. (2) is given in the Supplementary Material). Once the potential reaches a threshold voltage , the membrane potential dynamics are interspersed, and then the potential is then reset after the spike following re-initialization at a resting potential of . The term is obtained by comparing the RHS of Eq. (1) and Eq. (2). The response from the firing rate of the proposed neuron model is analytically calculated as the first derivative of , i.e.
It is observed that the derivative satisfies the properties of nonlinear neuron model, i.e.
Furthermore, this nonlinear model also meets the requirements of the condition of the spike sloping factor ), i.e.
The proposed function has a lower order than the other spiking functions including , and proposed earlier. Biologically plausible spikes are generated by this proposed function. The LHS of Eq. (1) can be denoted by , a nonlinear potential of the membrane, and this is given as:
where, ; is a constant; * is the multiplier; R is the resistance of the membrane; and
is the external input current (and thus the product of the latter two parameters represents the voltage). The spikes obtained using a two-dimensional function from Eq. (2), at are shown in Figure 3(b). Izhikevich (23) stated that function should satisfy non-degeneracy and transversality conditions. Eq. (5) shows that a partial derivative of with respect to is not equal to zero. Hence, also satisfies the property of transversality and satisfies the property of non-degeneracy, since the second derivative is not equal to zero.
Spike dynamics (a) IFN, (b) ISI-BPNN
The ISI is the main source of information exchange, and appears in mammalian neurons (19). The zero-order solution of Eq. (2) gives an ISI that is responsible for inter-neuron communication. The ISI in the proposed model is given by Eq. (7) as follows:
The firing rate or frequency () is the inverse of time, and thus :
The spike generation timing is also known as the ISI, as shown in Eq. (7), and is necessary for the biological neurons to communicate. The integrated solution is given in Eq. (7) and is used in the construction of the aggregation function, which is also used as an activation function in the ISI-BPNN. The firing pattern exhibited by the model is shown in Figure 3. We can see from Figure 3(a) and Figure 3(b) that the spikes generated by IFN and ISI-BPNN are similar. The key benefit of the proposed spike-generating function is that it contains lower-order terms than other existing quadratic and exponential neuron models. The spike-generating function also reduces the computational complexity.
The new aggregation function for ISI-BPNN is derived from Eq. (2), as explained in this section. A parametric representation of Eq. (7) can be given as:
The computation of the new ISI-based BNN is shown in Figure 4. The network diagram consists of two layers. Input has attributes, and the first layer has neurons for each distinct feature and the second layer is the output layer.
Computation of the aggregated weight function
Assuming that the input to the neuron is and that the corresponding weights are , and that input neurons are connected to the neuron in the second layer, then the weighted aggregate at neuron is defined as:
where is the number of input neurons.
This subsection explains the development of ISI-BPNN and the training algorithm used. After the construction of the proposed network is explained, the training algorithm is given based on the steepest-descent formulae.
In the creation of the proposed network, is treated as the input for the activation function and is considered to be analogous to the input to the neuron and the ISI. Hence, it can be assumed to be a function of the externally injected current . Weights are associated with the corresponding inputs for the temporal summation when other synapse inputs are present. The other part of the IFN is represented in terms of a threshold function. Here, to represent the activity of this block, a sigmoid function is used in which the aggregated function is used instead of . Thus, the sigmoid function is written as in Eq. (11):
where, y is an s-shaped sigmoid function that lies between zero and one, meaning that when the input tends to infinity, this function achieves its highest value of one, and when the input tends to negative infinity, it achieves its lowest value of zero.
The machine learning architecture for the proposed scheme is given in Figure 5, which illustrates the entire process from the very beginning, including data collection, to the evaluation and validation of the model. In the first step, the collected data were preprocessed and a dataset prepared for classification. The K2 and K10 protocols were then applied to the dataset to prepare the training and testing data. The training data were used in classifier training, which generates the training coefficients. These coefficients were then used to transform the test dataset to compute the predicted classes of malaria-prone regions, that is, high or low risk. This process was repeated for the K2 and K10 protocols and the MLP, SVM, IFN, GCNN classifiers. Cross-validation was used to compute the accuracy of the machine learning architecture. The results of the prediction were validated to ensure the robustness of the system.
Machine learning architecture
The developed model was tested against conventional classifiers such as MLP, IFN, SVM, and GCNN. The theoretical concepts underlying these classifiers are discussed in this section.
