In [ ]:

predictions = [0, 1, 0, 2, 1, 2, 0]
labels = [1, 1, 0, 0, 1, 2, 1]

n_correct = 0

for pred_idx in range(len(predictions)):
    if predictions[pred_idx] == labels[pred_idx]:
        n_correct += 1

accuracy = n_correct / len(predictions)
print(f'accuracy[%] = {accuracy*100:.2f}%')

accuracy[%] = 57.14%

Exercise.1 - 78: Confusion Vector 구하기 (confusion matrix)¶

Exercise.1 - 77까지 배운 내용을 이용하여 confusion vector를 구하는 방법을 배워봅니다.
모델의 성능평가 지표
https://wikidocs.net/194087

Confusion matrix는 다음과 같은 네 가지 항목으로 구성됩니다.

True Positive (TP): 실제값이 Positive이고 모델이 예측한 값이 Positive인 경우

False Positive (FP): 실제값이 Negative이고 모델이 예측한 값이 Positive인 경우

False Negative (FN): 실제값이 Positive이고 모델이 예측한 값이 Negative인 경우

True Negative (TN): 실제값이 Negative이고 모델이 예측한 값이 Negative인 경우

Confusion Matrix - Accuracy (정확도)¶

Accuracy = (TP + TN) / (TP + TN + FP + FN)

모델이 예측한 결과와 실제 결과가 일치한 비율

Confusion Matrix - Precision (정밀도)¶

Precision = TP / (TP + FP)

모델이 참으로 예측한 모든 데이터 중 실제로 참인 데이터의 비율

Confusion Matrix - Recall (재현율)¶

Recal = TP / (TP + FN)

실제로 양성인 것 중에서 모델이 양성으로 예측한 비율

In [ ]:

predictions = [0, 1, 0, 2, 1, 2, 0]
labels = [1, 1, 0, 0, 1, 2, 1]

n_classes = -1
for label in labels:
    if n_classes == None or label > n_classes:
        n_classes = label
n_classes += 1

class_cnts, correct_cnt, confusion_vec = [], [], []
for _ in range(n_classes):
    class_cnts.append(0)
    correct_cnt.append(0)
    confusion_vec.append(None)

for pred_idx in range(len(predictions)):
    pred = predictions[pred_idx]
    label = labels[pred_idx]
    print(f'pred, label: {pred}, {label}')
    class_cnts[label] += 1
    if pred == label:
        print('--- correct! ---')
        correct_cnt[label] += 1
    print(f'class_cnts, correct_cnt: {class_cnts}, {correct_cnt}')
for class_idx in range(n_classes):
    confusion_vec[class_idx] = correct_cnt[class_idx] / class_cnts[class_idx]

print(f'confusion vector: {confusion_vec}')

pred, label: 0, 1
class_cnts, correct_cnt: [0, 1, 0], [0, 0, 0]
pred, label: 1, 1
--- correct! ---
class_cnts, correct_cnt: [0, 2, 0], [0, 1, 0]
pred, label: 0, 0
--- correct! ---
class_cnts, correct_cnt: [1, 2, 0], [1, 1, 0]
pred, label: 2, 0
class_cnts, correct_cnt: [2, 2, 0], [1, 1, 0]
pred, label: 1, 1
--- correct! ---
class_cnts, correct_cnt: [2, 3, 0], [1, 2, 0]
pred, label: 2, 2
--- correct! ---
class_cnts, correct_cnt: [2, 3, 1], [1, 2, 1]
pred, label: 0, 1
class_cnts, correct_cnt: [2, 4, 1], [1, 2, 1]
confusion vector: [0.5, 0.5, 1.0]

Exercise.1 - 79: Histogram 구하기¶

For loop와 if statement를 이용하여 histogram을 구하는 방법을 배워봅니다.

