evaluation metrics

multiple classifier

outputs = model(data).to(device)
# omitted ...
predicted = torch.argmax(outputs, axis=1)

for true_class, pred_class in zip(target, predicted):
    conf_mat[true_class, pred_class] += 1

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• Accuracy

def Accuracy(conf_mat):
    TP = torch.diagonal(conf_mat)
    return (torch.sum(TP)/torch.sum(conf_mat)).item()

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• Precision ( Positive Predictive Value )

def Precision(conf_mat, class_num):
    TP = torch.diagonal(conf_mat)
    FP = torch.sum(conf_mat, dim=0) - TP
    
    precision = 0.0
    for i in range(class_num):
        precision += TP[i] / (TP[i] + FP[i])
    
    return precision.item()/class_num

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• Recall ( True Positive Rate )

def Recall(conf_mat, class_num):
    TP = torch.diagonal(conf_mat)
    FN = torch.sum(conf_mat, dim=1) - TP
    
    recall = 0.0
    for i in range (class_num):
        recall += TP[i] / (TP[i] + FN[i])
    
    return recall.item()/class_num

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• F1-Score

$({\rm F1-score}) = 2 \times \frac{1}{\frac{1}{\rm Precision} + \frac{1}{\rm Recall}} = 2 \times \frac{\rm Precision \times Recall}{\rm Precision + Recall}$

기하학적으로 이해해 보자면, 단순 평균 보다는 작은 길이 쪽으로 치우치게 되고, 따라서 큰 쪽과 작은 쪽의 사이의 값을 가진 평균을 사용하게 된다. 조화평균을 이용하므로써 산술 평균에서의 (큰 쪽의) bias 가 줄어들게 된다.

def F1Score(conf_mat, class_num):
    TP = torch.diagonal(conf_mat)
    FP = torch.sum(conf_mat, dim=0) - TP
    FN = torch.sum(conf_mat, dim=1) - TP
    
    f1score = 0.0
    for i in range (class_num):
        precision = TP[i] / (TP[i] + FP[i])
        recall = TP[i] / (TP[i] + FN[i])
        f1score += 2 * (precision * recall) / (precision + recall)
    
    return f1score.item()/class_num