A novel supervised machine learning algorithm to detect Parkinson’s disease on its early stages

: Early and accurate Parkinson’s disease (PD) diagnosis are usually complex as clinical symptoms often onset only when there is extensive loss of dopaminergic neurons in substantia-nigra and symptoms are atypical at an early stages of the disease. Recent brain imaging modality such as single photon emission computed tomography (SPECT) with 123 I-Ioflupane (DaTSCAN) have shown to be a better diagnostic tool for PD even in its initial stages. Presently machine learning algorithms have become trendier and play important role to automate PD diagnosis and predict its progression. In machine learning community, support vector regression (SVR) has recently received much attention due to its ability to negotiate between fitting accuracy and model complexity in training prediction models. This work presents an optimized SVR with weights associated to each of the sample data to automate PD diagnosis and predict its progression at primary stages. The proposed algorithm (W-SVR) is trained with motor and cognitive symptom scores in addition to striatal binding ratio (SBR) values calculated from the 123 I-Ioflupane SPECT scans (taken from the Parkinson’s progression markers initiative (PPMI) database) for early PD prognosis accurately. In model building, different kernels are used to check the accuracy and goodness of fit. We observed promising results obtained by W-SVR in comparison with classic Support vector regression.


Introduction
Parkinson's disease (PD) is a brain disorder that eventually affects motor and cognitive behavior.The main neuro-pathological characteristic of PD is gradual loss of dopaminergic (DA) neurons in the substantia-nigra and basal ganglia, which includes the caudate and putamen nucleus [1].As a result, there is a decrease of dopamine content in the striatum, and a corresponding dissipation of dopamine transporters (DAT).These DATs are responsible for controlling functions like movement, cognition, mood and reward [2].Thus, the loss will lead to deterioration in nervous system which gives rise to: motor disturbances that include slowness of movement, resting tremor, muscular rigidity and impaired co-ordination [3]; and cognitive illness like depression, olfactory, and sleep disturbances [4].As the disease continues to progress, one can observe significant change in motor and cognitive behavior worsening by the day.
Studies verify that there is currently no way to repair neurons once they have been destroyed and clinical symptoms in PD arise only when there is more than 60% loss of dopaminergic (DA) neurons [5].However, by the time of symptoms of PD are detectable clinically, critical nigrostriatal dopaminergic neurons would have already been damaged.Conversely, the disease continues to progress with accumulation of significant motor and cognitive disability, worsening quality of life, reduced productivity, nursing home placement, and increased mortality [6].There is still no standard cure for PD because the cause for death of DA cell is still mysterious.The main challenge of clinical diagnosis of PD is to properly identify the PD subjects at an early stage when symptoms are atypical.However, early signs and symptoms of this disease may go unnoticed as they can overlap with other disease's symptoms.Thus, timely and clear-cut diagnosis of PD is important for initiating neuro-protective therapies.These treatments can assist the PD subjects to recover and retain their quality of life without further deterioration.
To detect PD further in its early stages, researchers have resorted to neuroimaging techniques.Applications of brain imaging techniques in the process of diagnosis of neurological disorders have increased the accuracy rate for predicting the disease at an early stage.The introduction of brain imaging modalities such as Single photon emission computed tomography (SPECT) with 123 I-Ioflupane (DaTSCAN), a pre-synaptic radiopharmaceutical of the dopaminergic transporters (DAT) showing a substantial uptake decrease in basal ganglia of PD subjects.These DaTSCANs have revealed that there is a significant depletion of DAT in PD subjects even in their early stages [7][8][9][10].Therefore, DaTSCANs are suggested to be a suitable method for the clinician to increase the diagnostic accuracy for predicting the disease even in its initial stages [11,12].Conventionally, the DaTSCAN images obtained from suspected PD individuals are exposed to a visual analysis performed by clinical experts.A predefined rating is given according to Tolosa et al. (2007) [13] or the analysis of regions of interest (ROIs) attributed by Lozano et al. (2010) [14] typically involves in this process.This procedure is independent and can be susceptible to error, since it relies on overall changes in dopamine concentration throughout the ROI.
Recently, machine learning paradigms are used to automate the prediction of neurological disease progression and assess the stage of pathology, yielding to the construction of computer-aided-diagnosis (CAD) systems.These systems are applied to semi quantitative parameters to train an automatic classifier like support vector machines (SVM) indistinguishing PD subjects.Hence, some researchers have applied machine learning techniques to estimate clinical scores from brain SPECT image [15][16][17][18][19][20] and found reliable correlation between estimated clinical scores and different PD progression stages.Therefore, appropriate and targeted treatment can then be carried out to treat PD effectively.
SVM have become popular in machine learning community.An important property of SVMs is, the determination of model parameters is a convex optimization problem so the solution is always global optimum and has emerged as an important learning technique for solving classification problems in various fields with excellent performance [24][25][26][27][28].With the introduction of ε-insensitive loss function (ε: error deviation), SVM has been extended to solve the regression problems called support vector regression (SVR) [25].SVR has recently received much attention due to its competitive performance compared to other regression techniques such as logistic regression, and Neural Networks (NN).In general, SVR constructs decision functions in high dimensional space for linear regression while the training data is mapped to a higher dimension in kernel Hilbert space.ε-SVR is the first popular SVR strategy [26].ε-SVR aims to find a function whose deviation is not more than ε, thus forming the ε-tube, to fit all training data.In order to find the best fitting surface, ε-SVR tries to maximize the minimum margin containing data points in the εtube as much as possible.
In PD diagnostic system, the data is mostly imbalanced.In such scenario, a classic implementation of SVR is inefficient as they may provide inaccurate results.This paper proposes a variant of SVR, optimized with weights associated to each of the sample dataset, which results in a new approach called as weighted support vector regression (W-SVR).This method gives more accuracy than the classical SVR, and the resulting support vectors are sparser and much more robust with respect to changes in the regularization hyperparameter, while retaining a comparable accuracy.A comparison of proposed algorithm (W-SVR) with standard SVR using kernels like linear, polynomial, sigmoid, radial basis function (RBF) and logistic over PD dataset indicates that W-SVR fits better and shows comparable accuracy for diagnosing Parkinson's data in less computational time.This work also gives the predictive model for PD dataset using multivariate logistic regression (MLR) to show the class probabilities.Thus, the proposed model can be used as a better tool for early detection of Parkinson's disease.