The MLP is a feedforward artificial neural network (36) with a minimum of three layers: the first is an input layer, the second a hidden layer and last an output layer. The activation function is used at each layer in the MLP except the input layer. Figure 6(a) shows the traditional model of a feedforward network.
Conventional classifiers (a) MLP, (b) SVM and (c) GCNN
Support vector machines (SVMs) (37) are supervised classifiers that are used in classification and regression tasks. An SVM has a separating hyperplane by which it classifies the data. It is the most suitable model for labeled data classification, and uses a representation of points in a hyperplane that are categorized in terms of a positive or negative class. It uses a certain margin, based on which the labels are categorized as shown in Figure 6(b).
A generalized-constraint neural network (GCNN) (38) consists of three units: an input, a processing unit, and an output unit. The processing unit contains two subunits: a neural network sub-model and a partially known relationship model. During execution, there is a coupling between the units that allows the system to classify the input data when partially known relationships are applied to the input. The model is shown in Figure 6(c), which explains the conceptual working of GCNN.
This section presents the details of the data collection and the experiments performed. The proposed ISI-BPNN model is applied to a real-time dataset of malaria disease. Throughout the work, in terms of achieving the goal, experimental paradigms are used. We develop the ISI from the proposed function, develop an aggregation function, and finally develop the ISI-BP model and obtain its learning rule based on the aggregated function. We compute cross-validation protocols to examine the quality with regard to the generalized datasets for each approach. The first experiment is performed to test the effect on accuracy by making changes in the size of training data, using two methods of K-fold validation (K2 and K10). In the second experiment, we increase the size of the dataset and then apply K-fold techniques. The model is also tested for accuracy.
The malaria data used in this study were collected from a government infectious disease (ID) hospital in Ponda, Goa, via a Department of Science and Technology (DST), Science and Engineering Research Board (SERB) project at the National Institute of Technology Goa, India.
The data was collected over a three-year period from January 2015 to December 2017. Four attributes were measured: temperature, humidity, rainfall and the number of patients taken from 43 villages. The cohort consisted of 2,210 females and 2,564 males. Each record consisted of three attributes: temperature, humidity and rainfall. In all, 4,744 records were collected over this period, and the distribution was as follows: for the first month, three attributes (temperature, humidity and rainfall) were recorded for 43 villages, giving 43x3=129 records. In the first six months, 43x3x6=774 records were taken; over the first year, the total records were: 43x3x12=1548; and over the entire three-year period, the total number of records was: 43x3x12x3=4,744. Patients were recorded as testing positive or negative for malaria based on blood sample examinations. All the recordings were done in the register by hospital nurses. Positive malaria cases were recorded as a value of 1 (with malaria) and blank columns were treated as a value of 0 (no malaria). These binary data formed the ground truth information for the study. The collected malaria data contained records on patient visits, residential location and gender information.
The dataset consisted of the metrological attributes of temperature, rainfall and humidity as input, and the number of patients from a specific location as the target values. Attribute values were as follows: Average temperature (month high (°C)/low (°C)): Jan 32/20, Feb 32/21, Mar 33/23, Apr 33/25, May 34/26, Jun 31/25, Jul 29/24, Aug 29/24, Sep 30/24, Oct 32/24, Nov 33/22, Dec 33/21. Relative humidity (month humidity (%)): Jan 63%, Feb 64%, Mar 65%, Apr 67%, May 69%, Jun 84%, Jul 87%, Aug 88%, Sep 85%, Oct 78%, Nov 68%, Dec 62%. Average rainfall (month rainfall (mm)): Jan 0, Feb 0, Mar 2.54, Apr 17.78, May 104.14, Jun 678.18, Jul 985.52, Aug 589.28, Sep 231.14, Oct 132.08, Nov 35.56, Dec 12.7.
The geographic locations of villages in the Ponda area are shown on the map of Goa (the study area is shown in the Supplementary Material). The dataset consisted of records of patients from 43 villages around Ponda, as follows: 1. Adcolna, 2. Adpai, 3. Bandora, 4. Betora, 5. Boma, 6. Borim, 7. Candepar, 8. Candola, 9. Codar, 10. 11. Conxem, 12. Cuncoliem, 13. Cundaim, 14. Curti, 15. Dhavali, 16. Durbhat, 17. Farmagudi, 18. Gangem, 19. Jay Cee Nagar, 20. Kaziwada, 21. Keri, 22. Khadpabandh, 23. Marcaim, 24. Nageshi, 25. Nirancal, 26. Orgao, 27. Ponchavadi, 28. Priol, 29. Quela, 30. Querim, 31. Sadar, 32. Sahapur, 33. Santa Cruz, 34. Shanti Nagar, 35. Siroda, 36. Telaulim, 37. Tisk, 38. Tivrem, 39. Undir, 40. Usgao, 41. Vagurbem, 42. Velinga, 43. Volvoi.