In [ ]:

scores = [50, 20, 30, 40, 10, 50, 70, 80, 90, 20, 30,]
cutoffs = [0, 2, 40, 60, 80,]
histogram = [0, 0, 0, 0, 0]

for score in scores:
    if score > cutoffs[4]:
        histogram[4] += 1
    elif score > cutoffs[3]:
        histogram[3] += 1
    elif score > cutoffs[2]:
        histogram[2] += 1
    elif score > cutoffs[1]:
        histogram[1] += 1
    else:
        pass

print(f'histogram of the scores: {histogram}')

histogram of the scores: [0, 6, 2, 2, 1]

Exercise.1 - 80: 절댓값 구하기¶

For loop와 if statement를 이용하여 원소들의 절댓값을 가진 list를 만드는 방법에 대해 연습해봅니다.

In [ ]:

numbers = [-2, 2, -1, 3, -4 ,9]
abs_numbers = []

for num in numbers:
    if num < 0:
        abs_numbers.append(-num) # abs(num)
    else:
        abs_numbers.append(num)

print(f'absolute numbers: {abs_numbers}')

absolute numbers: [2, 2, 1, 3, 4, 9]

Exercise.1 - 81: Manhattan Distance¶

원소들의 절댓값을 가진 list를 만드는 방법을 이용하여 Manhattan distance를 계산하는 방법에 대해 배워봅니다.

In [ ]:

v1 = [1, 3, 5, 2, 1, 5, 2]
v2 = [2, 3, 1, 5, 2, 1, 3]

m_distance = 0
for dim_idx in range(len(v1)):
    sub = v1[dim_idx] - v2[dim_idx]
    if sub < 0:
        m_distance += -sub # abs(sub)
    else:
        m_distance += sub

print(f'Mangattan distance = {m_distance}')

Mangattan distance = 14

Exercise.1 - 82: Nested List 만들기 & 원소 접근하기¶

2차원 정보를 List로 만드는 방법과 각 원소에 접근하면 나오는 결과를 연습해봅시다.

In [ ]:

scores = [[10, 20, 30,], [50, 60, 70]]

print(scores)
print(scores[0])
print(scores[1])
print(scores[0][0], scores[0][1], scores[0][2])
print(scores[1][0], scores[1][1], scores[1][2])

[[10, 20, 30], [50, 60, 70]]
[10, 20, 30]
[50, 60, 70]
10 20 30
50 60 70

Exercise.1 - 83: Nested List 원소 접근하기(2)¶

For loop을 통해 2차원 List의 원소에 접근하는 방법을 연습해봅니다.

In [ ]:

scores = [[10, 20, 30], [50, 60, 70]]

for student_scores in scores:
    print(student_scores)
    for score in student_scores:
        print(score)

[10, 20, 30]
10
20
30
[50, 60, 70]
50
60
70

Exercise.1 - 84: 학생별 평균점수 구하기¶

For loop을 통해 row-wise mean을 구하는 방법을 연습해봅니다.

In [ ]:

scores = [[10, 15, 20], [20, 25, 30], [30, 35, 40], [40, 45, 50]]

n_class = len(scores[0])
student_score_mean = []

for student_scores in scores:
    student_score_sum = 0
    for score in student_scores:
        student_score_sum += score
    student_score_mean.append(student_score_sum / n_class)

print(student_score_mean)

[15.0, 25.0, 35.0, 45.0]

Exercise.1 - 85: 과목별 평균 점수 구하기¶

For loop을 통해 column-wise mean 을 구하는 방법을 연습해봅니다.

