Week 5 Exercise – Neural Network

In this exercise, you will use the R Studio interface to run the Neural Network method.  You will run the method with different parameters and will interpret the results, including the classification accuracy.
Exercise Instructions

Step 1 – Complete an exercise in the Word document on diabetes dataset.  Get familiar with the neuralnet method and with available input parameters.  

Your results might be slightly different depending on the operating system and R Studio version.  You do not need to write a report for this part.

Part 2 –  Run an exercise on a column dataset and write a report on your findings and results interpretation in your own words. The report needs to cover the exercise key points below in order.

Download the CSV file to your hard drive. Click on a dataset description URL and read the dataset description. Note: I changed normal to 0 abnormal to 1

http://archive.ics.uci.edu/ml/datasets/Vertebral+Column#              

Exercise Key points

1. Introduction

· Which variable is the dependent variable in the column dataset?

· Which variables are the independent variables in the column dataset?

· What do you expect the neuralnet method to accomplish for the column data?

2. Data pre-processing – Load the data into R studio, and discuss the data preprocessing steps you run before running the neuralnet method. For each step, include the command you ran, the output, and an explanation of what the step accomplishes.

3.  Divide the data into training and test set, and explain why we do that. Include the commands and explanation in the report. Remember to set seed.

4. Running the method on a training set

· Run the neural net function to build the network, and store the result in a variable nn.  Include the command in the report, and discuss the input parameters you used.

· Enter nn at the prompt and hit enter. Interpret the output.  Include the command, the output, and output interpretation in the report.

· Run the command nn$result.matrix. Interpret the output.  Include the command, the output, and output interpretation in the report.

· Run the command nn$net.result[[1]][1:10] to preview the first 10 predicted values. What do the values mean?  Include the command, the output, and output interpretation in the report.

5. Network Visualization – Run the plot(nn) command to visualize the network, and interpret the model.  If the plot is hard to read, you may need to click on zoom button in the plot panel to view the model in a new window.  Included the command you ran, the plot, and plot interpretation in the report.

6. Confusion Matrix for the training data

· Run the following commands to extract and store the predicted values in a variable mypredict.  Round the predictions to the whole number. Display the first 10 values of mypredict.  Explain what the values mean.  Include the commands, the output, and output interpretation in the report.

mypredict<-compute(nn, nn$covariate)$net.result mypredict<-apply(mypredict, c(1), round)

mypredict[1:10]

· Run the table command to build the confusion matrix.  Explain what the matrix shows.  Include the command you ran, the matrix, and matrix interpretation in the report.

7. Use the test data to evaluate the model.

· Use the test set to run the compute command, and store the predicted values in the variable testpred. Run the second command to run round the predictions. Include both commands in the report.

· Run the table command to build the confusion matrix for the test data.  Explain what the matrix shows.  Include the command you ran, the matrix, and matrix interpretation in the report.

· Compare the classification accuracy for the test data with the classification accuracy for the training data.

8. Different Input parameters.

· Repeat the steps 4-7 above with different input parameters.  You may change the number of hidden layers, and/or the number of nodes in the hidden layer, and/or you may use a subset of independent variables.  Include the command your ran, the output, and the output interpretation in the report.

· Compare the results of the two runs.  Which run has a higher classification accuracy and why?

9. Summary

· What differences between decision tree classification and neural network classification methods did you observe?

· Which part of this exercise did you find the most challenging, and what approach did you take to resolve the challenge?

Exercise Deliverables

Submit the following files in the Exercise 6 Assignment folder.

· The report addressing the key points above

· An R script with commands your ran and brief comments on the commands purpose

Exercise Grading

· This exercise is worth 2% of the course grade.  

· All questions must be answered in order and in your own words.  

· Grammatical and spelling errors may affect the assignment grade.

*** Start working on this exercise early in a week to allow sufficient time for debugging any potential R errors. ***  

This exercise may take 4-6 hours to complete. This estimate is a little higher than last week estimate because of the commands complexity. Post your question about this exercise in assignment 5 questions and answers discussion topic.

#Neural network method on diabetis data
#Run once to install the packaglibrary
# install.packages(“neuralnet”)
library(“neuralnet”)
#Read the diabetes data file. Change the file location.
setwd(“F:/Datasets”)
diabetes<-read.csv(file="diabetes.csv", head=TRUE, sep=",") #Preview the first 6 rows head(diabetes) #Run the summary command summary(diabetes) #scale the first 8 variables diabetes[1:8]<-scale(diabetes[1:8]) #make sure that the result is reproducible set.seed(12345) #split the data into a training and test set ind <- sample(2, nrow(diabetes), replace = TRUE, prob = c(0.7, 0.3)) train.data <- diabetes[ind == 1, ] test.data <- diabetes[ind == 2, ] #Build the model. If you receive a warning, rerun the command. nn<-neuralnet(formula = class~preg+plas+pres+skin+insu+mass+pedi+age, data = train.data, hidden=2, err.fct="ce", linear.output = FALSE) #names command displays the available neural network properties names(nn) #Run the commands to display the network properties nn$call # the command we ran to generate the model nn$response[1:10] # actual values of the dependent variable for first 10 records nn$covariate [1:12,] # input variables that were used to build the model for first 12 records nn$model.list # list dependent and independent variables in the model nn$net.result[[1]][1:10] # display the first 10 predicted probabilities nn$weights # network weights after the last method iteration nn$startweights # weights on the first method iteration nn$result.matrix # number of trainings steps, the error, and the weights plot(nn) # plot the network #Model evaluation; Round the predicted probabilities mypredict<-compute(nn, nn$covariate)$net.result mypredict<-apply(mypredict, c(1), round) mypredict [1:10] # confusion matrix for the training set table(mypredict, train.data$class, dnn =c("Predicted", "Actual")) mean(mypredict==train.data$class) # confusion matrix for the test set testPred <- compute(nn, test.data[, 0:8])$net.result testPred<-apply(testPred, c(1), round) table(testPred, test.data$class, dnn =c("Predicted", "Actual")) mean(testPred==test.data$class)

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4 132 86 31 0 28

63 0

3 158 70 30 328 35.5

35 1

0 123 88 37 0

0.197 29 0

4 85 58 22 49 27.8 0.306 28 0
0 84 82 31 125 38.2 0.233 23 0
0 145 0 0 0 44.2 0.63 31 1
0 135 68 42

24 1

1 139 62 41

21 0

0 173 78 32

58 0

4 99 72 17 0 25.6 0.294 28 0
8 194 80 0 0 26.1 0.551 67 0
2 83 65 28 66 36.8

24 0

2 89 90 30 0

42 0

4 99 68 38 0 32.8

33 0

4 125 70 18 122 28.9

45 1

3 80 0 0 0 0

22 0

6 166 74 0 0 26.6 0.304 66 0
5 110 68 0 0 26 0.292 30 0
2 81 72 15 76 30.1

25 0

7

70 33 145 25.1

55 1

6 154 74 32 193 29.3 0.839 39 0
2 117 90 19 71 25.2 0.313 21 0
3 84 72 32 0 37.2

28 0

6 0 68 41 0 39 0.727 41 1
7 94 64 25 79 33.3

41 0

3 96 78 39 0

0.238 40 0

10 75 82 0 0 33.3 0.263 38 0
0 180 90 26 90 36.5

35 1

1 130 60 23 170 28.6 0.692 21 0
2 84 50 23 76 30.4

21 0

8 120 78 0 0 25

64 0

12 84 72 31 0 29.7

46 1

0 139 62 17 210 22.1 0.207 21 0
9 91 68 0 0 24.2 0.2 58 0
2 91 62 0 0 27.3

22 0

3 99 54 19 86 25.6

24 0

3 163 70 18 105 31.6 0.268 28 1
9 145 88 34 165

53 1

7 125 86 0 0 37.6 0.304 51 0
13 76 60 0 0 32.8 0.18 41 0
6 129 90 7 326 19.6 0.582 60 0
2 68 70 32 66 25 0.187 25 0
3 124 80 33 130 33.2 0.305 26 0
6 114 0 0 0 0

