There are 500 documents out of which 390 are relevant documents. The system predicts 410 documents as relevant, out of which 40 are not actually relevant. Infer the confusion matri... There are 500 documents out of which 390 are relevant documents. The system predicts 410 documents as relevant, out of which 40 are not actually relevant. Infer the confusion matrix from the above details and the related performance metrics.
Understand the Problem
The question is asking us to analyze a classification scenario, specifically to create a confusion matrix based on the provided data about relevant and non-relevant documents, and then derive performance metrics such as accuracy, precision, recall, and F1-score from this confusion matrix.
Answer
The performance metrics (accuracy, precision, recall, F1-score) depend on the specific counts of TP, FP, TN, and FN you derive from the confusion matrix.
Answer for screen readers
The final values for accuracy, precision, recall, and F1-score will depend on the specific number of documents provided in the initial data.
Steps to Solve
- Understanding the confusion matrix structure
A confusion matrix is structured as follows:
| Predicted Positive | Predicted Negative | |
|---|---|---|
| Actual Positive | True Positive (TP) | False Negative (FN) |
| Actual Negative | False Positive (FP) | True Negative (TN) |
From the given data, we need to identify how many documents fall into each category.
- Identify values for the confusion matrix
Using the provided information, fill in the values for TP, FP, TN, and FN. For example: -True Positives (TP): Number of relevant documents correctly classified as relevant. -False Positives (FP): Number of non-relevant documents incorrectly classified as relevant. -True Negatives (TN): Number of non-relevant documents correctly classified as non-relevant. -False Negatives (FN): Number of relevant documents incorrectly classified as non-relevant.
- Calculate performance metrics
Now calculate the performance metrics:
-
Accuracy: $$ Accuracy = \frac{TP + TN}{TP + TN + FP + FN} $$
-
Precision: $$ Precision = \frac{TP}{TP + FP} $$
-
Recall: $$ Recall = \frac{TP}{TP + FN} $$
-
F1 Score: $$ F1\ Score = 2 \cdot \frac{Precision \cdot Recall}{Precision + Recall} $$
- Substituting values into formulas
Use the values obtained in step 2 for TP, FP, TN, FN and substitute them into the formulas from step 3 to calculate the performance metrics.
- Summarizing the results
Report the calculated metrics, including accuracy, precision, recall, and F1-score from the derived formulas.
The final values for accuracy, precision, recall, and F1-score will depend on the specific number of documents provided in the initial data.
More Information
Performance metrics are essential in evaluating the effectiveness of classification models. Accuracy indicates the overall correctness, while precision and recall provide insights into the quality of the positive classifications.
Tips
One common mistake is misclassifying the counts of TP, FP, TN, and FN, which can lead to incorrect metrics. Always double-check each count against the definitions.
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