Main points of the present work:
 We use 12 baseline features to train our algorithm.Due to the evident of substantial decrease of DAT in striatal regions of PD subjects [15][16][17][18][19][20], we choose four striatal binding ratio (SBR) values of left and right caudate, putamen nucleus as features.The age and gender also influence the classification and prediction accuracy, we use these two features.
 Motor impairment and cognitive are clinical symptoms of PD [16,17], we considered MDS-UPDRS, MoCA, Tremor dominant (TD), postural instability/gait difficulty (PIGD) scores as features.In addition to these, we also use Handedness, Family history as features to get better results.
 We use weighted SVR and MLR models to train the algorithm over PD dataset.A performance comparison of the proposed models with the classic SVR over a Parkinson's data is given.Our experimental results shows that proposed method provides better classification, predictive results than SVR and can be used as better diagnostic tool in medical system.
The rest of the paper is organized as follows.Section 2 contains related research Section 3 contains the description and analysis carried out on input data, Section 4 contains problem formulation and mathematical modeling, statistical analysis of features, building of classification and prediction/prognostic model and presents proposed W-SVR forecasting method.Experimental results are discussed and compared with existing models in Section 5. Finally conclusion is given in Section 6.  [23] assessed the potential of a set of features related to uptake ratios on the striatum, the estimated volume and length of the striatal region with normal uptake extracted from 123 I-FP-CIT SPECT brain images to diagnose Parkinson's disease, they obtained accuracy of 97.9% using SVM.

Related work
Although the authors have achieved high accuracy for classification but these procedural approaches require an effective algorithms for feature reduction and such techniques may also lead to lose of information which effects the decision making process.Consequently, these researchers have used standard support vector theory for automating classification of PD by considering large dataset.When standard SVR technique is used to deal with imbalanced medical data, it may decrease the generalization ability.
This work proposes an optimized SVR technique with weights associated to each of the sample dataset, which results in a new approach called as weighted support vector regression (W-SVR).This method gives better regression curve and good fit to data, and the resulting support vectors are sparser and much more robust with respect to changes in the regularization hyper-parameter, while retaining a comparable accuracy.A comparison of proposed algorithm (W-SVR) with standard SVR using kernels like linear, polynomial, sigmoid, radial basis function (RBF) and logistic over PD dataset indicates that W-SVR fits better and shows comparable accuracy for diagnosing Parkinson's data in less computational time.Thus, the proposed model can be used as a better tool for early detection of Parkinson's disease.