In [ ]:

scores = [[10, 15, 20], [20, 25, 30], [30, 35, 40], [40, 45, 50]]

n_student = len(scores)
n_class = len(scores[0])
class_score_mean = []

for idx_class in range(n_class):
    class_score_sum = 0
    for idx_student in range(n_student):
        class_score_sum += scores[idx_student][idx_class]
    print(f'class score sum: {class_score_sum}')
    class_score_mean.append(class_score_sum/n_student)

print(f'class score mean: {class_score_mean}')

class score sum: 100
class score sum: 120
class score sum: 140
class score mean: [25.0, 30.0, 35.0]

Exercise.1 - 86: Mean Substraction¶

In [ ]:

scores = [[10, 15, 20], [20, 25, 30], [30, 35, 40], [40, 45, 50]]

n_student = len(scores)
n_class = len(scores[0])
class_score_mean = []

for idx_class in range(n_class):
    class_score_sum = 0
    for idx_student in range(n_student):
        class_score_sum += scores[idx_student][idx_class]
    class_score_mean.append(class_score_sum/n_student)
    print(f'{idx_class+1} class score sum: {class_score_sum}')
    print(f'{idx_class+1} class score mean: {class_score_mean[idx_class]}')
    
print(f'class score mean: {class_score_mean}')

print('--- Mean Substraction ---')
for idx_class in range(n_class):
    for idx_student in range(n_student):
        scores[idx_student][idx_class] -= class_score_mean[idx_class]
print(f'mean substraction scores: {scores}')


for idx_class in range(n_class):
    class_score_sum = 0
    for idx_student in range(n_student):
        class_score_sum += scores[idx_student][idx_class]
    class_score_mean[idx_class] = class_score_sum/n_student
    print(f'{idx_class+1} class score sum: {class_score_sum}')
    print(f'{idx_class+1} class score mean: {class_score_mean[idx_class]}')


print(f'class score mean: {class_score_mean}')

1 class score sum: 100
1 class score mean: 25.0
2 class score sum: 120
2 class score mean: 30.0
3 class score sum: 140
3 class score mean: 35.0
class score mean: [25.0, 30.0, 35.0]
--- Mean Substraction ---
mean substraction scores: [[-15.0, -15.0, -15.0], [-5.0, -5.0, -5.0], [5.0, 5.0, 5.0], [15.0, 15.0, 15.0]]
1 class score sum: 0.0
1 class score mean: 0.0
2 class score sum: 0.0
2 class score mean: 0.0
3 class score sum: 0.0
3 class score mean: 0.0
class score mean: [0.0, 0.0, 0.0]

Exercise.1 - 87: Variances Standard Deviation¶

분산 표준편차

In [ ]:

scores = [[10, 15, 20], [20, 25, 30], [30, 35, 40], [40, 45, 50]]
n_student = len(scores)
n_class = len(scores[0])


print('--- mean of square ---') # 제평
mean_of_square = []
for idx_class in range(n_class):
    sum_of_square = 0
    for idx_student in range(n_student):
        sum_of_square += scores[idx_student][idx_class] ** 2
    mean_of_square.append(sum_of_square / n_student)
    print(f'{idx_class+1} class mean of square: {mean_of_square[idx_class]}')

print('--- square of mean ---') # 평제
square_of_mean = []
for idx_class in range(n_class):
    sum_of_class = 0
    for idx_student in range(n_student):
        sum_of_class += scores[idx_student][idx_class]
    square_of_mean.append((sum_of_class / n_student) ** 2)
    print(f'{idx_class+1} class square of mean: {square_of_mean[idx_class]}')

print('--- variance & std ---') # 제평 - 평제
variance_of_class = []
std_of_class = []
for idx_class in range(n_class):
    variance_of_class.append(mean_of_square[idx_class] - square_of_mean[idx_class])
    std_of_class.append(variance_of_class[idx_class] ** 0.5)
    print(f'{idx_class+1} class variance: {variance_of_class[idx_class]}')
    print(f'{idx_class+1} class standard deviation: {std_of_class[idx_class]}')

--- mean of square ---
1 class mean of square: 750.0
2 class mean of square: 1025.0
3 class mean of square: 1350.0
--- square of mean ---
1 class square of mean: 625.0
2 class square of mean: 900.0
3 class square of mean: 1225.0
--- variance & std ---
1 class variance: 125.0
1 class standard deviation: 11.180339887498949
2 class variance: 125.0
2 class standard deviation: 11.180339887498949
3 class variance: 125.0
3 class standard deviation: 11.180339887498949

