Cost Optimization using Normal Linear Regression

International Conference on Electronics, Communication and Aerospace Technology ICECA 2017

Cost Optimization using Normal Linear Regression Method for Breast Cancer Type I Skin Chandrasegar Thirumalai, IEEE Member,

Rashad Manzoor

School of Information Technology and Engineering, VIT University, Vellore, India. [email protected]

School of Information Technology and Engineering VIT University, Vellore, India. [email protected]

Abstract—There are six main categories of breast cancer be existent. In this paper, we have taken the Type 1 carcinoma cancer to support the decision making. For this, a novel machine learning based cost optimization is applied to make an efficient decision from the samples. Moreover, we have applied our methodology on the real datasets to predict cancer with appropriate parameters using Pearson correlation. This work can be used well on lightweight devices like smartphones or tablets to decide more precisely with primary factors. Keywords-component; Pearson Correlation Coefficient, Cost Optimization, Linear Regression.

I.

INTRODUCTION

Even though the chance of breast cancer in a young woman is less and few of them die, one should be aware of breast cancer preventions and impact [36]. To be in safe side, once the woman attains 25 ages, they should check by themselves once a year mammogram test [7], [26], [28]. Breast cancer can be predicted or decided with the biomedical application [8] by conducting various tests and early prediction models [37], [41], [45], [48]. Some of the prediction model includes heuristic fuzzy [10], [13], [18], Analytical Hierarchy Process (AHP) [20], Genetic Programming (GP) [25], machine learning based classification [46], [49] and agent-based model [23]. Breast cancer detection [17], [30], [39], [43] can be supported by single [2], [4], [6] and multi-attribute [1], [3], [5], [9], [14], [47] decision models. This will help the doctor to recommend appropriate treatment or surgery [21], [32]. In general, before prediction or decision sampling, data analysis methods like box plot and control charts [50] are applied to find the optimized result. Nowadays, breast cancer prediction and detection model are supported by cloud secure model [16], [33], [44]. The size of the medical image [11], [15], [19], [34] is in huge form and it is supported by the big data model. Initially, the patient undergoes various breast test conducted by physicians through the recommendation of a doctor. The test result of a patient is kept secret say mammogram results. Here the doctor will be residing at a remote location and looking for the pharmacist to send the patient detailed report. For this scenario, the sensitive and decision-making attributes of breast cancer are clustered with decisional attributes using AHP, intuitionistic fuzzy, machine learning based prediction model. These sensitive attributes are uplifted securely on common media though secured [12], [27], [29], authenticated [22], [24], [31] and multi-user support

[35], [38], [40], [42] methods. A portion of the previous techniques to gauge the choices in light of their relationship to quality are Spearman. For to make effective group decision from the various history of the patients heuristic prediction and machine learning models plays a major role. Decision making is a cognitive process for making the decision for an important process. The result obtained from the decision making should be the final choice i.e. the result obtained should be exact or the most suitable value. Breast cancer is undoubtedly the most common type of cancer diagnosed in women. Statistics have proven that even children are prone to breast cancer. The newly diagnosed breast cancer patients face difficulty in decision making due to the complexity of the different data obtained from different types of tests like MRI (magnetic resonance imaging), Mammogram, breast exam etc. To stage the level of breast cancer, various procedures are adopted. Some of the usual methods include blood test (blood count), mammography, breast MRI, bone scan, CT scan (computerized tomography) and PET scan (positron emission tomography). The breast cancer stages fall from 0-IV. Presently, many of the decision-making systems do not meet the quality of an efficient decision-making system. So, there is a need for different methodologies to improve the quality of decision making due to the sensitivity of data. Here, we have taken the real data set of breast cancer. The features of breast cancer includes IO – Impedivity (ohm) at zero frequency; PA500 –phase angle at 500 kHz; HFS –high-frequency slope of phase angle; DA –impedance distance between spectral ends; AREA – area under spectrum; A/DA –area normalized by DA; MAX IP – maximum of the spectrum; DR –distance between I0 and real part of the maximum frequency point; P – length of the spectral curve. There are two types of tumor namely, benign and malignant. A benign tumor is a non-cancerous condition which is very common whereas, a malignant tumor is a cancerous condition that starts from the cells of breast tissue and that may grow into surrounding tissues. There are six categories of breast cancer: Carcinoma – it develops from the epithelial cell of the lining. Fibroadenoma – it’s a benign tumor and its common symptoms are a lump. Mastopathy – caused by hormonal imbalance in the breast. Glandular – affect’s in breast glands.

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Connective – affect’s in connective tissue which provides support and shape. Adipose – affect’s in adipose which made up of fat and one of the most dangerous. TABLE I.

CARCINOMA CANCER DATASET.

No.