26 0

9 130 70 0 0 34.2 0.652 45 1
3 125 58 0 0 31.6 0.151 24 0
3 87 60 18 0 21.8 0.444 21 0
1 97 64 19 82 18.2 0.299 21 0
3 116 74 15 105

24 0

0 117 66 31 188 30.8

22 0

0 111 65 0 0 24.6 0.66 31 0
2 122 60 18 106 29.8

22 0

0 107 76 0 0 45.3 0.686 24 0
1 86 66 52 65 41.3

29 0

6 91 0 0 0 29.8

31 0

1 77 56 30 56 33.3

24 0

4 132 0 0 0 32.9 0.302 23 1
0 105 90 0 0 29.6 0.197 46 0
0 57 60 0 0

67 0

0 127 80 37 210 36.3

23 0

3 129 92 49 155

0.968 32 1

8 100 74 40 215 39.4

43 1

3 128 72 25 190 32.4

27 1

10 90 85 32 0 34.9

56 1

4 84 90 23 56 39.5

25 0

1 88 78 29 76 32 0.365 29 0
8 186 90 35 225 34.5

37 1

5 187 76 27 207 43.6

53 1

4 131 68 21 166 33.1 0.16 28 0
1 164 82 43 67 32.8

50 0

4 189 110 31 0

0.68 37 0

1 116 70 28 0 27.4 0.204 21 0
3 84 68 30 106 31.9

25 0

6 114 88 0 0 27.8 0.247 66 0
1 88 62 24 44 29.9 0.422 23 0
1 84 64 23 115 36.9 0.471 28 0
7 124 70 33 215 25.5 0.161 37 0
1 97 70 40 0 38.1

30 0

8 110 76 0 0 27.8 0.237 58 0
11 103 68 40 0 46.2 0.126 42 0
11 85 74 0 0 30.1 0.3 35 0
6 125 76 0 0 33.8

54 1

0 198 66 32

41.3

28 1

1 87 68 34 77 37.6

24 0

6 99 60 19 54

0.497 32 0

0 91 80 0 0 32.4

27 0

2 95 54 14 88 26.1

22 0

1 99 72 30 18

0.412 21 0

6 92 62 32 126 32 0.085 46 0
4 154 72 29 126

37 0

0 121 66 30 165 34.3 0.203 33 1
3 78 70 0 0 32.5 0.27 39 0
2 130 96 0 0 22.6 0.268 21 0
3 111 58 31 44 29.5 0.43 22 0
2 98 60 17 120 34.7

22 0

1 143 86 30

30.1

23 0

1 119 44 47 63 35.5 0.28 25 0
6 108 44 20 130 24

35 0

2 118 80 0 0 42.9

21 1

10 133 68 0 0 27

36 0

2 197 70 99 0 34.7

62 1

0 151 90 46 0 42.1

21 1

6 109 60 27 0 25

27 0

12 121 78 17 0 26.5 0.259 62 0
8 100 76 0 0 38.7 0.19 42 0
8 124 76 24

28.7 0.687 52 1

1 93 56 11 0 22.5

22 0

8 143 66 0 0 34.9 0.129 41 1
6 103 66 0 0 24.3

29 0

3 176 86 27 156 33.3

52 1

0 73 0 0 0 21.1

25 0

11 111 84 40 0 46.8

45 1

2 112 78 50 140 39.4

24 0

3 132 80 0 0 34.4

44 1

2 82 52 22 115 28.5

25 0

6 123 72 45 230 33.6 0.733 34 0
0 188 82 14

32

22 1

0 67 76 0 0 45.3

46 0

1 89 24 19 25 27.8 0.559 21 0
1 173 74 0 0 36.8 0.088 38 1
1 109 38 18 120 23.1 0.407 26 0
1 108 88 19 0 27.1 0.4 24 0
6 96 0 0 0 23.7 0.19 28 0
1 124 74 36 0 27.8 0.1 30 0
7 150 78 29 126 35.2 0.692 54 1
4 183 0 0 0 28.4 0.212 36 1
1 124 60 32 0 35.8 0.514 21 0
1 181 78 42 293 40

22 1

1 92 62 25 41

25 0

0 152 82 39 272 41.5 0.27 27 0
1 111 62 13 182 24

23 0

3 106 54 21 158 30.9 0.292 24 0
3 174 58 22 194 32.9

36 1

7 168 88 42 321 38.2 0.787 40 1
6 105 80 28 0 32.5

26 0

11 138 74 26 144 36.1 0.557 50 1
3 106 72 0 0 25.8 0.207 27 0
6 117 96 0 0 28.7

30 0

2 68 62 13 15

0.257 23 0

9 112 82 24 0 28.2

50 1

0 119 0 0 0 32.4

24 1

2 112 86 42 160 38.4

28 0

2 92 76 20 0 24.2

28 0

6 183 94 0 0

45 0

0 94 70 27 115 43.5

21 0

2 108 64 0 0 30.8

21 0

4 90 88 47 54 37.7

29 0

0 125 68 0 0 24.7 0.206 21 0
0 132 78 0 0 32.4

21 0

5 128 80 0 0 34.6

45 0

4 94 65 22 0 24.7 0.148 21 0
7 114 64 0 0 27.4

34 1

0 102 78 40 90 34.5 0.238 24 0
2 111 60 0 0 26.2 0.343 23 0
1 128 82 17 183 27.5

22 0

10 92 62 0 0 25.9 0.167 31 0
13 104 72 0 0 31.2

38 1

5 104 74 0 0 28.8

48 0

2 94 76 18 66 31.6

23 0

7 97 76 32 91 40.9

32 1

1 100 74 12 46 19.5

28 0

0 102 86 17 105 29.3

27 0

4 128 70 0 0 34.3

24 0

6 147 80 0 0 29.5

50 1

4 90 0 0 0 28 0.61 31 0
3 103 72 30 152 27.6 0.73 27 0
2 157 74 35

39.4

30 0

1 167 74 17 144

33 1

0 179 50 36 159 37.8

22 1

11 136 84 35 130

0.26 42 1

0 107 60 25 0 26.4

23 0

1 91 54 25 100 25.2 0.234 23 0
1 117 60 23 106 33.8 0.466 27 0
5 123 74 40 77 34.1 0.269 28 0
2 120 54 0 0 26.8 0.455 27 0
1 106 70 28 135 34.2 0.142 22 0
2 155 52 27

38.7 0.24 25 1

2 101 58 35 90 21.8

22 0

1 120 80 48

41 0

11 127 106 0 0 39 0.19 51 0
3 80 82 31 70 34.2

27 1

10 162 84 0 0 27.7

54 0

1 199 76 43 0 42.9

22 1

8 167 106 46 231 37.6

43 1

9 145 80 46 130 37.9

40 1

6 115 60 39 0 33.7 0.245 40 1
1 112 80 45 132 34.8

24 0

4 145 82 18 0 32.5 0.235 70 1
10 111 70 27 0 27.5 0.141 40 1
6 98 58 33 190 34 0.43 43 0
9 154 78 30 100 30.9

