A New-fangled Classification Algorithm for Medical Heart Diseases Analysis using Wavelet Transforms

1. INTRODUCTION

Data mining is a process of searching for the correct information from a large amount of data set. There are many techniques available in the research, such as Artificial Neural Networks [1], Genetic algorithms [2], Association rules, and Clustering [3]. Classification of the data has been considered one of the important techniques in data mining [4, 5]. Several different approaches are made to construct accurate classifiers, e.g., Bayesian classifier [6, 7], Decision tree [8, 9, 10], Support Vector Machine (SVMs) [11, 12, 13, 14] and associative classifiers [15]. In the classification of data, the training data set is given as input data. The input data consists of two attributes: numerical attribute and categorical attribute or alpha-numeric attribute. For example, Cp represents the Chest Pain type of a patient, Fbs represents the Fasting blood sugar of a person that falls under the category of a numerical attribute, Furthermore, the categorical attribute has values from an unordered domain, such as whether the person is illiterate or literate, male or female, and so on [3, 16, 17]. Classification is the method of splitting a dataset into another group, called a class, which depends on suitable attributes. A rule-based algorithm can generate multiple splitting points of the concept [18, 19, 20]. In this algorithm, a set of rules is framed as follows:

IF < conditions > THEN < (class value) >

The algorithm is applied to each node, and if the “IF” condition is satisfied, it travels to the left side of the node, or if the “IF” condition is not satisfied, it travels to the right side of the node, or “else” the condition is counting the missing values. This rule is applied to all the attributes. Finally, it counts the class value.

A Wavelet transform is a mathematical transform that was applied in various branches of science and engineering, such as geology, signal processing, astronomy, and computer science. The wavelet transform's ability to divide the data, or functions, into discrete data elements accounts for its success. Subsequently, it examines every element independently using a matching resolution [21].

Thus, it provides more information about the data in an informative manner [22]. In recent years, many computer software packages have been easily available to perform wavelet transforms in an elegant approach. The availability of more wavelet packages has gained the most popularity among engineers.

In this paper, the Haar wavelet algorithm is applied to the MMDBM algorithm result (Refer to Tables 1-2). This proposed (MMDBM) method is the best classifier compared to 19 supervised learning techniques (Including SVM and KNN) and has a higher rate of accuracy in detecting breast cancer cases from the given datasets [13]. In a study [23], eight supervised learning methods using eight different types of databases are compared. The proposed method, the MMDBM algorithm, is accomplished with the highest accuracy rate. The proposed algorithm is more prominent and robust considering all aspects of accuracy and computational time.

The structure of this document is as follows. In Section 2, the relevant works addressed are discussed. In Section 3, MMDBM algorithms are briefly covered. In Section 4, the results of an experimental evaluation based on the MMDBM algorithm are explained, and the histogram of each distribution is computed. The conclusion is discussed in Section 5.

2. RELATED WORKS

The MMDBM algorithm depends on two algorithms, namely SLIQ and SPRINT. SLIQ means Supervised Learning in Quest. This algorithm was created by the IBM group under the direction of Rakesh Agrawal in the 1990s to determine processing time using both numerical and categorical variables. In addition, to determine the tree growth phase, he developed a method known as pre-sorting [17]. SPRINT is another classifier, which is a parallel algorithm developed by the same group at the end of the '90s. It is a planned classification that shows the decision-tree method's memory constraints are removed and demonstrates how quick and effective the intended algorithm is as a classifier [17, 23-25].

A new decision tree classifier known as the MMDBM algorithm handles both numerical and categorical attributes in huge datasets. This classifier can manage huge databases with a broad set of data or a huge number of binary attributes. Here, all the numerical attributes and qualifying midpoints are taken into consideration. However, this point is calculated at every level of the Gini index. Every distribution of the considered position is taken for examination in histogram estimation.

The first step is sorting the entire attribute and then taking the midpoint. This midpoint is not static due to inserting one record in this dataset. The midpoint is automatically changed. This proposed algorithm dynamically changes the midpoint value of each execution of the program.

The following is the basic concept of the Gini-Index theory. It can be assumed that S is a collection of s samples with k distinct classes (C_i,i = 1,...,k). Among the samples (S_i, i = 1,...,k), there are the k subsets of S, which are partitioned based on the differences in classes. It can also be assumed that Si is the sample set from class C_i. Thus, set S's Gini-Index is:

Where Pi is the probability that any sample belongs to Ci, it is calculated using s_i/s. Since all of the set's members fall into the same class and Gini(S) has a minimum of 0, the greatest amount of meaningful information may be gleaned. The least amount of meaningful information may be gathered when Gini(S) is at its maximum, which happens when all of the samples in the set are distributed evenly for each class. Nevertheless, the majority of Gini-Index research has simply divided decision tree features.