The collected malaria data were given ethical approval from the Infectious Disease Hospital, Ponda, Goa, India. The patient records were maintained manually in the registers and these records were then converted into computerized datasheets by the hospital before being transferred for this study. During the study, double checking for errors was carried out after the data had been transferred from the hospital to Institute. During computerization, the patient records were anonymized.
The motive for performing this experiment was to examine the effects of changes in accuracy by making changes in the training set using the K2 and K10 protocols. Each fold is a subset of our dataset; K2 means that the data were divided in to two parts in a 1:1 ratio, i.e. half (50%) for training and half (50%) for testing, whereas K10 means that the data were divided into 10 parts in a 9:1 ratio, meaning that 90% of data were used for training and 10% for testing. These experiments were repeated 10 times on a random basis, and the average accuracy was recorded.
The motive for this experiment was to identify changes in performance by making changes to the dataset sample size. The sample size played a vital role in both performance and computation time during every iteration. We used four sizes of datasets: monthly, half-yearly, yearly and combined three-year data, and these were termed CN1, CN2, CN3 and CN4 which contains 129, 774 , 1548 and 4744 records respectively. It was therefore necessary to run K-fold protocols for these four types of datasets.
The aim of this experiment was to perform a comparative analysis of ISI-BPNN and calculate the mean accuracies for other classifiers including SVM, IFN, GSNN and MLP.
This section presents the experimental results, and is divided into three subsections. In the first subsection, the results of Experiment 1 are presented and a comparative analysis is carried out; in the second subsection, the results obtained in Experiment 2 are presented; and in the third subsection, the results of Experiment 3 are given in detail. Symbols used in this paper are listed in Table 2.
|SN||Symbols||Description of Symbol|
|1||Constant associated with aggregated function|
|2||Constant associated with aggregated function|
|3||Constant associated with aggregated function|
|4||Constant associated with aggregated function|
|5||Constant associated with aggregated function|
|6||Constant associated with aggregated function|
|7||Constant associated with aggregated function|
|8||Constant associated with aggregated function|
|9||Constant associated with aggregated function|
|10||Derived intermediate variables|
|11||Derived intermediate variables|
|12||Derived intermediate variables|
|13||Derived intermediate variables|
|14||Derived intermediate variables|
|15||Derived intermediate variables|
|16||Derived intermediate variables|
|17||Derived intermediate variables|
|18||Derived intermediate variables|
|19||Derived intermediate variables|
|20||Derived intermediate variables|
|21||Derived intermediate variables|
|22||Derived intermediate variables|
|23||Derived intermediate variables|
|31||Leak conductance of the membrane|
|35||η(k, I, t)||Accuracy for protocol, , and trial|
|37||Total size of malaria dataset|
|38||Total number of trials|
|43||Number of inputs|
|44||Exposure index of segregation|
|45||Isolation index of segregation|
|47||Total number of patients|
|48||Number of malaria positive cases|
|52||Non exposed diseased|
|53||Non exposed healthy|
The system accuracy () can be expressed using the following function:
where, is the partition protocol i.e. K2 or K10. are the number of trials, the index of the trial number, the dataset index and the size of the data respectively, as shown in Figure 7, in the figure, numbers on the bar are standard deviation. The accuracies for the K2 and K10 protocols are represented in green and purple, respectively. As can be seen from the figure, the proposed ISI-BPNN scheme exhibited an average accuracy for K2 and K10 of 91.78% and 98.06%, respectively. Figure 8, Figure 9 and Figure 10 show the monthly prediction results of our proposed algorithm for the years 2014, 2015 and 2016 respectively. We can observe from these Figures that our proposed algorithm gives the desired results, as the predictions are much closer to the actual cases. Here, we can clearly observe that for consecutive years, our model gave very accurate predictions and performed well, requiring less computational time.
Prediction results of ISI-BPNN for K-fold protocols (numbers on the bar are standard deviation)
Actual vs. predicted malaria patients for the year 2014
Actual vs. predicted malaria patients for the year 2015
. Actual vs. predicted malaria patients for the year 2016
To identify the effects of the size of the training data on the ISI-BPNN and other classifiers, we carried out an experiment by varying the size of the dataset. We conducted experiments on datasets of different sizes, i.e. CN1, CN2, CN3 and CN4. The accuracies for the K10 protocol obtained from these varying data are shown in Figure 11 (a) and the corresponding data are given in Table 3 where we can conclude that as the size of the dataset increased, the model became well-trained, and outperformed the other methods by yielding accuracies of 98.67% for DC3 and 99.28% for the DC4 dataset.