45 0

6 165 68 26 168 33.6

49 0

1 99 58 10 0 25.4 0.551 21 0
10 68 106 23 49 35.5 0.285 47 0
3 123 100 35 240

0.88 22 0

8 91 82 0 0

68 0

6 195 70 0 0 30.9

31 1

9 156 86 0 0 24.8 0.23 53 1
0 93 60 0 0 35.3 0.263 25 0
3 121 52 0 0 36 0.127 25 1
2 101 58 17 265 24.2

23 0

2 56 56 28 45 24.2

22 0

0 162 76 36 0

0.364 26 1

0 95 64 39 105

22 0

4 125 80 0 0 32.3 0.536 27 1
5 136 82 0 0 0 0.64 69 0
2 129 74 26 205 33.2 0.591 25 0
3 130 64 0 0 23.1 0.314 22 0
1 107 50 19 0 28.3

29 0

1 140 74 26 180

23 0

1 144 82 46 180 46.1

46 1

8 107 80 0 0 24.6

34 0

13 158 114 0 0 42.3 0.257 44 1
2 121 70 32 95 39.1

23 0

7 129 68 49 125 38.5

43 1

2 90 60 0 0 23.5

25 0

7 142 90 24 480 30.4 0.128 43 1
3

74 19 125 29.9 0.268 31 1

0 99 0 0 0 25

22 0

4 127 88 11 155 34.5

28 0

4 118 70 0 0

26 0

2 122 76 27 200 35.9

26 0

6 125 78 31 0 27.6

49 1

1 168 88 29 0 35 0.905 52 1
2 129 0 0 0 38.5 0.304 41 0
4 110 76 20 100 28.4

27 0

6 80 80 36 0 39.8

28 0

10 115 0 0 0 0 0.261 30 1
2 127 46 21 335 34.4

22 0

9 164 78 0 0 32.8 0.148 45 1
2 93 64 32 160 38 0.674 23 1
3 158 64 13

31.2

24 0

5 126 78 27 22 29.6 0.439 40 0
10 129 62 36 0

38 1

0 134 58 20

26.4

21 0

3 102 74 0 0 29.5

32 0

7 187 50 33

33.9

34 1

3 173 78 39 185 33.8

31 1

10 94 72 18 0 23.1

56 0

1 108 60 46 178 35.5 0.415 24 0
5 97 76 27 0 35.6 0.378 52 1
4 83 86 19 0 29.3

34 0

1 114 66 36 200 38.1 0.289 21 0
1 149 68 29 127 29.3 0.349 42 1
5 117 86 30 105 39.1 0.251 42 0
1 111 94 0 0 32.8

45 0

4 112 78 40 0 39.4 0.236 38 0
1 116 78 29 180 36.1 0.496 25 0
0 141 84 26 0 32.4 0.433 22 0
2 175 88 0 0 22.9

22 0

2 92 52 0 0 30.1 0.141 22 0
3 130 78 23 79 28.4 0.323 34 1
8 120 86 0 0 28.4 0.259 22 1
2 174 88 37 120 44.5

24 1

2 106 56 27 165 29

22 0

2 105 75 0 0

0.56 53 0

4 95 60 32 0 35.4 0.284 28 0
0 126 86 27 120 27.4

21 0

8 65 72 23 0 32 0.6 42 0
2 99 60 17 160 36.6

21 0

1 102 74 0 0 39.5

42 1

11 120 80 37 150 42.3

48 1

3 102 44 20 94 30.8 0.4 26 0
1 109 58 18 116 28.5 0.219 22 0
9 140 94 0 0 32.7

45 1

13 153 88 37 140 40.6

39 0

12 100 84 33 105 30

46 0

1 147 94 41 0

27 1

1 81 74 41 57

32 0

3 187 70 22 200 36.4

36 1

6 162 62 0 0 24.3 0.178 50 1
4 136 70 0 0 31.2

22 1

1 121 78 39 74 39 0.261 28 0
3 108 62 24 0 26 0.223 25 0
0 181 88 44

43.3

26 1

8 154 78 32 0 32.4 0.443 45 1
1 128 88 39 110 36.5

37 1

7 137 90 41 0 32 0.391 39 0
0 123 72 0 0 36.3 0.258 52 1
1 106 76 0 0 37.5 0.197 26 0
6 190 92 0 0 35.5

66 1

2 88 58 26 16 28.4

22 0

9 170 74 31 0 44 0.403 43 1
9 89 62 0 0 22.5 0.142 33 0
10 101 76 48 180 32.9

63 0

2 122 70 27 0 36.8 0.34 27 0
5 121 72 23 112 26.2 0.245 30 0
1 126 60 0 0 30.1 0.349 47 1
1 93 70 31 0 30.4 0.315 23 0