Exercise.1 - 88: Standardization¶

표준화

In [ ]:

scores = [[10, 15, 20], [20, 25, 30], [30, 35, 40], [40, 45, 50]]

n_student = len(scores)
n_class = len(scores[0])

print('--- mean of square ---') # 제평
mean_of_square = []
for idx_class in range(n_class):
    sum_of_square = 0
    for idx_student in range(n_student):
        sum_of_square += scores[idx_student][idx_class] ** 2
    mean_of_square.append(sum_of_square / n_student)
    print(f'{idx_class+1} class mean of square: {mean_of_square[idx_class]}')

print('--- square of mean ---') # 평제
square_of_mean = []
for idx_class in range(n_class):
    score_of_class = 0
    for idx_student in range(n_student):
        score_of_class += scores[idx_student][idx_class]
    square_of_mean.append((score_of_class / n_student) ** 2)
    print(f'{idx_class+1} class square of mean: {square_of_mean[idx_class]}')

print('--- variance & std ---') # 제평 - 평제
variance_of_class = []
std_of_class = []
for idx_class in range(n_class):
    variance_of_class.append(mean_of_square[idx_class] - square_of_mean[idx_class])
    std_of_class.append(variance_of_class[idx_class] ** 0.5)
    print(f'{idx_class+1} class variance: {variance_of_class[idx_class]}')
    print(f'{idx_class+1} class standard deviation: {std_of_class[idx_class]}')

print('--- Standardization ---')
for idx_class in range(n_class):
    for idx_student in range(n_student):
        scores[idx_student][idx_class] = (scores[idx_student][idx_class] \
                                          - square_of_mean[idx_class]**0.5) / \
                                            std_of_class[idx_class]
print(f'Standardization score: {scores}')

print('--- mean of square ---') # 제평
mean_of_square = []
for idx_class in range(n_class):
    sum_of_square = 0
    for idx_student in range(n_student):
        sum_of_square += scores[idx_student][idx_class] ** 2
    mean_of_square.append(sum_of_square / n_student)
    print(f'{idx_class+1} class mean of square: {mean_of_square[idx_class]}')

print('--- square of mean ---') # 평제
square_of_mean = []
for idx_class in range(n_class):
    score_of_class = 0
    for idx_student in range(n_student):
        score_of_class += scores[idx_student][idx_class]
    square_of_mean.append((score_of_class / n_student) ** 2)
    print(f'{idx_class+1} class square of mean: {square_of_mean[idx_class]}')

print('--- variance & std ---') # 제평 - 평제
variance_of_class = []
std_of_class = []
for idx_class in range(n_class):
    variance_of_class.append(mean_of_square[idx_class] - square_of_mean[idx_class])
    std_of_class.append(variance_of_class[idx_class] ** 0.5)
    print(f'{idx_class+1} class variance: {variance_of_class[idx_class]}')
    print(f'{idx_class+1} class standard deviation: {std_of_class[idx_class]}')

--- mean of square ---
1 class mean of square: 750.0
2 class mean of square: 1025.0
3 class mean of square: 1350.0
--- square of mean ---
1 class square of mean: 625.0
2 class square of mean: 900.0
3 class square of mean: 1225.0
--- variance & std ---
1 class variance: 125.0
1 class standard deviation: 11.180339887498949
2 class variance: 125.0
2 class standard deviation: 11.180339887498949
3 class variance: 125.0
3 class standard deviation: 11.180339887498949
--- Standardization ---
Standardization score: [[-1.3416407864998738, -1.3416407864998738, -1.3416407864998738], [-0.4472135954999579, -0.4472135954999579, -0.4472135954999579], [0.4472135954999579, 0.4472135954999579, 0.4472135954999579], [1.3416407864998738, 1.3416407864998738, 1.3416407864998738]]
--- mean of square ---
1 class mean of square: 1.0
2 class mean of square: 1.0
3 class mean of square: 1.0
--- square of mean ---
1 class square of mean: 0.0
2 class square of mean: 0.0
3 class square of mean: 0.0
--- variance & std ---
1 class variance: 1.0
1 class standard deviation: 1.0
2 class variance: 1.0
2 class standard deviation: 1.0
3 class variance: 1.0
3 class standard deviation: 1.0