Prediction accuracies for (a) different data sizes (b) different classifiers (numbers on the bar are standard deviation)
The results for different classifiers are shown in Figure 11 (b), and the corresponding data are given in Table 3. The SVM, IFN, MLP, GCNN, and ISI-BPNN classifiers exhibited average accuracies of 85.14%, 89.8%, 87.6%, 87.0% and 91.78%, respectively, for the K2 protocol. Prediction results for the K2 and K10 protocols are listed in Table 4 respectively. In Table 5, the average improvement in accuracy for the K2 and K10 protocols is compared with the ISI-BPNN scheme; the ISI-BPNN model exhibited an 11.9% increase in accuracy over the conventional classifiers.
Any modeling procedure needs to be subjected to testing, verification and validation. These procedures are used to determine an accurate fit of the model to the phenomenon being modeled. Regardless of which modeling procedure is followed, the performance of the model shows the first insight of representation as expected for a real-time scenario in systems.
The performance of the model can be assessed based on very different aspects. The primary purpose of the verification process is to confirm whether or not the desired output is obtained. The quality of the model is always a critical issue (24), and this study therefore implements a two-phase performance evaluation to ensure both the reliability and the stability of the system.
The receiver operating characteristic (ROC) curve is used to validate the diagnostic capability of the ISI-BPNN classifier. The plotted curve and corresponding area under the curve (AUC) is shown in Figure 12. The AUC is 0.9636 for ISI-BPNN, implying a 96% chance (or probability of 0.96) that model classifies the data correctly. Thus, the system is accurate enough to perform binary classification. Conventional classifiers have a lower AUC(s).
ROC curve and corresponding area under the curve
In the sample dataset, as shown in Table 6, there are four features to be input to the system and one response variable. The ground truth variables are the maximum and minimum temperatures, rainfall, and humidity. The threshold for maximum temperature is 40 ± 2.5°C, for minimum temperature 15 ± 2.5°C, for rainfall 120 ± 5 mm and for humidity 40 ± 5%. The accuracies are recorded in order to analyze the sensitivity to the variables, and are shown in Figure 13, Figure 14, Figure 15, and Figure 16, for the four variables. It is clear from the standard deviation shown in Table 7 that the model has low sensitivity (< 5%) to all parameters. Other classifiers also have low sensitivity; however, ISI-BPNN is more robust than IFN, MLP, SVM and GCNN.
Sensitivities to minimum temperature
Sensitivities to maximum temperature
Sensitivities to rainfall
Sensitivities to humidity
|WN||T max (°C)||T min (°C)||Humidity (%)||Rainfall (mm)||# patients|
Validation defines the stability and robustness of the system. In this study, the aggregated function can control the system dynamics. To validate the ISI-BPNN, two synthetic datasets are used and the malaria segregation index is calculated. In order to validate the proposed model, we use two datasets from the UCI machine learning repository called Thoraric Surgery (https://archive.ics.uci.edu/ml/datasets/Thoracic+Surgery+Data#) and Parkinson’s Disease (https://archive.ics.uci.edu/ml/datasets/parkinsons). The UCI repository has the largest available collection of datasets for performing tests on machine learning and artificial intelligence. The Thoracic Surgery dataset has 17 attributes and 470 instances associated with classification problems. It has two classes, true (Y) and false (N), and of the 470 records, 70 are true instances and 400 false.
Segregation analysis is performed in order to statistically validate the developed model. The index of dissimilarity, segregation, exposures and odds ratio/risk ratio are calculated. These as given as follows:
To find the dissimilarity, we need to calculate the distribution of malaria and non-malaria throughout the evaluations of a particular village. The index has a minimum value of zero and a maximum of 100.
where , , , and are the number of cases in a particular village, the non-malaria cases in that village, total number of malaria patients throughout the year, total number of non-malaria cases throughout the year and the number of villages considered, respectively. The summation is applied to the total number of villages and the respective numbers of cases in that location. The average dissimilarity index for the nine villages in the Ponda area was 5.670. Using a normalization scale of between zero and one, the DI is 0.0567. The similarity can be computed as , giving a percentage similarity of 94.3%. From the above analysis, we conclude that ISI-BPNN is statistically significant, validating our hypothesis.