preg	plas	pres	skin	insu	mass	pedi	age	class
																																																	6																																																																																																																																																																																																																																																																																																																																																																																																																				1																																																																				4																																								8																																																7																																																																																																							2																																																																													3																																																									5																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															0																																						33			0.6																																																									27																												50
														85																																							66		2																												9																																																						26		0.3										51																																													31
1									83																																																64																																																																	23	0.6																																														72																																																													32
						89																				94																																																													28		0.							16																																																																											21
																					13																																		40																											35		1																																																		68																					43	2.2																																						88
																	11																																																											74																																																																								25	0.														20																																																									30
																																																		78	0.																																																															24
																												10			1																15				35.3		0.1																												34																																																		29
																		19																																																													70																									45																								54							30.5	0.	1																														58							53
																				12														96				0.2
														110																				92																																							37					0.19
					168																											38	0.537
1																																		39																																														80			27.1		1.4																																							41									57
																						18																																													60																																			84									30.1	0.3						98				59
			166	1													75		25.8		0.5									87
																										100	0.																	48
					118										47		230	45.8	0.									55
										107				29.6						0.254
								103					43.3			0.18
												115					34.6	0.																						52
											126	235	39.3	0.704
																			99				35.4			0.38
			196																																					90		39.8			0.4
											119					0.26
									14	1																								46																																				36
												125	31.1	0.		205
						147																																														76							39.4			0.257
								97														140			23.2	0.487																																																																																									22
							145																																				82		22.2	0.	245
	1															17				34.1				0.33
											109	0.546
								158								3	1.6	0.851
		24.8	0.2						67
19.9	0.			188
														122							27.6		0.51
	192	0.966
				138							33.2	0.																															42
													102									32.9	0.6												65
			38.2	0.503
													111		207		37.1	1.39																						56
											180	0.2								71
				133	40.2	0.		69
																			106	22.7				0.23
			171		240	45.4	0.721
		159					27.4				0.29
1.8							93
								146								29.7		0.56
0.5																									86
			39.1	0.3																							44
																							105			0.305
19.4	0.													49
								101						24.2				0.52
		24.4	0.	342
				176	300					33.7		0.46
				150				34.7	0.718
			73			0.24
			187	304					37.7
	46.8	0.9																																							62
		40.5	1.7								81
					142		41.5	0.						173
			0.304
			0.27
0.58
				141												128				25.4	0.699
													114									32.8			0.	258
	0.203
					32.5	0.855
	42.7		0.84
															95			19.6		0.334
					28.9	0.			189
0.867
						139		28.6	0.411
	43.4			0.583
														129	270			35.1	0.		231
				79	0.396
				24.7		0.14
32.6		0.3										91
	0.37
				131	43.2
													112	0.307
				113		22.4
0.102
				29.3	0.767
			24.6			0.	237
						137																108	48.8		0.22
									32.4	0.698
			36.6	0.		178
					38.5		0.324
							136	0.		153
		26.5	0.								165
19.1			0.258
								123			0.443
46.7	0.2					61
					134		23.8	0.2				77
	0.761
								144	228		33.9	0.	255
			31.6	0.13
	20.4		0.323
						28.7		0.356
	220	49.7	0.			325
1								63	1.222
					151			26.1	0.					179
		22.5		0.262
		26.6				0.28
39.6	0.93
					152	0.801
				0.207
				29.5	0.287
					34.3		0.336
		37.4		0.247
									135										33.3	0.	199
								155		495		0.543
											31.2		0.192
0.391
				160				175	0.588
0.539
										124
	0.654
	28.2
	0.223
					162	53.2	0.759
							34.2
						33.6	0.404
						132				26.8	0.	186
0.	278
		0.496
																		120				42.9			0.452
			0.261
								117					34.5		0.403
	27.9	0.741
	0.361
1.114
			170		225
38.3	0.457
			21.1			0.64
				33.8		0.088
								30.8	0.597
0.532
0.703
		36.9			0.15
				0.268
		39.5		0.286
0.	318
0.	272
					154	284	0.237
0.572
0.096
	0.21
			27.3		0.085
204	0.399
		21.9			0.43
					156	1.189
485				40.6				0.68
	47.9		0.137
	0.63
					25.2	0.833
0.229
	163		40.9	0.817
0.294
			37.2		0.204
	285		44.2					167
	0.368
0.743
							104					29.9	0.722
				148			0.256
0.709
	31.9		0.471
					28.4	0.495
															130		0.542
0.773
	43.5		0.678
		32.7	0.719
0.382
67.1	0.319
				143
0.956
0.084
					34.9	0.725
			27.7				0.299
	0.244
					194					35.9	0.745
				181		0.61
1.	321
	22.6			0.142
		33.1	0.374
						30.4	0.383
	52.3	0.578
0.136
				210	0.395
			24.3			0.187
	22.9
	34.8		0.905
				30.9
0.874
40.1			0.236
	0.787
0.235
				190
	23.9		0.407
280		37.5		0.605
		0.151
	0.289
			184							35.5	0.355
42.8	0.	375
0.			164
42.6	0.431
271	41.8	0.742
				35.8		0.514
0.464
	1.224
		37.8
177	478	1.072
0.805
	0.209
	28.8	0.687
		23.6			0.66
0.101
			35.7	0.	198
	0.652
		197	744	36.7	2.329
45.2	0.089
0.645
370		46.2					0.238
0.394
0.		293
	43.6	0.479
0.586
44.1		0.686
0.831
18.4		0.582
29.2
0.446
				25.6	0.	402
1.318
0.329
1.213
680	0.427
	0.282
	0.143
			0.284
0.	249
0.926
	0.557
0.092
		193							25.9	0.655
1.353
	191
32.1	0.612
0.226
0.997
		36.3	0.933
1.101
		25.1	0.078
				27.5
	45.6	1.136
	0.128
		0.422
	0.251
0.677
0.296
							116							27.8	0.454
24.9	0.744
	25.3		0.88
	37.9
		161		0.16
				0.259
0.647
545			38.7	0.619
0.808
	20.8			0.34
		36.1			0.263
	0.434
0.757
			182
0.613
			0.692
360
		215	30.7
	0.412
		32.3		0.839
0.156
52.9
39.7	0.215
	25.5	0.	326
1.391
	0.875
			26.2		0.313
	0.433
0.626
1.						127
	0.315
19.3
0.345
		38.1
		23.5		0.129
	0.527
			0.197
	0.73
		0.148
	157	0.123
45.5		0.127
0.122
			23.1	1.476
0.166
0.932
	0.343
0.893
		39.9	0.331
0.472
0.673
		0.389
					36.8	0.485
		0.349
				21.8	0.279
0.346
42.2
	0.252
			34.4	0.243
	27.2
	0.559
	0.302
0.962
0.569
	0.378
			36.5
		29.8
	39.2
0.385
0.499
	0.306
	0.234
465		38.4	2.137
1.731
0.545
0.225
36.2	0.816
	0.528
0.509
48.3
1.021
0.821
0.947
1.268
0.221
22.3		0.205
0.239
0.949
	0.444
45.7
415		23.7
	22.1	0.463
0.803
275
0.944
0.196
0.241
	0.161
0.135
	42.1
0.376
1.191
172	579			42.4	0.702
	0.674
310	1.076
0.534
474
1.095
0.554
		18.2	0.624
		26.4		0.219
		45.3	0.507
0.561
0.421
0.516
277	0.264
0.	328
	0.233
0.108
		0.551
	0.167
24.5	1.138
0.147
	0.727
0.435
32.2		0.497
0.955
59.4	2.42
0.658
	0.285
21.2		0.415
0.381
0.832
0.498
	0.212
26.7
30.2		0.364
			37.6	1.001
	0.733
0.416
0.705
1.022
	0.269
0.			183
	46.1	0.571
		41.3	0.607
0.17
38.8
	0.126
0.231
0.711
	0.466
0.162
0.419
0.344
	35.2
250			42.3		0.365
	480	40.7		0.536
	265	46.5	1.159
0.629
33.5			0.292
0.145
1.144
0.		174
0.547
	195	0.163
0.267
0.738
37.3
	0.314
	0.968
0.409
0.297
0.525
0.154
30.3	0.771
0.189
26.3	0.107
0.493
0.717
0.917
0.501
1.251
21.7	0.735
0.804
	36.4
0.661
0.549
0.825
0.159
0.423
1.034
0.341
		28.5
	0.591
0.218
0.						121
274	0.502
0.401
26.9
0.601
0.748
38.6
31.3	0.338
0.198
330	0.892
0.813
0.693
		0.245
0.575
0.371
	0.206
600
0.417
0.249
1.154
0.342
0.925
0.175
0.402
1.699
	185	0.682
0.194
1.258
	19.5	0.482
0.138
0.593
0.878
0.157
20.1
1.282
		0.141
0.246
1.698
40.8	1.461
0.347
0.158
0.362
0.393
0.144
0.732
0.115
0.465
0.153
0.649
0.871
0.	149
0.695
0.303
	0.178
440	0.134
23.4	0.447
	0.455
	28.3
0.133
540
0.155
			200	38.9	1.162
1.292
0.182
1.394
0.165
0.637
0.217
0.164
0.631
57.3
	35.6	0.587
0.328
0.614
0.332
49.6
44.6	0.366
0.181
24.1	0.828
0.	335
0.856
0.886
	0.439
0.191
169
0.253
0.598
	44.5	0.904
0.483
0.565
0.118
0.177
0.176
387	0.295
41.2	0.441
291	0.352
0.121
392	0.826
0.97
0.595
0.317
0.265
0.326
0.646
0.426
23.3
0.515
0.453
0.293
0.785
0.734
1.174
0.488
49.3	0.358
46.3	1.096
0.408
1.182
510	0.222
1.057
0.278
0.766
0.171

