Predicting Kids Malnutrition Using Multilayer Perceptron with Stochastic Gradient Descent

Nowadays, most of the kids under the age of five in rural areas are mainly suffering from malnutrition and it was a significant general medical issue in India [1]. In addition to that, the lack of healthy sustenance issue in India is highly concentrated on a generally modest number of states, local, and towns that represents an enormous portion of the unhealthiness trouble. In 2016, it was estimated that about 155 million children who are under the age of 5 were suffering from stunting and over 41 million children were recorded to be overweight or obese. Malnutrition in all its forms includes under-nutrition (wasting, stunting, and underweight), inadequate vitamins or minerals, overweight, obesity, and resulting diet-related no communicable diseases [2].

The malnutrition deficiency among the children who reside in the slum areas of Mumbai by using Logistic Regression (LR) and reported that lack of financial crisis in the family leads to having under nutrition to those children [3-5]. Earlier studies are performed by the American Alliance for Health, Physical Education, and Recreation & Dance (AAHPERD) test through the Descriptive-correlation method to analyze the correlation between the heights and weights among 9-18 years children's in Iran concerning malnutrition [6]. The proposed Boosting Additive Quantile Regression (BAQR) method was used to determine the risk factor of severe childhood malnutrition of children in India based on demographic and health surveys for the year 2005-2006. A recent article [7] analyzed that disease burden attributable to maternal and child malnutrition, this literature took the data from 1990 to 2017 in every state of India utilizing total availability data from more than one source. Mohammad Mohseni [8, 9] and the team analyzed present policies of malnutrition prevention in kids less than framework policy study was conducted to analyze the policies of malnutrition. One of the recent articles [10] shown the impact of COVID-19 on kids' malnutrition and mortality nutrition-related. In Saharan Africa and South Asia before the COVID-19 pandemic, an estimated 47 million children less than 5 years were normally or severely diseased.

From the whole literature study, we can understand that only analysis and some correlations are found but this article created a malnutrition predictive model. The capability to predict the kid's malnutrition is highly beneficial to take remedial actions in the present context of kids' malnutrition in the form of recommending healthy food to children and their parents physically [11, 12].

The upcoming portions are arranged as follows section 2 contains Data and its visualization, section 3 is about our proposed model, section 4 describes the result analysis of the proposed model, and finally, section 5 contains the conclusion.

The overall process involved in the proposed model is shown in Figure 4. It operates at various stages namely; raw data, pre-processing, and normalization that used to reduce the attribute values to a small range [0.0 to 1.0], FS is used for selecting the best features with higher ranks using filter-based methods. MLP with SGD classifier techniques is used for removing the misclassified instances after pre-processing and normalizing the data. Once the classification process is done, a set of experiments will be carried out to measure the results of the developed model. Accuracy made by the proposed model is higher than the existing traditional classifiers namely; Naïve Bayes (NB), Support Vector Machine (SVM), and Decision Tree (DT).

3.1 Pre-processing

Before applying the algorithms of ML on the data set, the pre-processing of data is required [9]. It contains the cleaning of data, best feature selection, the transformation of data [10].

3.2 Feature selection

In the pre-processing section, selecting the features is the primary task. An information gain selection algorithm is applied to evaluate the feature rank filter method. Every feature will get rank according to features influence on the classification of data during the selection of best features are shown in Figure 5. the reason for choosing filter-based methods compared to other methods in feature selection is, selection of feature in filter-based method technique based on scores in various statistical tests for their correlation with the outcome variable and it is computationally very simple and flexible but other methods are computationally very expansive. Here top 8 rank features are selected as the best features such as children's age, weight, height, children's parents (mother and father) weight and height, the overall health of children mother these features are playing a key role in building an effective prediction model for kids malnutrition. Marriage Consanguineous, the overall health of father and kids gender position to the last 3 ranks.

4.jpg

Figure 4. Proposed model for predicting the malnutrition kids

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Figure 5. Evaluation of feature selection using filter-based

3.3 Multi-layer perceptron with stochastic gradient descent

MLP with one hidden layer called a discriminant nonlinear function shown in Eq. (1).

$y=f_{\theta}(x)=\sigma(b+B . \sigma(A+A . x))$   (1)

where, A, B are two matrices, θ denote two vectors a, b, and vector element-wise sigmoid function is σ (...).