The isolation index of segregation is given by:
where is the isolation index of segregation, and is the total population of the village. The isolation index obtained for the villages was very close to zero, meaning that the predictions made by ISI-BPNN were very close to the actual results. The isolation index obtained was 0.0011, implying that the majority (malaria) population and minority (non-malaria) populations are equally distributed among the villages.
The exposure index of segregation is given by:
where is the exposure measure of segregation, is the total population of the village, is the number of non-malaria cases in that village and is the number of villages. A lower exposure index means a lower dissimilarity between the predicted and actual results. All values are calculated based on the predicted number of cases with respect to the total population. The exposure index obtained for Ponda was 0.0149, meaning that ISI-BPNN exhibited a very low dissimilarity between the actual and predicted results.
Odds ratios are the measure of the outcome and exposure of the disease. This measure is used to compute the stability of a system. If the odds ratio (OR) is equivalent to the risk ratio (RR), then system is considered to be stable. The values of exposed/non-exposed vs. diseased/healthy populations used to calculate the OR and RR are given in Table 8. The risk ratio and odds ratio are calculated as and , where is exposed diseased, is non-exposed diseased, is exposed healthy, non-exposed healthy, is the odds ratio and is the risk ratio, we have:
|Odds Ratio Index||Diseased||Healthy|
Here, we can observe
i.e. the values obtained for OR and RR for malaria cases are approximately similar, showing that we have a low dissimilarity in malaria classifications between the actual number of cases and the predicted number of cases used to identify malaria-prone zones. This validates the hypothesis and demonstrates the superior performance of ISI-BPNN.
The Thoracic Surgery dataset is multivariate, and the attributes are an integer and a real number. The data are from primary lung cancer patients who underwent major lung resections. The dataset is related to patients who survived for one or more years after the operation, and life expectancy is used as the class in the dataset. Patients who survived for one or more years are classified as True (T) and patients who did not survive as False (N).
The Parkinson’s dataset contains values of biomedical voice measurements of patients with Parkinson’s disease. There are 23 records of Parkinson’s disease among the 31 records in the dataset. The dataset consists of 23 attributes and 197 instances, and is a multivariate dataset containing real attributes that are specifically used for classification problems. This was originally used in a feature selection method for voice disorders using recorded speech signals. The improvement shown by ISI-BPNN in comparison with conventional classifiers on the Thoracic Surgery and Parkinson’s datasets for the K2 and K10 protocols is given in Table 9. The comparative analysis of validation datasets is shown in Figure 17.
Validation accuracy for the dataset (a) Thoracic Surgery and (b) Parkinson’s
Experiments were carried out to test the robustness and validate the proposed method using the Thoracic Surgery and Parkinson’s datasets. The average accuracy for the Thoracic Surgery dataset for the K2 protocol was found to be 0.7588, and for the K10 protocol, this was 0.8236; the average accuracy for the Parkinson’s dataset for the K2 protocol was found to be 0.8175, and for the K10 protocol, this was 0.8818, as represented below in Figure 18.
Bar representation of accuracies for two datasets (numbers on the bar are standard deviation)
The improvements offered by ISI-BPNN over conventional classifiers on these two datasets were found to be 11.4% for the Thoracic Surgery dataset and 6.05% for the Parkinson’s dataset. These values show that if the size of the training dataset is increased, the accuracy of the system is high compared with the smaller dataset provided during execution. In the K2 protocol, half of the data are used for training and the other half for testing, giving lower accuracy for both datasets compared to the K10 protocol, where 90% of the data are used for training and 10% for testing. Thus, the proposed method is validated against two datasets.
We trained ISI-BPNN using the training data, and then used the testing data to generate predictions. This process was repeated with the MLP, GCNN, SVM, and IFN schemes. Table 9 shows the results using the proposed method and other existing methods such as MLP, IFN, SVM and GCNN using K10. We can easily see that ISI-BPNN outperforms the other models, giving accuracies of 89.93%, 98.67%, and 99.28% for monthly and yearly data and historical data over three years.
To validate the proposed methodology, we performed these tests on two more datasets called Parkinson's and Thoraric Surgery, retrieved from the UCI Repository. The results are shown in Table 10. After every round, the dataset was shuffled and the protocol was applied. The results obtained from these validation experiments shows that the accuracy of ISI-BPNN increases as the size of the training dataset.