278

75

53

1675

1

7

822

.99595951

1

7

93

1

.65287791

4

1

1

1

12

1

1

1

1

1

1

1

1

33.11134196

1

1

1

6299592

1

31

1

1

1

1

1

1

29

1

1

14

1

46.99999999

1

1

1

1

1

8057555

1

1

1

1

1

1

1

1

1

1

1

1

1

46.99999999

1

1

1

34

1

1

34

1

27.7

1

1

34

1

1

1

1

38

1

35

1

1

1

1

1

1

1

1

56.30993248

1

56.30993248

1

1

1

51.99999999

1

1

1

35.41705528

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

3842852

1

1

1

1

55.17551084

1

45

1

1

1

1

1

1

1

1

1

1

47.29061004

1

1

45

1

42.64670314

1

1

1

1

32.5

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

55.12467166

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

63.43494882

1

1

55.92280472

1

1

38

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

51.99999999

1

1

1

1

1

1

1

1

1

1

1

1

34.38034472

1

62.99999999

1

1

46.16913933

1

1

1

1

1

0

0

35.41705528

0

0

0

0

0

0

35 35.6553281

0

0

0

52.99999999 49.08561678

0

0

0

0

0

0

0

29.7448813

0

0

0

38.99999999

0

0

0

41.99999999

0

0

63.99999999

0

57.99999999 48.17983012

0

0

0

0

35

0

0

0

0

53.99999999

0

39.99999999

0

28

0

0

37

0

0

0

57.99999999

0

0

0

52.88313932

0

47.99999999 45

0

41.99999999 53.13010235

0

0

0

42.99999999

0

0

0

25.5

0

46.99999999

0

0

0

0

0

24

0

0

41.99999999

0

37

0

0

0

50.99999999

0

0

43.99999999

0

0

51.99999999 30.78414653

0

0

0

0

35.88213725

0

43.19915768

0

0

0

0

58.84069549

0

30.25643716

0

0

0

0

43.31531568

0

37

0

39.80557109

0

0

0

0

0

35

0

0

33.11134196

0

0

0

36

0

33.21525149

0

0

0

0

pelvic_incidence	pelvic_tilt	lumbar_lordosis	sacral_slope	pelvic_radius	degree_spondylolisthesis	class
63.																																																																																																				0																																																																																																																																																																																																																		1	22.55258597	39.60911701	40.4752	31	98.67	29	-0.254399986
39.05695098	10.06099	14	25.015			37		28	114.4054254	4.5642586			45
68.83202098	22.21848205	50.09219				35	46.6135		38	105.9851355	-3.530317314
69.29700807		24	44.31123813	44.64413017	101.8684951	11.21152			34
49.71285934	9.652074879	28.317406	40.06078446	108.1687249	7.918500615
40.25019968	13.92190658	25.1249496	26.32829311	130.3278713	2.230651729
53.43292815	15.8643	36	37.16593387	37.56859203	120.5675233	5.988550702
45.36675362	10.75561143	29.03834896	34.61114218	117.2700675	-10.67587083
43.79019026	13.5337531	42.69081398		30.25643716	125.0028927	13.28901817
36.68635286	5.010884121	41.9487509	31.67546874	84.24141517	0.664437117
49.70660953	13.04097405	31.33450009	36.66563548	108.6482654	-7.825985755
31.23238734	17.71581923	15.5	13.51656811	120.0553988	0.499751446
48.91555137	19.96455616	40.26379358	28.95099521	119.321358	8.028894629
53.5721702	20.46082824	33.1			33.11134196	110.9666978	7.044802938
57.30022656	24.1888846				46.99999999	116.8065868	5.766946943
44.31890674	12.53799164	36.098763	31.78091509	124.1158358	5.415825143
63.83498162	20.36250706	54.55243367	43.47247456	112.3094915	-0.622526643
31.27601184	3.14466948		32.5	28.13134236	129.0114183	3.623020073
38.69791243	13.44474904	25.25316339	123.1592507	1.429185758
41.72996308	12.25407408	30.12258646	29.475889	116.5857056	-1.244402488
43.92283983	14.17795853	37.8325467		29.7448813	134.4610156	6.451647637
54.91944259	21.06233245	42.19999999	33.85711014	125.2127163	2.432561437
63.07361096	24.41380271		53.99999999	38.65980825	106.4243295	15.77969683
45.54078988	13.06959759	30.29832059	32.47119229	117.9808303	-4.987129618
36.12568347	22.75875277	13.3669307	115.5771163	-3.237562489
54.12492019	26.65048856	35.32974693	27.47443163	121.447011	1.571204816
26.14792141	10.75945357	15.38846783	125.2032956	-10.09310817
43.58096394	16.5088837	27.07208024	109.271634	8.992815727
44.5510115	21.93114655	26.78591597	22.61986495	111.0729197	2.652320636
66.87921138	24.89199889	49.27859673	41.9872125	113.4770183	-2.005891748
50.81926781	15.40221253	42.52893886			35.41705528	112.192804	10.86956554
46.39026008	11.07904664	32.13655345	35.31121344	98.77454633	6.386831648
44.93667457	17.44383762		27.7	27.49283695	117.9803245	5.569619587
38.66325708	12.98644139		39.99999999	25.67681568	124.914118	2.703008052
59.59554032	31.99824445	46.56025198	27.59729587	119.3303537	1.474285836
31.48421834	7.82622134	24.28481815	23.657997	113.8331446	4.393080498
32.09098679	6.989378081	35.99819848	25.10160871	132.264735	6.413427708
35.70345781	19.44325311	20.7	16.26020471	137.5406125	-0.263489651
55.84328595	28.84744756	47.69054322	26.99583839	123.3118449	2.812426855
52.41938511	19.01156052	35.87265953	33.40782459	116.5597709	1.694705102
35.49244617	11.7016723	15.59036345	23.79077387	106.9388517	-3.460357991
46.44207842	8.39503589	29.0372302	38.04704253	115.4814047	2.045475795
53.85479842	19.23064334	32.77905978	34.62415508	121.6709148	5.329843204
66.28539377	26.32784484	47.49999999	39.95754893	121.2196839	-0.799624469
56.03021778	16.2979149	62.27527456	39.73230287	114.0231172	-2.325683841
50.91244034	23.01516931	27.89727103	117.4222591	-2.526701511
48.332638	22.22778399	36.18199318	26.10485401	117.3846251	6.481709096
41.35250407	16.57736351	30.70619135	24.77514057	113.2666746	-4.497957556
40.55735663	17.97778407	22.57957256	121.0462458	-1.537383074
41.76773173	17.89940172	20.0308863	23.86833001	118.3633889	2.062962549
55.28585178	20.44011836	34.84573342	115.8770174	3.558372358
74.43359316	41.55733141	32.87626175	107.9493045	5.000088788
50.20966979	29.76012218	36.10400731	20.44954761	128.2925148	5.740614083
30.14993632	11.91744524	18.23249108	112.6841408	11.46322327
41.17167989	17.32120599	33.46940277	23.85047391	116.3778894	-9.569249858
47.65772963	13.27738491	36.67998541		34.38034472	98.24978071	6.273012173
43.34960621	7.467468964	28.06548279		35.88213725	112.7761866	5.753277458
46.85578065	15.35151393	31.50426672	116.2509174	1.662705589
43.20318499	19.66314572	23.54003927	124.8461088	-2.919075955
48.10923638	14.93072472	35.56468278	33.17851166	124.0564518	7.947904861
74.37767772	32.05310438	78.77201304	42.32457334	143.5606905	56.12590603
89.68056731	32.70443487	83.13073216	56.97613244	129.9554764	92.02727682
44.529051	9.433234213				51.99999999	35.09581679	134.7117723	29.10657504
77.69057712	21.38064464	64.42944191			56.30993248	114.818751	26.93184095
76.1472121	21.93618556	82.96150249	54.21102654	123.9320096	10.43197194
83.93300857	41.28630543	61.99999999		42.64670314	115.012334	26.58810016
78.49173027	22.1817978	59.99999999	118.5303266	27.38321314
75.64973136	19.33979889	64.14868477	95.9036288	69.55130292
72.07627839	18.94617604		50.99999999	53.13010236	114.2130126	1.01004051
58.59952852	-0.261499046	51.49999999	58.86102756	102.0428116	28.05969711
72.56070163	17.38519079		55.17551084	119.1937238	32.10853735
86.90079431	32.9281677	47.79434664	53.97262661	135.0753635	101.7190919
84.97413208	33.02117462	60.85987263	51.95295747	125.6595336	74.33340864
55.512212	20.09515673		43.99999999	122.648753	34.55294641
72.2223343	23.07771056	90.99999999	49.14462374	137.7366546	56.80409277
70.22145219	39.82272448	68.11840309	30.39872771	148.5255624	145.3781432
86.75360946	36.04301632	69.22104479	50.71059314	139.414504	110.8607824
58.78254775	7.667044186	53.33894082	51.11550357	98.50115697	51.58412476
67.41253785	17.44279712	60.14464036	49.96974073	111.12397	33.15764573
47.74467877	12.08935067		38.99999999		35.6553281	117.5120039	21.68240136
77.10657122	30.46999418	69.48062839	46.63657704	112.1516	70.75908308
74.00554124	21.12240192	57.37950226		52.88313932	120.2059626	74.55516588
88.62390839	29.08945331	47.56426247	59.53445508	121.7647796	51.80589921