I0

PA500

HFS

DA

Area

A/DA

Max IP

DR

P

1

524

0.18

0.03

228

6843

29.9

60.2

220

556

2

330

0.22

0.26

121

3163

26.1

69.7

99

400

3

551

0.23

0.06

264

11888

44.8

77.7

253

656

4

380

0.24

0.28

137

5402

39.2

88.7

105

493

5

362

0.20

0.24

124

3290

26.3

69.3

103

424

6

389

0.15

0.09

118

2475

20.8

49.7

107

429

7

290

0.14

0.05

74

1189

15.9

35.7

65

330

8

275

0.15

0.18

91

1756

19.1

39.3

82

331

9

470

0.21

0.22

184

8185

44.3

84.4

164

603

10

423

0.21

0.26

172

6108

35.4

79.0

153

558

11

410

0.31

0.29

255

10622

41.5

67.5

246

508

12

500

0.22

0.05

219

9819

44.7

76.8

207

602

13

438

0.21

0.06

120

4879

40.3

80.7

89

525

14

366

0.28

0.25

172

7064

40.8

75.6

155

471

15

485

0.23

0.13

253

8135

32.0

64.8

245

541

16

390

0.35

0.20

245

10055

40.9

70.3

236

477

17

269

0.20

0.03

80

1963

24.4

44.7

66

329

18

300

0.19

0.16

97

3039

31.3

51.3

82

387

19

325

0.22

0.28

229

5705

24.8

35.6

227

462

20

294

0.20

0.46

194

5541

28.4

36.7

191

445

21

500

0.19

0.19

144

3055

21.1

96.5

107

542

II.

EXISTING SYSTEM

2. Find out the most similar distance between of two points by using the Euclidean distance function

v  ( xi1  x j1 ) 2  ........( xin  x jn ) 2 . 3. Scaling each attribute by the maximum diff of each xij value, v  . ij max k xkj  min k xkj C. ID3 1. Begins with the root node S of the discrete set. 2. Iterate through every unused attribute of the discrete data set. 3. Calculate the entropy H (S ) . 4. Split the discrete set by the selected attribute and produce subsets of the current discrete set. 5. Iterate until the sets are diluted and obtain the tree structure. III.

PROPOSED METHODOLOGIES

A. Linear Regression 1. Get the two data sets with n examples and let us denoted it as xi and yi for each. 2. Find out the variable m by using the equation, ( i xi yi )  nx y . m

(i xi2 )  nx

2

3. Then find out the variable b  y  mx .

b by using the equation,

4. At last substitute the value of b and m in the linear

f  x   mx  b we can predict any value of y when x as input. regression equation,

B. Nearest Neighbor 1. Start

with

two

points

( xi1, xi 2 ......xin )

and

( x j1 , x j 2 ,.....x jn ) . Figure 1. Proposed Decision Making Model.

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For analyzing the dataset and to obtain the best alternative solutions which are related to the problem there are different kinds of methodologies available and each of them works in different ways. By choosing the best methodologies we can obtain more efficient decision and alternative solution for the decision making process.

2. Select the attribute a1...an of carcinoma breast tissue from

A. Pearson Correlation Coefficient Method

5. 6. 7. 8. 9.

Pearson correlation coefficient or PPMC is the measure of correlation (linear) between two variables x and y i.e. to measure how the variables x and y are related to each other and the relationship between x and y denoted by r and obtained from the equation,

r

n( xy )  ( x)( y )

[n x 2  ( x) 2 ][ n y 2  ( y ) 2 ]

{A}

3. Choose the primary by applying Pearson correlation among the attributes. 4. Create similarity index r , for every attribute pair (ai , a j ) using Pearson method. Select the attribute pair with high correlation. Compute mean for all attributes. Compute variance for high correlated attributes. Compute standard deviation for step 6. For every pair compute the linear variable S .D( y ) . br S .D( x)

10. Compute a  y  bx . Where y and x are the corresponding mean. 11. Now predict y from x using the form a  bx . 12. Correlate the image with respect to skin disease class.

If the values from the above equation lies,

IV.

Between 0 and  1 then, positive correlation. On 0, no correlation. Between  1 and 0 then, negative correlation.

TABLE III.

PEARSON, MACHINE LEARNING, AND LINEAR REGRESSION

Attributes

A1

A2

A3

A4

P VS IO

P VS DA

P VS AREA

P VS A/DA

Pearson (r)

0.922541

0.73183

0.78832

0.72586

Cost by machine learning

12974.3

3445.731

15708603

554.495

Optimized, θ

1.5

1.5

2

0

Std ( y) Std ( x)

0.861747

0.43715

26.83599

0.072288

a  y  bx

-19.6385

-68.9831

-7158.27

-2.69839

From these correlation values, we can find out which are highly correlated and the variables which are least correlated. TABLE II.