Materials
Work flow of the proposed prognostic model using Parkinson's data is shown in Figure 1.Statistical significance test was performed on all the features before going ahead with classification and prediction of PD.

Statistical analysis of features
Linear regression analysis is used for obtaining statistically significant features (predictors).All statistical analysis was carried out using SPSS 25 software (SPSS Inc., Chicago, IL).ρ < 0.05 was considered to be the threshold value.When dealing with a large number of features in multivariate analysis, it is important to find those features that are independent and overlap.i.e., groups of thee may be dependent in regression.
Figure 2 shows the Glyph plot that depicts the multi-variability of randomly chosen 50 samples from PD dataset.It is detected from Figure 2 that the multi-variability is high among the samples and hence leading to difficulty in classification of the problem.The histograms and notched box plots are plotted for each SBR feature to visualize its distribution for healthy and early PD population with its gender category.Figure 3 shows severe reductions in the dopamine concentration of striatum in PD patients, with greater reduction in putamen than the caudate compared to healthy subjects.The notched box plots fig.3: (b,d,f,h) show that the notches for early PD and healthy subjects are fairly separated indicating the significance of these features.The histogram plots fig.3: (a,c,e,g) show that amount of overlap of distribution between the healthy and early PD population.Overlapping is comparatively higher for the caudate SBRs (both left and right) when compared to the putamenal SBRs (both left and right).In fig.3: (e,f), the amount of overlapping between Healthy and PD subjects is less for the left putamenal SBR values, indicating that this predictor has high discriminant power in classification problem. Figure 4 depicts mean and regression lines of SBR values of Female and Male PD population.It is shown that female subjects have lower SBR values than male population in all striatal regions with respect to age indicating the significance of these predictors.
From above figures it is witnessed that, multi-variability among samples are more (Figure 2) and the amount of overlap for SBR features is relatively high between healthy and early PD subjects (Figure 3, Figure 4).The amount of multi-variability and the overlap of the distributions of SBR values determine the difficulty of the classification or prediction problem, i.e., classifying or predicting early PD from healthy subjects.Higher the overlap/multi-variability, the more difficult it is the classification.Hence, we resort to machine learning tools to make this complex problem simpler.The research has shown that SVMs is widely used in automating PD diagnosis [18,19,[21][22][23]28].Though SVMs give better accuracy than when compared to its counterparts, but when standard SVM technique is used to deal with regression estimation problems especially in medical data where samples are unbalanced, the performance may decrease.
Therefore, there is a need for an effective classification/predictive technique which can improve the accuracy and reduce the computation time.Thus, in the present work, we propose a modified form of SVR which overcomes the above shortfalls.

Support vector regression theory
Let T = {f (x1, y1), (x2, y2), , , , (xn, yn)} be a training set of n samples, where xi ∈ R m are the input values and yi ∈ R are the corresponding target values.Support vector regression, which evolved from the support vector classification by introduction of the ε-insensitive loss function, is a data-driven machine learning methodology for regression tasks.For linear regression, the objective function is given in Equation (1).
Where w ∈ R m and φ is the mapping function induced by a kernel K, i.e., K (xi, xj) = φ (xi) • φ (xj), which projects the data to a higher dimensional space.The function f (x) should loosely fit the training data and be as flat as possible to avoid over-fitting problem by minimizing the ||w||.To cope with these infeasible constraints, two slack variables ξi and ξ i * are introduced to measure the amount of difference between the estimated value and the target value.That is, ξi approximates the number of misclassified samples.This convex optimization problem is feasible based on the assumption that a function exists which approximates every data pair (xi, yi) with acceptable ε accuracy.Then, the objective function f (x) is represented by the following constrained minimization problem in Equation (2).

s.t ( ) ( ) * *
C is a constant known as the penalty factor that denotes the trade-off between error and margin.i.e., the optimization criterion penalizes data points whose y-values differ from f (x) by more than ε.After applying the Lagrange multiplier, the minimization problem can be handled as the dual optimization problem as: Thus from Equation ( 4), one can observe that with the help of kernels the complexity of a function is independent of the dimensionality of the input space, and depends only on the number of support vectors.