81.10410039	24.79416792	77.88702048	56.30993247	151.8398566	65.21461611
76.32600187	42.39620445	57.19999999	33.92979742	124.267007	50.12745689
45.44374959	9.906071798	44.99999999	35.53767779	163.0710405	20.31531532
59.78526526	17.87932332	59.20646143	41.90594194	119.3191109	22.12386874
44.91414916	10.21899563	44.63091389	34.69515353	130.0756599	37.36453993
56.60577127	16.80020017				41.99999999		39.80557109	127.2945222	24.0185747
71.18681115	23.89620111	43.6966651		47.29061004	119.8649383	27.28398451
81.65603206	28.74886935	58.23282055	52.9071627	114.7698556	30.60914842
70.95272771	20.15993121	62.85910914	50.7927965	116.1779325	32.522331
85.35231529	15.84491006	71.66865979	69.50740523	124.4197875	76.0206034
58.10193455	14.83763914	79.64983825	43.26429541	113.5876551	50.23787808
94.17482232	15.38076983	67.70572132	78.79405249	114.8901128	53.25522004
57.52235608	33.64707522	50.90985841	23.87528085	140.9817119	148.7537109
96.65731511	19.46158117	90.21149828	77.19573393	120.6730408	64.08099841
74.72074622	19.75694203	82.73535954	54.96380419	109.3565941	33.30606685
77.65511874	22.4329501	93.89277881	55.22216863	123.0557067	61.2111866
58.52162283	13.92228609	41.46785522	44.59933674	115.514798	30.3879839
84.5856071	30.36168482	65.47948563	54.22392228	108.0102185	25.11847846
79.93857026	18.7740711	63.31183486	61.16449915	114.787107	38.53874133
70.39930842	13.46998624	61.19999999	56.92932218	102.3375244		25.5
49.78212054	6.46680486		52.99999999		43.31531568	110.8647831	25.33564729
77.40933294	29.39654543	63.23230243	48.0127875	118.4507311	93.56373734
65.00796426	27.60260762	50.94751899	37.40535663	116.5811088	7.015977884
65.01377322	9.838262375	57.73583722	94.73852542	49.69695462
78.42595126	33.42595126	76.27743927	138.5541111	77.15517241
63.17298709	6.330910974		62.99999999	56.84207612	110.6440206	42.60807567
68.61300092	15.0822353	63.01469619	53.53076561	123.4311742	39.49798659
63.90063261	13.7062037	62.12433389	50.19442891	114.1292425	41.42282844
84.99895554	29.61009772	83.35219438	55.38885782	126.9129899	71.32117542
42.02138603	-6.554948347	67.89999999	48.57633437	111.5857819	27.33867086
69.75666532	19.27929659	48.49999999	50.47736873	96.49136982	51.1696403
80.98807441	36.84317181	86.96060151	44.1449026	141.0881494	85.87215224
129.8340406	8.404475005	48.38405705	121.4295656	107.690466	418.5430821
70.48410444	12.48948765	62.41714208	57.99461679	114.1900488	56.90244779
86.04127982	38.75066978	47.87140494	122.0929536	61.98827709
65.53600255	24.15748726	45.77516991	41.3785153	136.4403015	16.37808564
60.7538935	15.7538935		43.19915768	113.0533309	31.69354839
54.74177518	12.09507205	40.99999999	117.6432188	40.3823266
83.87994081	23.07742686	87.14151223	60.80251395	124.6460723	80.55560527
80.07491418	48.06953097	52.40343873	32.00538321	110.7099121	67.72731595
65.66534698	10.54067533	56.48913545		55.12467166	109.1627768	53.93202006
74.71722805	14.32167879	60.39554926	107.1822176	37.01708012
48.06062649	5.687032126	57.05716117	42.37359436	95.44375749	32.83587702
70.67689818	21.70440224	59.18116082	48.97249594	103.0083545	27.8101478
80.43342782	16.998479	66.53601753		63.43494882	116.4389807	57.78125
90.51396072	28.27250132	69.8139423	62.2414594	100.8921596	58.82364821
77.23689752	16.73762214	49.77553438	60.49927538	110.6903772	39.7871542
50.06678595	9.120340183	32.16846267	40.94644577	99.71245318	26.76669655
69.78100617	13.77746531			57.99999999	56.00354085	118.9306656	17.91456046
69.62628302	21.12275138	52.76659472	48.50353164	116.8030913	54.81686729
81.75441933	20.12346562	70.56044038	61.63095371	119.4250857	55.50688907
52.20469309	17.21267289	78.09496877	34.9920202	136.9725168	54.93913416
77.12134424	30.3498745	77.48108264	46.77146974	110.6111484	82.09360704
88.0244989	39.84466878	81.77447308		48.17983012	116.6015376	56.76608323
83.39660609	34.31098931	78.42329287		49.08561678	110.4665164	49.67209559
72.05403412	24.70073725	79.87401586	47.35329687	107.1723576	56.42615873
85.09550254	21.06989651	91.73479193	64.02560604	109.062312	38.03283108
69.56348614	15.4011391	74.43849743	54.16234705	105.0673556	29.70121083
89.5049473	48.90365265	72.0034229	40.60129465	134.6342912	118.3533701
85.29017283	18.27888963	100.7442198	67.0112832	110.6607005	58.88494802
60.62621697	20.5959577	64.53526221	40.03025927	117.2255542	104.8592474
60.04417717	14.30965614	58.03886519	45.73452103	105.1316639	30.40913315
85.64378664	42.68919513	78.7506635	42.95459151	105.1440758	42.88742577
85.58171024	30.45703858	78.23137949	114.8660487	68.37612182
55.08076562	-3.759929872	55.99999999		58.84069549	109.9153669	31.77358318
65.75567895	9.832874231	50.82289501		55.92280472	104.3949585	39.30721246
79.24967118	23.94482471	40.79669829	55.30484647	98.62251165	36.7063954
81.11260488	20.69044356	60.68700588	60.42216132	94.01878339	40.51098228
48.0306238	3.969814743	58.34451924	44.06080905	125.3509625	35.00007784
63.40448058	14.11532726	48.13680562	49.28915333	111.9160075	31.78449499
57.28694488	15.1493501		63.99999999	42.13759477	116.7353868	30.34120327
41.18776972	5.792973871	42.86739151	35.39479584	103.3488802	27.66027669
66.80479632	14.55160171	72.08491177	52.25319461	82.45603817	41.6854736
79.4769781	26.73226755	70.65098189	52.74471055	118.5886691	61.70059824
44.21646446	1.507074501	46.11033909	42.70938996	108.6295666	42.81048066
57.03509717	0.34572799	49.19800263	56.68936918	103.0486975	52.16514503
64.27481758	12.50864276	68.70237672	51.76617482	95.25245421	39.40982612
92.02630795	35.39267395	77.41696348	56.633634	115.72353	58.05754155
67.26314926	7.194661096	51.69688681	60.06848816	97.8010854	42.13694325
118.1446548	38.44950127	50.83851954	79.69515353	81.0245406	74.04376736
115.9232606	37.51543601	76.79999999	78.40782459	104.6986033	81.19892712
53.94165809	9.306594428	43.10049819	44.63506366	124.3978211	25.0821266
83.7031774	20.26822858	77.1105979	125.4801739	69.279571
56.99140382	6.87408897	57.00900516	50.11731485	109.978045	36.81011057
72.34359434	16.42078962	59.86901238	70.08257486	12.07264427
95.38259648	24.82263131	95.15763273	70.55996517	89.3075466	57.66084135
44.25347645	1.101086714	43.15238973	98.27410705	23.9106354
64.80954139	15.17407796	58.83999352	49.63546343	111.679961	21.40719845
78.40125389	14.04225971	79.69426258	64.35899418	104.7312342	12.39285327
56.66829282	13.45820343	43.76970978	43.21008939	93.69220863	21.10812135
50.82502875	9.064729049	56.29999999	41.7602997	78.99945411	23.04152435
61.41173702	25.38436364	39.09686927	36.02737339	103.4045971	21.84340688
56.56382381	8.961261611	52.57784639	47.6025622	98.77711506	50.70187326
67.02766447	13.28150221	66.15040334	53.74616226	100.7154129	33.98913551
80.81777144	19.23898066	61.64245116	61.57879078	89.47183446	44.167602
80.65431956	26.34437939	60.89811835	54.30994017	120.1034928	52.46755185
68.72190982	49.4318636	68.0560124	19.29004622	125.0185168	54.69128928
37.90391014	4.47909896	24.71027447	33.42481118	157.848799	33.60702661
64.62400798	15.22530262	67.63216653	49.39870535	90.298468	31.32641123
75.43774787	31.53945399	89.59999999	43.89829388	106.8295898	54.96578902
71.00194076	37.51577195	84.53709256	33.48616882	125.1642324	67.77118983
81.05661087	20.80149217	91.78449512	60.2551187	125.430176	38.18178176
91.46874146	24.50817744	84.62027202	66.96056402	117.3078968	52.62304673
81.08232025	21.25584028	78.76675639	59.82647997	90.07187999	49.159426
60.419932	5.265665422	59.8142356	55.15426658	109.0330745	30.26578534
85.68094951	38.65003527	82.68097744	47.03091424	120.8407069	61.95903428
82.4065243	29.27642195	77.05456489		53.13010235	117.0422439	62.76534831
43.7182623	9.811985315	33.90627699	88.43424213	40.88092253
86.472905	40.30376567	61.14101155		46.16913933	97.4041888	55.75222146
74.46908181	33.28315665	66.94210105	41.18592517	146.4660009	124.9844057
70.25043628	10.34012252	76.37007032	59.91031376	119.2370072	32.66650243
