From 079e760e6b30482b7f088eae2fc7048259f77053 Mon Sep 17 00:00:00 2001 From: Kaka Date: Tue, 4 Jun 2024 10:06:09 +0800 Subject: [PATCH] feat(metrics): update the introduction of metrics 1. update the metric of classification 2. update the metric of object detection 3. add the metric of segmentation --- content/posts/ML/Metrics/classification.md | 141 ++++++++++++--- .../posts/ML/Metrics/images/bounding_box.png | Bin 0 -> 142906 bytes .../ML/Metrics/images/confusion_matrix.png | Bin 31536 -> 99535 bytes .../Metrics/images/confusion_matrix_seg.png | Bin 0 -> 192061 bytes .../Metrics/images/confusion_matrix_seg_2.png | Bin 0 -> 73923 bytes .../Metrics/images/confusion_matrix_seg_3.png | Bin 0 -> 267707 bytes content/posts/ML/Metrics/images/iou_2.png | Bin 0 -> 90302 bytes content/posts/ML/Metrics/images/iou_seg_1.png | Bin 0 -> 223788 bytes content/posts/ML/Metrics/images/iou_seg_2.png | Bin 0 -> 289410 bytes content/posts/ML/Metrics/images/pr_roc.png | Bin 0 -> 9077 bytes 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100644 static/images/ml/metrics/images/segmentation.png delete mode 100644 static/images/ml/metrics/object_detection/confusion_matrix.png delete mode 100644 static/images/ml/metrics/object_detection/precision_recall_curves.png diff --git a/content/posts/ML/Metrics/classification.md b/content/posts/ML/Metrics/classification.md index d9e84740..57eb6e36 100644 --- a/content/posts/ML/Metrics/classification.md +++ b/content/posts/ML/Metrics/classification.md @@ -8,25 +8,36 @@ categories: [ML/DL] # 分類指標 (Classification Metrics) +> 2024/6/4 updated! + ## Confuion Matrix (混淆矩陣) +分類器的目的在對樣本進行分類,例如,將樣本中的男女進行區分。不過,在預測分類的過程中,會有預測正確與預測錯誤兩種結果。因此,將分類狀況與預測結果進行排列組合,即可得到以下四種情境: + + | | Predict Positive | Predict Negative | | :--: | :--------: | :---------: | | Actual Positive | True Positive (TP) | False Negative (FN) | | Actual Negative | False Positive (FP) | True Negative (TN) | +## Accuracy, Precision, and Recall + +> Recall 及 Precision 都適合用於`類別不平均的資料集` +> +> 因為在算式中並沒有考慮 True Negatives (TN),只專注於正確判斷正樣本,因此,就算資料集中負樣本的數目遠大於正樣本,Recall 及 Precision 仍是有效的參考指標 -## Recall and Precision +### Accuracy (準確率) + +所有預測為 True 的樣本佔總識別樣本的比例。 + +- 缺點: 類別比例不均時會影響評價效果 -### Recall (召回率) ``` -Recall = TP / (TP + FN) +Acc = TP + TN / (TP + TN + FP + FN) ``` -表示在所有正樣本中,能夠預測到多少個正樣本。 (`針對原來的樣本`) - -### Precision (準確率) +### Precision (精確率) ``` Precision = TP / (TP + FP) @@ -34,63 +45,143 @@ Precision = TP / (TP + FP) 為在所有預測為正樣本中,有多少實際為正樣本。 (`針對預測結果`) +### Recall (召回率; TPR; Sensitive) + +> 就是 True Positive Rate (TPR), 又稱為敏感度 (Sensitive) + +``` +Recall = TP / (TP + FN) +``` + +表示在所有正樣本中,能夠預測到多少個正樣本。 (`針對原來的樣本`) + ### 應用場景 #### 1. 當今天你加裝了一個人臉辨識的門鎖時,哪個指標比較重要呢? ``` -準確率比較重要,因為你不會希望別人的臉可以打開你家的鎖,判斷成正樣本就一定要是對的 +Precision(精確率)比較重要,因為你不會希望別人的臉可以打開你家的鎖,判斷成正樣本就一定要是對的 -召回率低的話就只是常常無法判斷出你的臉,無法開門而已 +Recall(召回率)低的話就只是常常無法判斷出你的臉,無法開門而已 ``` #### 2. 廣告投放系統 ``` -Recall比較重要,因為重視潛在客戶,我全都要 (實際正向客戶中我預測到多少個) +Recall 比較重要,因為重視潛在客戶,我全都要 (實際正向客戶中我預測到多少個) -準確率就沒那麼重要,不在意預測正向(廣告投出)答對多少 +Precision 就沒那麼重要,不在意預測正向(廣告投出)答對多少 ``` ### 小結 -1. Precision高,Recall低的模型 +通常在分類問題中,採用 `Top N` 返回結果的 Precision 和 Recall 來衡量模型的性能,表示為 `Precision@N` 和 `Recall@N`。 + +1. `Precision 高,Recall 低的模型` `謹慎的模型`, 雖然常常無法抓到,但只要有預測到的幾乎都是正確的 -2. Recall高,Precision低的模型 +2. `Recall 高,Precision 低的模型` `寬鬆的模型`, 雖然有可能預測錯誤,但只要是該預測的都可以預測到 -但魚與熊掌不可兼得,如果我們同時想要兼顧兩個指標怎辦呢?這時候就要看 `F1-score`了。 +Precision 和 Recall 是相反的指標,當分類的 threshold 越高時,Presicion 提高但 Recall 降低,反之則 Precision 降低但 Recall 升高。魚與熊掌不可兼得,如果我們同時想要兼顧兩個指標怎辦呢?這時候就要看 `F1-score`了。 ## F1-score (F1-Mesure) -他是`F-score`的一個特例,當`beta=1`時就是`F1-score`。 +> 他是`F-score`的一個特例,當`beta=1`時就是`F1-score`。 + +`F1-score` 是 recall 和 precision 的 加權調和平均數,顧名思義就是為了調和 recall 和 precision 之間增減反向的矛盾,對 recall 和 precision 進行加權調和,公式如下: + +$$ F1 = 2 * \frac{Precision * Recall}{Precision + Recall}$$ + + +`F1-score`最理想的數值是`趨近於1`,就是讓 precision 和 recall 都有很高的值。假設兩者皆為1,則`F1-score = 1 (100%)`,代表該演算法有著最佳的精確度 + +### F-score (F-Mesure) + +公式如下: + +$$ F = \frac{(1 + \beta^2) * Precision * Recall}{(\beta^2 * Precision) + Recall}$$ -`F1-score`最理想的數值是`趨近於1`,就是讓precision和recall都有很高的值。 + +1. `beta=0`: 就是 Precision +3. `beta=1`: 就是 F1-score +2. `beta無限大`: 就是 Recall + +所以當我想多看重一點 Precision 時,beta 就可以選小一點,當我想多看重 Recall 時,beta就可以選大一點。 + +## PR curve and ROC curve + +- `PR curve`: 適合`類別不均`的情況 + + 因為是 Precision 與 Recall 並沒有考慮 TN,只專注於正確判斷正樣本,因此,就算資料集中負樣本的數目遠大於正樣本,Recall 及 Precision 仍是有效的參考指標 + +- `ROC curve`: 適合`類別平均`的情況 + +### PR Curve (Precision-Recall Curves, 精確召回曲線) + +PR 曲線以 Recall 為 X 軸, Precision 為 Y 軸,每一個點代表設定不同的門檻值所得到的不同的 Recall 及 Precision,最後繪製成一條曲線。如下所示: + +![](images/pr_roc_1.png) +![](/my-blog/images/ml/metrics/images/pr_roc_1.png) + + +一般來說,Precision 與 Recall 越高,代表模型的效益越高,也就是 `PR 曲線越往右上方靠近越好`。 + +### ROC Curve (Receiver Operator Characteristic Curve, 接收器工作特性曲線) + +ROC 曲線以 FPR (False Positive Rate) 為 X 軸, TPR (True Positive Rate) 為 Y 軸,每一個點代表設定不同的門檻值所得到的不同的 FPR 及 TPR ,最後繪製成一條曲。