This paper used 30000 records in the Heart disease dataset taken from the UCI repository. In the final phase, 9365 records are counted for patients who smoke regularly, 7134 records for those who do not smoke, 6679 documents for those who smoke tobacco, and 6822 records for missing data.

The Gini index for the overall collection of the above original dataset is:

The Gini index for the overall class is updated. Similarly, the gini index for other attributes like Sex, Age, CP, Fbs, Trestps, and Year are found using the above gini equation.

There are two sections to this algorithm. The algorithm is explained in depth in the first section using a predictive classifier, and the Java program implementation is provided in the second section on object-oriented design [1, 3]. Furthermore, to check the validity of our classifier (MMDBM), we must have a large data set from which we obtain the medical data (no specific reason for choosing the heart database) from the UCI repository.

In a study [23, 26], the time and space complexity of the MMDBM Algorithm with efficient parallel quick sort and radix sort algorithms in GPU are discussed, which results from the Comparison of computational acceleration ratio (speed-up) and efficiency of processing time of CPU and GPU computing in MMDBM Classifier. The main results are used to compare the classifier with an existing CPU- quick sort and radix sort for the MMDBM classifier and GPU- quick sort and radix sort algorithms provide rapid and exact results with minimum execution time and support real-time applications.

3. METHODOLOGY

Moreover, To test the robustness of our classification algorithm, we studied from the medical database where the risk person affected by Heart disease has the habit of smoking, non-smoking, and smoking with tobacco data obtained from the UCI repository. The distribution of the node count value is based on the predicted rules obtained from the database, as represented in Fig. (1). The data sets that hold entries for the characteristics mentioned above.

This algorithm uses two categorical attributes, 'Sex' and 'Smoking.' The 'Sex' attribute is categorized as male or female, while 'Smoking' is categorized as S-Smoking, NS-No Smoking, and ST-Smoking with Tobacco. In addition to these, five numerical attributes are considered, such as 'Age' representing the person's age, and 'Cp,' which denotes the chest pain type.It assigns Value 1 for typical angina, Value 2- for typical angina, and Fbs denotes the Fasting blood sugar. If Fb >120 mg/dI, then Trestbps (resting blood pressure in mm Hg at hospital admission) and Year (total number of years smoked) are 1=true; 0 is false.

We have used 30000 records in the Heart disease dataset from the UCI repository. The proposed MMDBM algorithm checks the condition from the root node to the terminal node, which is called one distribution. If any one of the values is missing from this distribution, it is considered as one missing value, and again, the missing value is repeated in the same distribution. Then, the missing count value is updated as M=M+1. The code has already been created for those missing values in our data pre-processing, as mentioned in section 2.1. In our MMDM algorithm, there is no need to classify those missing values (in the cell), outliers, or feature selection.

Thus, under the above assumptions. We classified all the attributes where 23 different distributions of the nodes were noted and more than 30,000 records of patients with Heart disease problems were analyzed. Finally, it counts the number of patients with the habit of smoking data – 9365 records, No Smoking- 7134 records, Smoking with Tobacco- 6679 records, and missing data-6822 records. Each distribution has been produced by various IF < condition >, followed by the Then rule.

This rule is dynamically constructed based on the predicted rule of the class count values. The traveled path and node count distributions are determined, and they are shown in Fig. (2) and Table 1.

Additionally, to categorize all the attributes, a classification tree is ultimately built. As a result, we can obtain the traveling path and distribution of 23 node count values for each of the 30,000 examples (see Table 2).

Wavelet means a small function with finite compact support denoted by the symbol whose translations and dilation form an unconditional basis [27]. The wavelet can break down a piece of data into many smaller parts without changing the information contained in the original data since it forms an unconditional basis. Thus, each piece of data that contains complicated information can be represented in a simple form by using wavelet transform. In data mining processes, discrete wavelet transform (DWT), which is predicated on the Multiresolution Analysis (MRA) tool, is the key concept. The multiresolution analysis is Hilbert Space decomposition. L²(R) on a series of closed subspaces such that it satisfies the following mathematical properties [28-30].

i) Each Closed Subspace is contained in one another.

ii) The union of Closed Subspace is equal to the original space.

iii) The closed subspace forms a Reisz basis for L²(R).