Reducing the few main functions including y, these attributes are optimized always through SGD and real classification data. C(θ) is the objective function. There is more effort to effectively carry out SGD optimization. Commonly, function $f_{\theta}$  comprises numerous local minima.  By training the small Neural Network (NN), local minima are observed frequently over issues such as parity, spiral, and XOR. More effort is exhausted during training irrespective of such local minima. Due to the $f_{\theta}$  symmetry additionally single local minimum offers higher local minima within the parameter vector. At various scales, C(θ) might comprise minimal hierarchy generally. During NN training, many schemes are gained through these assumptions. At smaller scales, momentum is subjected to mold out the local minima and the schedules of learning rate are probably ready at various scales as same as simulated annealing. In weighted space, the MLPs convergence observation and the various weight settings offer an equal output. Besides, it is composite to discover the MLP in high dimensional weight space. For various starting points, C(θ) is the optimization tracing. It employs a $\left\{\xi_{1}, \ldots \xi_{N}\right\}$  as sample test set collection despite θ parameters comparing and estimating the respective vector as shown in Eq. (2).

$\tau(\theta)=\left(f_{\theta}\left(\xi_{1}\right), \ldots, f_{\theta}\left(\xi_{N}\right)\right)$  (2)

It is needed for $\tau(\theta) \approx \tau\left(\theta^{\prime}\right)$ for θ and $\theta^{\prime}$ as two weight vectors. In the NN-SGD optimization method, when the standard view is correct that is below predictions might be given as true where there exist many local minima. SGD will pursue an applied learning rate till the learning rate becomes large and the search moves over an arbitrary walk around the local minimum. θ parameter space must be separated from the areas for an applied learning rate i.e. everyone belongs to basin over a local minimum respective towards the learning rate.

Defining the SGD in the proposed work is to tackle the problem of massive data classification over MLP. With examples $S=\left\{\left(x_{i}, y_{i}\right), i=1, \ldots, N\right\}$, assume the problem of binary classification, wherever d-dimensional input vector in the form of sample $x_{i} \in R^{d}$ and the label is denoted through $y_{i} \in\{+1,-1\}$. MLP classifier training is represented in Eq. (3).

$f(x)=\operatorname{sgn}\left(w^{T} x\right)$  (3)

By employing S, with every input, weights vector w is linked that is formed as in Eq. (4) optimization problem solving

$\min p_{t}(w)=\frac{\lambda}{2}\|w\|^{2}+l\left(w ;\left(x_{t}, y_{t}\right)\right)$   (4)

where, hinge loss function is denoted by $l\left(w ;\left(x_{t}, y_{t}\right)\right)=$$\max \left(0,1-y_{t} w^{T} x_{t}\right)$ and the regularization parameter is denoted through $\lambda \geq 0$ that is employed to the complexity control model. Iteratively, the SGD works. It begins with primary model weight assume $w_{1}$ and present weight $w_{t}$. Updation is done at t^th round as shown in Eq. (5) and (6).

$w_{t+1}=w_{t}-\eta_{t} \nabla_{t} p_{t}\left(w_{t}\right)\left(1-\eta_{t} \lambda\right) w_{t}+\eta_{t} 1\left[y_{t}\left\langle w_{t}\right\rangle\right.$  (5)

$1\left[y_{t}\left\langle w_{t}, x_{t}\right\rangle<\emptyset\right]\left\{\begin{array}{ll}1, & \text { if } y_{t}\left\langle w_{t}, x_{t}\right\rangle \\ 0, & \text {otherwise}\end{array}\right.$   (6)

If the threshold value is less than 0.5 then it treats as 0 and if it is greater than it is 1. It will iterate the steps until the model fit to the respective data set. The indicator function denotes the value when the argument is true and over example (x, y)), the non-zero loss is gained or zero. By employing $\eta_{t}=1 /(\lambda t)$ in stepwise function and update it. The final output provides $w_{t+1}$ iteration after the predetermination of T iterations.

3.4 Validation

In this paper, 10 fold cross-validation data is used to train the classifier models. Dataset is divided into 10 subparts of similar size by using a cross-validation method, for training nine subsets data and testing one subset of data. This methodology is executed 10 times on test samples to estimate the average error rate as a final result. The validation process starts when the classification model is trained. The validation method is the last phase to develop the predictive model. Testing the performance of the predictive model on real-time data is called validation