如下所示: + +![](images/pr_roc_2.png) +![](/my-blog/images/ml/metrics/images/pr_roc_2.png) + +ROC 曲線呈現分類器在`效益(真陽性率)`與`成本(偽陽性率)`之間的相對關係。其中點(0,1)代表完美分類,代表效益最大,成本最低。所以`ROC 曲線越靠近左上方越好`。 + +#### FPR (False Positive Rate, 偽陽性率) + +FPR 表示成 `1-特異度`。 + + - 特異度(Specificity): 代表正確判斷負樣本的機率。 + + ``` + 特異度越高、FPR 越低,模型越能夠正確判斷負樣本、表現越好 + ``` + +公式如下: ``` -F1-score = 2 * ((Precision * Recall) / (Precision + Recall)) +Specificity = TN / (TN + FP) + +FPR = 1 - Specificity + = FP / (TN + FP) ``` -$$ F1 = 2 * \frac{Precision * Recall}{Precision + Recall}$$ +#### TPR (True Positive Rate, 真陽性率) +TPR 又稱為`敏感度(Sensitivity)`,它也是我們熟知的`召回率(Recall)`,也就是正確判斷出正樣本的機率。 -假設兩者皆為1,則`F1-score = 1 (100%)`,代表該演算法有著最佳的精確度 +``` +故 TPR 越高則模型越能夠正確判斷正樣本、表現越好 +``` -### F-score (F-Mesure) +公式如下: ``` -F-score = ((1 + beta)^2 * Precision * Recall / (beta^2 * Precision) + Recall) +TPR = Sensitivity = Recall = TP / (TP + FN) ``` -$$ F = \frac{(1 + \beta^2) * Precision * Recall}{(\beta^2 * Precision) + Recall}$$ +## AUC (Area under curve, 曲線下面積) + +AUC(Area Under Curve)代表在ROC曲線下的面積,能表示分類器預測能力的一項常用的統計值。前面提到,ROC曲線越靠近左上方越好,因此,ROC曲線下的面積越大越好,代表模型的效益越高。 +- AUC = 1: 是完美分類器。絕大多數預測的場合,不存在完美分類器。 +- 0.5 < AUC < 1: 優於隨機猜測。這個分類器妥善設定閾值的話,能有預測價值。 +- AUC = 0.5: 跟隨機猜測一樣(例:丟銅板),模型沒有預測價值。 +- AUC < 0.5: 比隨機猜測還差;但只要進行反預測,就優於隨機猜測。 -1. `beta=0`: 就是Precision -3. `beta=1`: 就是F1-score -2. `beta無限大`: 就是Recall +## Reference -所以當我想多看重一點Precision時,beta就可以選小一點,當我想多看重Recall時,beta就可以選大一點。 +- [行銷資料科學, 分類器評估方法 — ROC曲線、AUC、Accuracy、PR曲線](https://medium.com/marketingdatascience/%E5%88%86%E9%A1%9E%E5%99%A8%E8%A9%95%E4%BC%B0%E6%96%B9%E6%B3%95-roc%E6%9B%B2%E7%B7%9A-auc-accuracy-pr%E6%9B%B2%E7%B7%9A-d3a39977022c) +- [深入介紹及比較ROC曲線及PR曲線](https://medium.com/nlp-tsupei/roc-pr-%E6%9B%B2%E7%B7%9A-f3faa2231b8c) diff --git a/content/posts/ML/Metrics/images/bounding_box.png b/content/posts/ML/Metrics/images/bounding_box.png new file mode 100644 index 0000000000000000000000000000000000000000..f683940996373549b3b2802d50fc3b95bc848492 GIT binary patch literal 142906 zcmeFYWmuH$zcwm@igZc0NJ~qHfFNBW-6`E&Dh?qHQW67FA_4-^3`k2OUBgIAj&#F& z4X*!Q>%;qP?fq@f!E?X^_kG1L&R?BIYN$QO#iGQzb?X+cqQWz+TemO}w{D>qVcrG5 zA*lZi1>Z0{WE8bA!6y*YDgyjJg{PdJ=L;7bPaku4>sz+YE>6~uJuKa=t(`qyxp*Sc zTO@DYqQ9m1Oj_GFa|?dzVYrr+bH2uT3-8u#3?D5lr0*yjh8XuBu?r5&?ncs!U*~N_n?H}MFcj9()~_%NWLCD+dC4*$0loWrk;0}8wsmDHG)5f)gG2;o?^ 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