In [ ]:

import numpy as np
scores = [[10, 15, 20], [20, 25, 30], [30, 35, 40], [40, 45, 50]]
print(f'mean by class: {np.mean(scores, axis=0)}')
print(f'variance by class: {np.var(scores, axis=0)}')
print(f'std by class: {np.std(scores, axis=0)}')

scores = (np.array(scores) - np.mean(scores, axis=0)) / np.std(scores, axis=0)
print(f'Standardization: \n{scores}')

print(f'mean by class: {np.mean(scores, axis=0)}')
print(f'variance by class: {np.var(scores, axis=0)}')
print(f'std by class: {np.std(scores, axis=0)}')

mean by class: [25. 30. 35.]
variance by class: [125. 125. 125.]
std by class: [11.18033989 11.18033989 11.18033989]
Standardization: 
[[-1.34164079 -1.34164079 -1.34164079]
 [-0.4472136  -0.4472136  -0.4472136 ]
 [ 0.4472136   0.4472136   0.4472136 ]
 [ 1.34164079  1.34164079  1.34164079]]
mean by class: [0. 0. 0.]
variance by class: [1. 1. 1.]
std by class: [1. 1. 1.]

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현재글[핀테커스] 230921 python 수학 실습

For Engineering

[핀테커스] 230921 python 수학 실습

Exercise.1 - 77: Accuracy 구하기¶

Exercise.1 - 78: Confusion Vector 구하기 (confusion matrix)¶

Confusion Matrix - Accuracy (정확도)¶

Confusion Matrix - Precision (정밀도)¶

Confusion Matrix - Recall (재현율)¶

Exercise.1 - 79: Histogram 구하기¶

Exercise.1 - 80: 절댓값 구하기¶

Exercise.1 - 81: Manhattan Distance¶

Exercise.1 - 82: Nested List 만들기 & 원소 접근하기¶

Exercise.1 - 83: Nested List 원소 접근하기(2)¶

Exercise.1 - 84: 학생별 평균점수 구하기¶

Exercise.1 - 85: 과목별 평균 점수 구하기¶

Exercise.1 - 86: Mean Substraction¶

Exercise.1 - 87: Variances Standard Deviation¶

Exercise.1 - 88: Standardization¶

'새싹 > TIL' 카테고리의 다른 글

'새싹/TIL'의 다른글

티스토리툴바

[핀테커스] 230921 python 수학 실습

Exercise.1 - 77: Accuracy 구하기¶

Exercise.1 - 78: Confusion Vector 구하기 (confusion matrix)¶

Confusion Matrix - Accuracy (정확도)¶

Confusion Matrix - Precision (정밀도)¶

Confusion Matrix - Recall (재현율)¶

Exercise.1 - 79: Histogram 구하기¶

Exercise.1 - 80: 절댓값 구하기¶

Exercise.1 - 81: Manhattan Distance¶

Exercise.1 - 82: Nested List 만들기 & 원소 접근하기¶

Exercise.1 - 83: Nested List 원소 접근하기(2)¶

Exercise.1 - 84: 학생별 평균점수 구하기¶

Exercise.1 - 85: 과목별 평균 점수 구하기¶

Exercise.1 - 86: Mean Substraction¶

Exercise.1 - 87: Variances Standard Deviation¶

Exercise.1 - 88: Standardization¶

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