72.64385013	18.92911726	67.99999999	53.71473287	116.9634162	25.38424676
71.24176388	5.268270454	85.99958417	65.97349342	110.703107	38.2598637
63.7723908	12.76338484	65.36052425	51.00900596	89.82274067	55.99545386
58.82837872	37.57787321	125.7423855	21.25050551	135.6294176	117.3146829
74.85448008	13.90908417	62.69325884	60.9453959	115.2087008	33.17225512
75.29847847	16.67148361	61.29620362	58.62699486	118.8833881	31.57582292
63.36433898	20.02462134	67.49870507	43.33971763	130.9992576	37.55670552
67.51305267	33.2755899	96.28306169	34.23746278	145.6010328	88.30148594
76.31402766	41.93368293	93.2848628	132.2672855	101.2187828
73.63596236	9.711317947	63.92464442	98.72792982	26.97578722
56.53505139	14.37718927	44.99154663	42.15786212	101.7233343	25.77317356
80.11157156	33.94243223	85.10160773	125.5936237	100.2921068
95.48022873	46.55005318	58.99999999	48.93017555	96.68390337	77.28307195
74.09473084	18.82372712	76.03215571	55.27100372	128.4057314	73.38821617
87.67908663	20.36561331	93.82241589	67.31347333	120.9448288	76.73062904
48.25991962	16.41746236	36.32913708	31.84245726	94.88233607	28.34379914
38.50527283	16.96429691	35.11281407	21.54097592	127.6328747	7.986683227
54.92085752	18.96842952	51.60145541	35.952428	125.8466462	2.001642472
44.36249017	8.945434892	46.90209626	129.220682	4.994195288
48.3189305	17.45212105		47.99999999	30.86680945	128.9803079	-0.910940567
45.70178875	10.65985935	42.5778464	35.0419294	130.1783144	-3.38890999
30.74193812	13.35496594	35.90352597	17.38697218	142.4101072	-2.005372903
50.91310144	6.6769999	30.89652243	44.23610154	118.151531	-1.057985526
38.12658854	6.557617408	50.44507473	31.56897113	132.114805	6.338199339
51.62467183	15.96934373	129.385308	1.00922834
64.31186727	26.32836901	50.95896417	37.98349826	106.1777511	3.118221289
44.48927476	21.78643263	31.47415392	22.70284212	113.7784936	-0.284129366
54.9509702	5.865353416	126.9703283	-0.631602951
56.10377352	13.10630665	62.63701952	42.99746687	116.2285032	31.17276727
69.3988184	18.89840693	75.96636144	50.50041147	103.5825398	-0.44366081
89.83467631	22.63921678	90.56346144	67.19545953	100.5011917	3.040973261
59.72614016	7.724872599	55.34348527	52.00126756	125.1742214	3.235159224
63.95952166	16.06094486	63.12373633	47.8985768	142.3601245	6.298970934
61.54059876	19.67695713	52.89222856	41.86364163	118.6862678	4.815031084
38.04655072	8.30166942	26.23683004	123.8034132	3.885773488
43.43645061	10.09574326	36.03222439	33.34070735	137.4396942	-3.114450861
65.61180231	23.13791922	62.58217893	42.47388309	124.1280012	-4.083298414
53.91105429	12.93931796	40.97173633	118.1930354	5.074353176
43.11795103	13.81574355	40.34738779	29.30220748	128.5177217	0.970926407
40.6832291	9.148437195	31.02159252	31.53479191	139.1184721	-2.511618596
37.7319919	9.386298276	28.34569362	135.740926	13.68304672
63.92947003	19.97109671	40.17704963	43.95837332	113.0659387	-11.05817866
61.82162717	13.59710457	48.22452261	121.779803	1.296191194
62.14080535	13.96097523	133.2818339	4.955105669
69.00491277	13.29178975	55.5701429	55.71312302	126.6116215	10.83201105
56.44702568	19.44449915	43.5778464	37.00252653	139.1896903	-1.859688529
41.6469159	8.835549101	36.03197484	32.8113668	116.5551679	-6.054537956
51.52935759	13.51784732	38.01151027	126.7185156	13.92833085
39.08726449	5.536602477	26.93203835	33.55066201	131.5844199	-0.75946135
34.64992241	7.514782784		42.99999999	27.13513962	123.9877408	-4.082937601
63.02630005	27.33624023	51.60501665	35.69005983	114.5066078	7.439869802
47.80555887	10.68869819	37.11686068	125.3911378	-0.402523218
46.63786363	15.85371711		30.78414653	119.3776026	9.06458168
49.82813487	16.73643493	33.09169994	121.4355585	1.91330704
47.31964755	8.573680295	35.56025198	38.74596726	120.5769719	1.630663508
50.75329025	20.23505957	30.51823068	122.343516	2.288487746
36.15782981	-0.810514093	33.62731353	36.96834391	135.9369096	-2.092506504
40.74699612	1.835524271	49.99999999	38.91147185	139.2471502	0.668556793
42.91804052	-5.845994341	48.76403486	121.6068586	-3.362044654
63.79242525	21.34532339	65.99999999	42.44710185	119.5503909	12.38260373
72.95564397	19.57697146	61.00707117	53.37867251	111.2340468	0.813491154
67.53818154	14.65504222	58.00142908	123.6322597	25.9702063
54.75251965	9.752519649	123.0379985	8.235294118
50.16007802	-2.970024337	131.8024914	-8.290203373
40.34929637	10.19474845	37.96774659	30.15454792	128.0099272	0.458901373
63.61919213	16.93450781	49.34926218	46.68468432	117.0897469	-0.357811974
54.14240778	11.93511014	42.20729763	122.2090834	0.153549242
74.97602148	14.92170492	53.73007172	60.05431656	105.6453997	1.594747729
42.51727249	14.37567126	25.32356538	28.14160123	128.9056892	0.75702014
33.78884314	3.675109986	30.11373315	128.3253556	-1.776111234
54.5036853	6.819910138	47.68377516	111.7911722	-4.406769011
48.17074627	9.594216702	39.71092029	38.57652956	135.6233101	5.360050572
46.37408781	10.21590237	42.69999999	36.15818544	121.2476572	-0.54202201
52.86221391	9.410371613	46.98805181	43.4518423	123.0912395	1.856659161
57.1458515	16.48909145	42.84214764	40.65676005	113.8061775	5.0151857
37.14014978	16.48123972	20.65891006	125.0143609	7.366425398
51.31177106	8.875541276	56.99999999	42.43622979	126.4722584	-2.144043911
42.51561014	16.54121618	25.97439396	120.631941	7.876730692
39.35870531	7.011261806	32.3474435	117.8187599	1.904048199
35.8775708	1.112373561	43.45725694	34.76519724	126.9239062	-1.632238263
43.1919153	9.976663803	28.93814927		33.21525149	123.4674001	1.741017579
67.28971201	16.7175142	50.5721978	137.5917777	4.960343813
51.32546366	13.63122319	33.25857782	37.69424047	131.3061224	1.78886965
65.7563482	13.20692644	52.54942177	129.3935728	-1.982120038
40.41336566	-1.329412398	30.98276809	41.74277806	119.3356546	-6.173674823
48.80190855	18.01776202	139.1504066	10.44286169
50.08615264	13.43004422	34.45754051	36.65610842	119.1346221	3.089484465
64.26150724	14.49786554	43.90250363	49.76364169	115.3882683	5.951454368
53.68337998	13.44702168	41.58429713	40.23635831	113.9137026	2.737035292
48.99595771	13.11382047	51.87351997	126.3981876	0.535471617
59.16761171	14.56274875	44.60486296	121.0356423	2.830504124
67.80469442	16.55066167	43.25680184	51.25403274	119.6856451	4.867539941
61.73487533	17.11431203	46.89999999	44.6205633	120.9201997	3.087725997
33.04168754	-0.324678459	19.0710746	33.366366	120.3886112	9.354364925
74.56501543	15.72431994	58.61858244	105.417304	0.599247113
44.43070103	14.17426387	32.2434952	131.7176127	-3.604255336
36.42248549	13.87942449	20.24256187	22.543061	126.0768612	0.179717077
51.07983294	14.20993529	35.95122893	36.86989765	115.8037111	6.905089963
34.75673809	2.631739646	29.50438112	32.12499844	127.1398495	-0.460894198
48.90290434	5.587588658	55.49999999	137.1082886	19.85475919
46.23639915	10.0627701	36.17362905	128.0636203	-5.100053328
46.42636614	6.620795049	48.09999999	130.3500956	2.449382401
39.65690201	16.20883944	36.67485694	23.44806258	131.922009	-4.968979881
45.57548229	18.75913544	33.77414297	26.81634684	116.7970069	3.131909921
66.50717865	20.89767207	31.72747138	45.60950658	128.9029049	1.517203356
82.90535054	29.89411893	58.25054221	53.01123161	110.7089577	6.079337831
50.67667667	6.461501271	44.2151754	116.5879699	-0.214710615
89.01487529	26.07598143	69.02125897	62.93889386	111.4810746	6.061508401
54.60031622	21.48897426	29.36021618	118.3433212	-1.471067262
34.38229939	2.062682882	32.39081996	32.31961651	128.3001991	-3.365515555
45.07545026	12.30695118	44.58317718	32.76849908	147.8946372	-8.941709421
47.90356517	13.61668819	34.28687698	117.4490622	-4.245395422
53.93674778	20.72149628	29.22053381	114.365845	-0.421010392
61.44659663	22.6949683	46.17034732	38.75162833	125.6707246	-2.707879517
45.25279209	8.693157364	41.5831264	36.55963472	118.5458418	0.214750167
33.84164075	5.073991409	36.64123294	28.76764934	123.9452436	-0.199249089