In this study, we proposed a new spiking function embedded in the BPNN framework called ISI-BPNN, which was applied to predict the occurrence of malaria disease in different geographical regions of Goa. The sensitivity of ISI-BPNN towards metrological factors was analyzed. The model was benchmarked against a set of four conventional classifiers: MLP, IFN, SVM, and GCNN. ISI-BPNN showed superior performance, yielding a cross-validation accuracy of 93.22% using K2 (50% training) and 99.28% using K10 (90% training). Our benchmarking results showed an improvement of 11.9% against an MLP and 9.19% against IFN models. ISI-BPNN was also tested for reliability and stability. The hypothesis for the model was validated using the two synthetic datasets called Thoracic Surgery and Parkinson's. The results showed very low deviation (<5%), thus demonstrating the robustness of the model. The study was carried out on a system with the following specifications: 8 GB RAM, Intel® Xeon® CPU E5-2620 v4@ 2.10 GHz, 64-bit operating system, x64-based processor, using the software application MATLAB R2015a.
We performed this study using data for the western coastal regions of India, where the population index is low compared with the northern regions and the local flora and other metrological indices are very different. These coastal areas are very suitable for the survival of malaria-carrying parasites. Based on the relevant metrological and environmental factors, we prepared the model to predict the incidence of malaria. Malaria is a major problem in India and its neighboring countries, this study is an attempt to model an Indian region to propose a model which can identify malaria-free zones in India. A target of the WHO is to make India malaria-free by 2030, and support for this study was provided by the Indian Government, with the aim of researching public epidemics and healthcare and preventing the spread of this life-threatening diseases. In the future, this work will be extended and used to eliminate malaria to meet the goal of zero cases of this disease.
Validation protocols like segregation analysis were applied to the obtained results, and we can see that the proposed model outperforms existing methods. Better prediction results and higher accuracy are obtained as the data size is increased; if the training dataset is small, the accuracy is low and when we increase the size of the training dataset, the accuracy increases to a satisfactory level. The performance of the proposed method is also evaluated using malaria data. Monthly, half-yearly data, annual and five-year combined data are used for this performance evaluation. A workflow model is given in Figure 2, and this illustrates the process of this study. Firstly, the collected data were preprocessed and missing values cleaned. The dataset was divided into training and testing data according to the K-fold technique; here, 10-fold cross-validation (10 CV or K10) and 2-fold cross-validation (2 CV or K2) were carried out. We considered several estimation parameters such as the accuracy and stability over the datasets. The dataset was shuffled using the 10-CV method (which uses 90% data for training and 10% for testing) and the 2-CV method (50% data for training and 50% data for testing). The performance evaluation phase of the proposed system gives very interesting results, as shown above. A segregation analysis is also performed to test the similarity and dissimilarity index of the model. For each village in Ponda, the value of the dissimilarity (out of 100) is obtained as follows: 5.49 for Cundaim, 5.009 for Querim, 4.880 for Adcolna, 4.255 for Ponchawadi, 5.653 for Durbhat, 3.204 for Codar, 5.213 for Niranchal and 3.363 for Siroda. In these experiments, we used data from 2014 and 2015 for training and 2016 data for testing. From the above dissimilarity index analysis, we conclude that the villages of Siroda, Codar, Ponchawadi, Adcolna and Niranchal have an accuracy close to 97%, and thus are prone to malaria. If we consider Ponda as an overall location, we need to find the total population and the total number of cases in all the villages of Ponda; this gives the total population of Ponda as 165,830 including both urban and rural areas, and the number of malaria cases is found to be around 2,853 from entire dataset. Using these values in the evaluation, we obtained a dissimilarity index of 5.670 for the entire Ponda location, with a ground similarity of about 94.30. We can conclude that the Ponda area is not malaria-prone, because there was a decrease in the average number of malaria patients in 2016 compared to 2014 and 2015. In addition to the dissimilarity index, we also computed the isolation and exposure indices and showed that the ISI-BPNN exhibits very low dissimilarity to the number of actual and predicted malaria cases.