Building of the Proposed W-SVR model to classify and predict early PD from healthy controls
Proposed algorithm uses SVR which uses weights associated with each of the training sample.This approach allows learning individual samples by retaining KKT conditions on all previously seen samples.A Leave-oneout cross validation is implemented in which a single sample of PD data is used for testing and rest are used for training.This process is repeated for every sample in the data.
The dataset can be represented as xi ∈ R m ; i = 1, ..., n, where n = 634, is the number of samples and m is the number of features which is equal to 12 in both the classes (Healthy and early PD) and the binary class label y ∈ R; yi ∈ (EarlyPD = −1, Healthy = +1).Total number of samples included in the analysis is shown in Table 3.

Prediction/Prognostic model for early PD using multivariate logistic regression
Multivariate binomial logistic regression technique is also used to develop prediction/prognostic models in order to estimate the probability of risk in PD [31,32].We also applied Logistic regression method to our data to compare and analyze performance in diagnosis process.Logistic regression predicts the logit of outcome (early PD or healthy) from a set of predictors.The predicted probabilities (occurrence of class label PD) obtained from logit can then be revalidated with the actual outcome to determine if high probabilities are truly associated with higher risk of PDand low probabilities with lower risk of PD.In this model, 5 predictors (UPDRS, Lt.Cad, Rt.Cad, Lt.Put, Rt.Put) are used to fit a logit transformation as they are most characteristic features (as per Table 4).The probability of PD for each sample (ni) is given in Equation ( 9).

( ) ( ) ( )
For each subject ni, the πi (likelihood of class label to be PD) is given in Equation ( 10).
Where α is the intercept (constant), β = {β 1 , . . .,β k } are the regression coefficients for the predictors and X i : X i = [x 1i , . . ., x ki ] is a sample with a set of k features.The regression coefficients are obtained using maximum likelihood approximation, and then solving the logit, probability of PD for each sample is obtained.The risk predictor is given in Equation ( 11).

( ) ( )
This PD risk estimation might be useful to categorize subjects into different risk categories.

Results and discussion
The experimental results of the proposed W-SVR for the prediction of PD progression are explained in this section.The number of samples for both the cases (Healthy, PD) and their features used to build the model is shown in table 1 and table 2. The dataset used for implementation are normalized for balancing the influence of each feature.After normalization, we take statistical analysis with the contribution to 95% for feature extraction.All statistical analysis of PD dataset is shown in table 4 and was carried out using SPSS 25 software (IBM SPSS Inc., Chicago, IL).The threshold of significance was de-fined as ρ < 0.05.During the construction of the regression model, we divide the dataset into training set and testing set.For implementation, we set optimal hyper parameter values for PD dataset as ε = 2e −5 , C = 10 and Te (toleranceerror) = 1e −6 .We evaluate confusion matrix values and performance measures for the linear, polynomial order 4, sigmoid, RBF and Logistic kernels.All runs were performed on a computer with 3.4 GHz Intel i7 2600 CPU and 6 GB RAM using MATLAB 2017a.

Statistical analysis of input features
In machine learning, properly optimized feature extraction is the key to effective model construction.So to prove our most efficient regression model, we assessed the statistical significance of all 12 features through Linear regression.Table 4 shows the result of regression analysis of feature set: Age, Gender, Handedness(Handed), Family History (F.History), MDS-UPDRS (UPDRS), MoCA, TD, PIGD, left caudate (Lt.Cad), Right caudate (Rt.Cad), Left putamen (Lt.Put), Right putamen (Rt.Put) SBR.It is observed that all of the ten features except Age and Gender are statistically significant with ρ < 0.05.The table also shows the R 2 and Mean Square error (MSE).High R 2 and Low Residual values are obtained for putamenal SBR (both right and left) when compared to the caudate SBR.This indicates that putamenal SBR had higher discriminative power than caudate SBR in distinguishing early PD from healthy controls.This is also evident from the histogram plots which shows lower overlaps for putamenal SBRs (Figure 3: (e,g)) than for caudate SBRs (Figure 3: (a,c)).Table 4: Statistical testing of each feature through Linear regression.β is the value of regression coefficient for the predictor in the model, SE is its standard error, F is F-statistic value, df is the degree of freedom, ρ-value is the significance of regression coefficient, R 2 is the measure of coefficient of determination that tells how close the data to the fitted regression line.MSE is the Mean square error.Note: the table does not show the constants obtained in the model.