DATA 630

Assignment 4: Neural Network

1

. Introduction

Inspired by human neural biology, neural networks (NN) were first envisaged by psychologists and neurologists in the 1940s. NNARE once again experiencing resurgence in data science and machine learning.

In simple terms, an NN is a connected network of nodes or neurons representing input and output, along with appropriate weights associated with connections between neurons. NN are used in many applications such as image and speech recognition, robotics, numerical control, game playing, cancer diagnostics, and more. NN can employ both as supervised and unsupervised learning techniques. There are a number of different NN architectures and algorithms available, one popular algorithm is known as back-propagation.

2.

Steps to Completion

For each study the general procedure is to:

· Review theoretical background based on available resources in the course content

· Select a dataset from the module’s recommended datasets list

· Run an analysis, perform evaluation, and capture the results

· Document your findings and analysis in a data mining analytical report

3. Deliverables

Submit your analysis report by addressing the following critical areas:

· Introduction: give some background and context about the domain of application, provide the rationale for the type of analysis, and state the objective clearly.

· Analysis: describe the data both qualitatively and quantitatively through exploratory analysis, perform necessary preprocessing activities, give some intuition about the algorithm and core parameters, demonstrate the model building steps along with parameter tuning, and explain all your assumptions.

· Result: explain the result and interpret the model output using terms that reflect the application area, perform model evaluation using the appropriate metrics, and leverage visualization.

· Conclusion: summarize your main findings, discuss experimental limitations related to the data and/or implementation of the algorithm, and suggest improvement areas as a potentiation future work.

· Miscellaneous:

· Proof read your report for correct structure, grammar, and spelling

· Follow appropriate APA formatting and provide all references

· Include your R script and extended model outputs in an Appendix section.

The length of the report should be 7-10 pages excluding the title page, appendix and R script.

4. Grading Rubric

Criteria

Weight
(%)

Introduction, objective, rationale.

10

Analysis and Demonstration of Model Development

40

Result Interpretation and Model Evaluation

40

Conclusion, limitations, improvement suggestions

10

Total

100

1