The benchmarking study and comparative analysis is shown in chronological order, and the attributes are depicted in the columns of the Table 11. As can be observe, none of the previous studies applied the CV protocol (see column C6). Although many authors have worked on malaria disease, most have used laboratory data from blood samples, and have classified malaria-infected and healthy cells. These authors have also included malaria parasite and species data to identify the disease in their study. In some of these studies, metrological data were also used. In the present study, we focused on metrological data and obtained malaria data from a regional government hospital. Scientific validation is given in column C7. The proposed method exhibits better accuracy than other methods (see column C9). As completely different approaches have been developed over the last ten years, many experiments have been carried out to achieve the present state of the art. However, despite the large variety of studies, current performance is not satisfactory for clinical use. Several prior articles simply discuss the sensitivity and specificity of classification, representing just one in operation purpose on a receiver in operation characteristic. Some publications aim to identify the progress and control status, which may add an additional complete analysis of any technique for various sensitivity necessities.
|R1||(33)||Laboratory data||Bayesian net||Environmental variables, clinical treatments||7||N+||Y#||580||80%|
|R2||(36)||Malaria species data||MLP||Color, morphological, texture||-||N+||N+||205||90.34%|
|R3||(35)||Laboratory data||SVM, MLP||Images||-||N+||N+||140||87.8%|
|R4||(24)||Blood smear||Jordan-Elman NN||-||6||N+||Y#||450||96.4%|
|R5||(34)||Metrological data||SVM, MLP||Environmental variables||6||N+||Y#||1680||89%|
|R6||(31)||Laboratory data||MLP||RBC samples, images||6||N+||N+||48||90%|
|R7||(30)||Laboratory data||MLP||Blood samples, symptoms||-||N+||Y#||376||85%|
|R8||(12)||Clinical and metrological data||MLP||Environmental variables, clinical treatments||5||N+||Y#||52||80%|
|R10||Proposed work||Metrological data||ISI-BPNN||Environmental variables||4||K2||Y#||4744||88.09%|
|R11||Proposed work||Metrological data||ISI-BPNN||Environmental variables||4||K10||Y#||4744||98.67%|
Austeclino et al. (33) used immunological and epidemiological data and the past infection history of the patient for malaria diagnosis. An ANN and a Bayesian network (BN) were used with a comparison of the classification (diagnosis) results using light microscopy and polymerase chain reaction (PCR) laboratory methods. The authors reported improvements in accuracy of 18.75% and 6.25% for the ANN and BN, respectively, compared with microscopic laboratory tests. Memeu et al. (36) developed a method of identification of parasite life stages using blood smear images. These authors used an ANN for the classification of infected erythrocytes in different stages of the parasite life cycle. The results showed an accuracy of identification of species of the plasmodium family of 96.3%. Chavan et al. (35) used image processing method for malaria screening involving an SVM-based classifier, and used a gray-level co-occurrence matrix to extract features from RBC colored images (later converted to grayscale) which were used as input to an SVM and an ANN. These authors obtained classification accuracies of 98.25% and 78.53% for SVM and ANN, respectively. Chiroma et al. (24) discussed the classification of malaria using thin and thick blood smears with a Jordan-Elman neural network (recurrent neural network). These authors achieved a classification accuracy of 96.4%. Vijeta et al. (34) performed prediction of malaria outbreaks using SVM and ANN as data mining classifiers, and obtained RMSE values of 0.12 and 0.47, respectively, i.e. with superior performance from the SVM. Purnima et al. (31) developed an ANN-based classifier for the binary classification of red blood cells (infected vs. normal) taken from holographic images. This system was trained on the quantitative features derived from the cellular images, and demonstrated an accuracy of 90%. Rahila et al. (30) used the patient’s medical history (including shivering, vomiting, dry cough, back pain and headache) and symptoms as input to the MLP and performed malaria classification as positive or negative. Authors used backpropagation, backpropagation with momentum and a resilient propagation learning rule for MLP training, and obtained a classification accuracy of 85% in the backpropagation learning method. Santosh et al. (12) presented an ANN that used a sigmoid function as an activation function for a prediction model for the prevalence of malaria using big data processing; this was applied to the southern regions of India, and addressed the problem of scalability and time complexity for traditional machine learning algorithms. Belay (32) applied a support vector regression (SVR) and ANN in the classification of malaria data. The results showed values of root mean square error (RMSE) of 4.29 and 5.57, respectively, for the SVR and ANN. In the proposed method, we develop a new spiking function and obtain the ISI, which is aggregated and used as an input to the sigmoid function. The new sigmoid function is also used as an activation function in the backpropagation algorithm, and is called ISI-BPNN. Metrological factors are used as input data for the number of malaria cases within a particular geographical location. We also used K2 and K10 K-fold validation protocols, where we achieved accuracies of 88.09% and 98.67% for K2 and K10, respectively.