The consequences of the MRA is that it decomposes the Hilbert space as, and another one, .

Thus, any data can be split as an orthogonal sum of the scaling function at the J level and as a wavelet function. The rapid discrete wavelet transform algorithm is the direct use of multiresolution analysis in data mining. The goal is to maintain detail while following an iterative process to make the data smooth. Which is to analyze projections of f to W_j.

We use the Haar wavelet transforms algorithm to improve the data after it has been classified. The basic concept is to use the one-dimensional discrete Haar wavelet transform shown in Fig. (3) to classify the original data into different levels.

4. RESULT AND DISCUSSIONS

Consider the discrete data obtained after applying the MMDBM algorithm. Represent the data as d¹ = (d₁, d2_, d₃…....d_N ), where N is the positive even integer. Haar transform splits the discrete data into two sub-data of half its length. The first sub-data represents an average, which contains the approximate information of the input data, and another sub-data represents a difference average, which contains the detailed information of the input data.

The first average of sub-data, d¹ = (d₁, d₁, ... , d_N/2) , for the data d is calculated by taking the mean value. Its initial value, d₁, is calculated by fetching the mean of the initial pair of values d: (d₁ + d₂)/2. Likewise, its next value d₂ is calculated by fetching the mean of the next pair, which is d_{2 =}(d₃+d₄)/2. Following this procedure, each value of d¹ is generated by using a series of consecutive input data value pairs. The particular formula for d¹ is d_m = (d_2m-1+d_2m)/2 where m = 1,2,3,..N/2 correspondingly, another sub-data known as difference average denoted as e¹ = (e₁, e₂, e₃,....e_N/2) is computed by taking the difference average. This is how it can be computed as a difference. Its initial value, e₁ is determined by dividing the difference between the first two values of d by half. that is e₁ = (d₃-d₄)/2.

Likewise e₂ is computed by the second pair as e₂ = (d₃-d₄)/2

Continuing in this process, all the values e¹ are calculated, permitting the resulting general formula e_m = (d_2m-1-d_2m)/2 where m = 1,2,3……..N/2.

For example, consider the data obtained after applying the MMDBM algorithm in Table 2 as a = (2, 4, 9, 19, 38, 150, 190, 267). The Level-1 Haar wavelet transform is obtained by following the aforementioned approach as = (a¹|d¹), where d¹ = (3 14 94 228.5) and e¹ = (-1 -5 -56 -38.5), which is explained in the table below (Table 3).

After obtaining the Level-1 of Haar discrete wavelet transform, it is easy to obtain the Level-2 transform. Level-2 Haar wavelet transform can be obtained from Level-1 as follows. The second level average d² and difference e² is obtained from the approximation of the first Level d¹. The approximation information is considered: d¹ = [3 14 94 228.5] obtained from Level-1 as initial data for Level 2. Applying the same procedure described above, we obtained d² = [8.5 161.25] and e² = [-5.5 -67.25] (Table 4).

Thus Level-2 Haar wavelet transform of input data f = (d²|e²|d¹) = (8.5 161.25 | -5.5 -67.25| -1 -5 -56 -38.5). Similarly, Level-3 Haar wavelet transform can be obtained from Level-2 as follows. The third level average d³ and difference average e3 are obtained from the approximation of the second level d².

Thus Level-3 Haar wavelet transform of input f = (d³|e³|d²|d¹⁾ = (84.87 |-76.37| -5.5 -67.25| -1 -5 -56 -38.5) (Table 5).

Thus the initial classified data (2 4 9 19 38 150 190 267) is changed into another data using wavelet transform as (84.5 -76.37 -5.5 -67.25 -1 -5 -56 -38.5). Thus, we applied wavelet transform for all the classified data in Table 2, and the output is shown in Table 6.

CONCLUSION

In this paper, the researchers presented a novel data categorization algorithm based on Mixed Mode Database Miner (MMDBM). This algorithm is based on a decision tree classifier and tested on a heart disease database. MMDBM is applied to classify a large amount of data sets with both numerical and categorical attributes. Thus, an array is used to hold classified data. The data are compressed with the help of a one-dimensional wavelet transform. Moreover, by utilizing one of the properties of wavelet, the data are represented differently without affecting the dimensionality of the data. The experimental results are compared with the classified data to wavelet data output. These results prove that our presented technique is more prominent and robust in the analysis of heart diseases. This is one of the new approaches applied to classified data in real-time applications.

REFERENCES