W-SVR algorithm for classification and prediction to distinguish early PD from Healthy controls
The proposed Support vector regression algorithm optimized with weights associated to each sample is used to automate the prediction and diagnosis of early PD from healthy controls.W-SVR is used with different kernels such as linear, Polynomial, sigmoid, radial basis (RBF) and logistic to show the margin variations in classifying data and compared with standard SVR.W-SVR can be used as both classification and regression method by maintaining the main feature that characterize the algorithm i.e. maximal margin.In regression, a margin of tolerance ε is set in approximation to the support vectors.The main idea behind this work is (i) to minimize classification error and (ii) individualizing the hyper plane which maximizes the margin.These two objectives are achieved in W-SVR with better distance between classes of support vectors and reduced number of error vectors.

Performance Measure comparison
To measure the forecasting accuracy, some widely used scale-dependent and scale-independent statistical indicators were examined as follows: mean square error (MSE) [30], the coefficient of determination (R 2 ) [30].MSE is defined as the average of squares of the errors given in Equation (12).Smaller the value of MSE, better the forecasting performance of the model.R 2 ranging from 0 to 1 is a measure that allows one to determine the certainty of predictions from actual value given in Equation (13).
X ˆi is the vector denoting values of n number of predictions and X i is a vector representing n number of true values.The Figure 8   Table 6 gives the classification accuracy of proposed model with RBF kernel.The model achieved 96.73% accuracy in classifying the PD data which is more than the accuracy of standard SVR (see Table 5).

Prediction/Prognostic model for early PD using multivariate logistic regression
Logistic regression outputs the predicted probability of occurrence of the PD class.To validate these probabilities, the degree to which predicted probabilities agree with actual outcome is shown through a classification Table 7.The overall classification accuracy was as high as 93.5% indicating that the model with 5 predictors performs well in predicting the subject outcome.This PD risk estimation might be useful to categorize subjects into different risk categories.It is observed that the classification accuracy is not as high as that we obtained using proposed classifier with RBF kernel.This is because logistic regression models are discriminative models for classification that produces linear decision boundaries, and are not flexible as the non-linear models.
From above results, we observe that all the kernels functions used with proposed model are performed well compared to standard SVR giving the better accuracy of 96.73% with RBF kernel and also observe that high R 2 and low MSE values.This shows that the proposed algorithm works fine even with large data by taking less computation time.In comparison to the related researches [18,19,[21][22][23]28], all the studies have used either quantitative or semi-quantitative parameters obtained from neuroimaging data and applied classification techniques such as SVMs.In our work, large PD dataset with considerably high number of features are used to train SVR and classification margin is optimized with weighted method.Thus, this work automates the early detection of PD from healthy subjects with better accuracy.

Conclusion and Future work
Initial and accurate diagnosis of PD is very important to apply early management approaches.Automated PD diagnostic techniques mostly rely on standard SVMs which suffer with slow convergence rate.In this paper, a variant of standard SVR algorithm is proposed, named as W-SVR to classify early PD subjects and predict disease progression with accelerated convergence rate than standard SVR.The model is built with Linear, 4 th order Polynomial, Sigmoid, RBF, Logistic Kernel to obtain better classification and predict the disease progression.It is shown that the W-SVR algorithm comparatively achieved better performance in less amount of time than when compared to standard SVR for all kernel functions.From our work, we state that classification and prediction problems are solved in less computational time even when used with large dataset.
In future work, W-SVR can be applied to solve several real-world problems, including financial data prediction, weather forecasting and anomaly detection.

Author's contribution
Ms. Lavanya Madhuri Bollipo built the conceptual design of the research, performed data analysis, experimental results and wrote the first draft and also successive revision of the manuscript.Dr. Kadambari.KV involved in correcting the manuscript draft and obtained important intellectual content.

Conflicts of Interest
None

Figure 1 :
Figure 1: Scheme of the procedural work-flow

Figure 2 :
Figure 2: Glyph plot for the multivariate data.

Figure 3 :
Figure 3: Histogram and notched box plots of the striatal binding ratio (SBR) values in Healthy and PD subjects.Histogram plots show the amount of overlap of SBR values and box plots show the mean differences of SBRs in Healthy and PD subjects.Figure (a,b,c,d) show distribution of left, right caudate SBRs and corresponding mean difference; Figure (e,f,g,h) show distribution of left, right putamen SBRs and corresponding mean difference.In each notched box plot, the central mark is the median, the edges of the box are the 25 th and 75 th percentiles, the whiskers extend to the most extreme data points that are not considered outliers, and outliers are plotted individually.