The sigmoid function is an activation function used in a backpropagation algorithm. As the input to the conventional sigmoid function is replaced in the proposed model with an aggregated spiking function, the protocol is known as ISI-based backpropagation. The new sigmoid function plays a vital role in the system dynamics. Once all these analytical studies performed, we can see from many points that, the developed model is obtaining its goal. The hypothetical system used for the development of this model was evaluated using several measures, and those measures were justified by tests and analysis. One of the major factors in the success of the developed model is a lower computational complexity due to the spiking sigmoid function. The developed model has a lower order of computational function, making it faster and less complex than legacy models. Another factor is the use of K-fold protocols for shuffling the data during computation, which makes the system more reliable in terms of the different sizes of data inputs. We observed that for a smaller training dataset, the prediction accuracy was poor, but when of the size of the test dataset was increased, the accuracy increased. For the larger training set, the accuracy was about 99.28%, as shown in the benchmarking study. The learning behavior of the system is similar to the natural neurons in the human brain; as more knowledge is obtained, performance increases. In the same way, the accuracy of the proposed method is higher for larger training samples. From this point of view, we have achieved our goal of learning and developing a biological neuron model.
Neural networks are often used for classification and regression tasks. Feng et al. (25,26) discussed IFN models with current inputs as part of a development series of third-generation neural networks. A neuron model was trained and applied to a binary classification (zero or one) equivalent to XOR gates. A spike was generated if the voltage was greater than a threshold when the current was applied to an R-C circuit. Mishra et al. (22) applied single and quadratic IFN models to the binary classification of an XOR problem (similar to Feng et al. (25)) and to a linear regression-based classification. Wulfram et al. (27) showed mathematically that a single neuron can be used for classification, and referred to this as the plasticity phenomenon. Chandra et al. (28) presented a new neuron model similar to quadratic IFN for classification, using a lower-order activation function, and demonstrated a reduction in computational complexity. Schollas et al. (29) presented the modeling of bio-inspired neural network and applied to time domain beamforming, model was used for sonar ranging, focusing and steering. This work was influenced by two contributions from Yadav et al. (13) and Chandra et al. (28), in which a new spiking model was presented by the authors.
It can be observed that ISI-BPNN performs better in terms of prediction. Due to the use of a lower-order function, the model has a lower computational complexity than traditional models; as the size of the dataset and the number of iterations are increased, the proposed model performs faster, and the time complexity is lower. The scope of this experiment is limited to numerical types of data, and a limited amount of collected data is used. We can use this system for a broad range of datasets, and can extend the model to add more features such as the ratio of vegetation, water index, geographical area and population index to achieve better results. This model can also be applied to different datasets for the early prediction of disease. Based on our results, it is evident that our model can be used as an early predictor for malaria for epidemic-prone regions. We could also adapt fuzzy rule sets to give more robustness to the system. Through this study, we can serve public epidemic healthcare and prevent the spread of life-threatening diseases by the early prediction of disease. In future, this work will be extended to help ensure the goal of zero cases of malaria.
This study has presented an ISI-based BPNN (ISI-BPNN) architecture that uses a single-pass spiking learning strategy with a parallel structure that is useful for nonlinear regression tasks. We demonstrated that ISI-BPNN was more efficient than the MLP, IFN, SVM, and GCNN models. A malaria dataset was collected through the National Institute of Technology, Goa. The results demonstrated that ISI-BPNN shows superior performance, yielding a cross-validation accuracy of 93.22% for K2 (50% training data) and 99.28% for K10 (90% training data). Our benchmarking results showed an improvement of 11.9% against the multilayer perceptron and 9.19% against IFN models. ISI-BPNN was also tested for its reliability and stability. Our proposed ISI-BPNN model effectively predicted the class of malaria-prone regions as high or low risk for consecutive years. In future, ISI-BPNN could be extended to the prediction of malaria-prone areas in other Indian states and worldwide. This model could also be extended to the prediction of diseases in different geographical locations. We conclude that spiking model found to be efficient than classical neuron models for classification.
We are thankful to the Department of Science and Technology, Science and Engineering Research Board, New Delhi, India vide, Project No. ECR/2017/001074, for financial support. We also thank Dr. Pradip Shinkre, Medical Superintendent, SDH, Ponda for providing data used in this study and Dr. Ashwani Kumar, Scientist-F & Officer-In-Charge, National Malaria Research Institute, Goa for his key suggestions to carry out the research. Special thanks to Global Biomedical Technologies, Inc., Roseville, CA, USA in support throughout the project, especially in experimental design, performance evaluation and stability analysis.
Integrate and Fire Neuron
Spiking Neural Network
Generalized Constraint Neural Network
Support Vector Machine
Backpropagation Neural Network