NUMERICAL RESULTS

CARCINOMA ATTRIBUTE VALUES BY PEARSON

A1

A2

A3

A4

A5

A6

A7

A8

A9

A1

1.0

0.2

-0.3

0.6

0.7

0.5

0.7

0.6

0.9

A2

0.2

1.0

0.3

0.6

0.7

0.7

0.4

0.6

0.3

A3

-0.3

0.3

1.0

0.1

0.1

0.4

0.0

0.1

-0.8

A4

0.6

0.6

0.1

1.0

0.9

0.6

0.2

1.0

0.7

A5

0.7

0.7

0.1

0.9

1.0

0.8

0.4

0.9

0.8

A6

0.5

0.7

0.4

0.6

0.8

1.0

0.6

0.5

0.7

A7

0.7

0.4

0.0

0.2

0.4

0.6

1.0

0.1

0.7

A8

0.6

0.6

0.1

1.0

0.9

0.5

0.1

1.0

0.7

A9

0.9

0.3

-0.8

0.7

0.8

0.7

0.7

0.7

1.0

B. Machine Learning

b  r.

TABLE IV.

Machine learning is the ability of the computers to learn without being explicitly programmed. There are two types of machine learning, unsupervised and the supervised machine learning. The unsupervised machine leaning indicates that inferring a function from unlabeled data whereas the supervised machine learning is to infer the function from known datasets. 1. Input the image.

DERIVED LINEAR REGRESSION EQUATION FOR CARCINOMA Attribute

y  a  bx

P vs IO

y  19.6385  0.861747 x

P vs DA

y  68.9831  0.43715 x

P vs AREA

y  7158.27  26.83599 x

P vs A/DA

y  2.69839  0.072288 x

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V.

CONCLUSION

Here, we have taken the real dataset of breast cancer skin type-I (carcinoma). For each attribute, we have analyzed its correlation coefficient with other attributes, by using Pearson method. From these coefficient values, the attributes having values which are greater than 0.55 are taken into consideration. Further, machine learning method is used for finding out the least cost function and its corresponding theta value. By using simple linear regression method on the reduced attributes, we have obtained linear equations which have been represented in table IV. From these equations, we can find out the required attribute by giving the appropriate inputs. Moreover, from our proposed model one can take wise decisions with the help of handy electronic devices like smartphones and tabs. REFERENCES [1] Zhang, Xiaolu, and Zeshui Xu. "Hesitant Fuzzy Methods for Multiple Criteria Decision Analysis." Studies in fuzziness and soft computing, 2016. [2] Kwait, Rebecca M., et al. "Influential Forces in Breast Cancer Surgical Decision Making and the Impact on Body Image and Sexual Function." Annals of Surgical Oncology 23.10 (2016): 3403-3411. [3] Van Wersch, Anna, and Katherine Swainston. "Women’s experiences of treatment decision-making in breast cancer." Praeger, 2014. [4] Levine, Mark Norman, et al. "Population-based evaluation of 21-gene assay in treatment decision making for early breast cancer in Ontario." (2014): 583-583. [5] Augustovski, Federico, et al. "Decision-making impact on adjuvant chemotherapy allocation in early node-negative breast cancer with a 21gene assay: systematic review and meta-analysis." Breast cancer research and treatment 152.3 (2015): 611-625. [6] O’Brien, Mary Ann, et al. "Physician-related facilitators and barriers to patient involvement in treatment decision making in early stage breast cancer: perspectives of physicians and patients." Health Expectations 16.4 (2013): 373-384. [7] Vikhe, P.S., Thool, V.R. Contrast enhancement in mammograms using homomorphic filter technique, International Conference on Signal and Information Processing, IConSIP 2016. [8] Rama Devi, K., Rani, A.J., Prasad, A.M. Design of microstrip antenna with improved bandwidth for biomedical application (2017) Advances in Intelligent Systems and Computing, 468, pp. 201-215. [9] Zhang, G. Q., & Lu, J. (2003). An integrated group decision-making method dealing with fuzzy preferences for alternatives and individual judgments for selection criteria. Group Decision and Negotiation, 12, 501–515. [10] Kalaiarassan G, Krishan, Somanadh M, Chandrasegar Thirumalai, Senthilkumar M, "One-Dimension Force Balance System for Hypersonic Vehicle an experimental and Fuzzy Prediction Approach," Elsevier, ICMMM - 2017. [11] Viswanathan, P. "Fusion of cryptographic watermarking medical image system with reversible property." Computer Networks and Intelligent Computing. Springer Berlin Heidelberg, 2011. 533-540. [12] Chandrasegar Thirumalai, Viswanathan P, “Diophantine based Asymmetric Cryptomata for Cloud Confidentiality and Blind Signature applications,” JISA, Elsevier, 2017. [13] Ponnurangam, Dhavachelavan, and G. V. Uma. "Fuzzy complexity assessment model for resource negotiation and allocation in agent-based software testing framework." Expert Systems with Applications 29.1 (2005): 105-119. [14] Zhang, X. L., Xu, Z. S., & Wang, H. (2015). Heterogeneous multiple criteria group decision making with incomplete weight information: A deviation modeling approach. InformationFusion, 25, 25–62.

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