Figure 4 :
Figure 4: Notched box plots and regression graphs of the striatal binding ratio (SBR) values of female and male PD population.Regression plots show the change in SBR values with respect to age. Figure (a,b) shows mean difference and regression lines of left caudate SBRs; Figure (c,d) shows mean difference and regression lines of right caudate SBRs; Figure (e,f) shows mean difference and regression lines of left putamen SBRs; Figure (g,h) shows mean difference and regression lines of right putamen SBRs.

Figure 5 :
Figure 5: (a,b,c,d) Figure 6: (a,b,c,d) Figure7: (a,b) depicts contour plots showing distribution lines of regression, number of support vectors (SV) and error vectors (EV) for proposed W-SVR and standard SVR algorithms with Linear, Polynomial of order 4, sigmoid, RBF, Logistic kernel functions respectively.It can be seen that proposed model has achieved better margin distance between two classes of data for different kernels and the number of error vectors are drastically reduced than the standard SVR.This shows that the proposed model is performing better than standard SVR in classifying the data.Proposed model with RBF kernel has depicted large margin distribution with low error when compared to other kernels (Figure6: (c,d)).However sigmoid kernel gives large margin distribution, the number of error vectors are more as shown in Figure6: (a,b) and it is also evident in Figure6: (f) as its MSE is high.

Figure 5 :
Figure 5: Contour plots showing the regression distribution lines of two classes of PD data using proposed W-SVR and standard SVR algorithms with Linear and polynomial of order 4 kernels.Figure (a,b,c,d,) depicts the margin separating two classes of data (Healthy and PD) where SV=support vectors and EV=error vectors.It can be seen that W-SVR gives the large margin distribution with less EVs when compared to classic SVR.

Figure 6 :
Figure 6: Contour plots showing the regression distribution lines of two classes of PD data using proposed W-SVR and standard SVR algorithms with Sigmoid and RBF kernels.Figure (a,b,c,d,) depicts the margin separating two classes of data (Healthy and PD) where SV=support vectors and EV=error vectors.It can be seen that W-SVR gives the large margin distribution with less EVs when compared to classic SVR.

Figure 7 :
Figure 7: Contour plots showing the regression distribution lines of two classes of PD data using proposed W-SVR and standard SVR algorithms with Logistic kernel function.Figure (a,b) depicts the margin separating two classes of data (Healthy and PD) where SV=support vectors and EV=error vectors.It can be seen that W-SVR gives the large margin distribution with less EVs when compared to classic SVR.

Table 1 :
[29]the proposed work, 12 features were used: age, gender, handedness, family history, Movement Disorder Society Unified Parkinson's Disease Rating Scale (MDS-UPDRS) total Pre-Dose, Montreal Cognitive Assessment (MoCA), tremor dominant (TD) score, postural instability/gait difficulty (PIGD) score, striatal binding ratio (SBR) values of the four striatal regions (left and right caudate, left and right putamen) that were computed from DaTSCAN SPECT images[29].Table2describes 9 predictors with respective mean and standard deviations.In the early PD group, all subjects were in their initial stage of the disease.All subjects were in Hoehn and Yahr (HY) stage 1, 2 with mean ± standard deviation of HY as 1.57 ± 0.48.
Database of Healthy and early PD population: Number of samples of Female and Male subjects in both the population (Gender), family history of PD (F.history) and handedness of subjects (Handedness).

Table 3 :
Case processing summary of model describes a comparison of MSE values for proposed and existing algorithms by depicting the boxplot of MSE values for Linear, Polynomial order 4, Sigmoid, RBF and Logistic kernels.Boxplot show the minimum, median and maximum values of MSE.Results indicate that proposed W-SVR achieved the lower values of MSE with each kernel functions when compared with standard SVR, which means that W-SVR can provide better fitting quality.Table5summarizes the results of performance measures.It is observed that W-SVR performs better and can provide better fitting quality than SVR by achieving small MSE and large R 2 values and also consumes less time than standard SVR in each of the kernel used.

Table 6 :
Classification table using W-SVR RBF

Table 5 :
Confusion matrix and performance measures for the W-SVR and classic SVR with different kernels

Table 7 :
Classification table using Logistic regression