Test - Revision history

Cwillis: /* Three-Layer Precision, Three-Layer Recall, and Three-Layer F1 Score */

2013-08-13T19:57:12Z

‎Three-Layer Precision, Three-Layer Recall, and Three-Layer F1 Score

2013-08-13T19:57:03Z

2013-08-13T19:55:48Z

‎Three-Layer Precision, Three-Layer Recall, and Three-Layer F1 Score

2013-08-13T19:55:20Z

‎Three-Layer Precision, Three-Layer Recall, and Three-Layer F1 Score

2013-08-13T19:55:10Z

‎Three-Layer Precision, Three-Layer Recall, and Three-Layer F1 Score

2013-08-13T19:54:57Z

2013-08-13T19:31:33Z

2013-08-13T19:30:33Z

‎Three-Layer Precision, Three-Layer Recall, and Three-Layer F1 Score

2013-08-13T19:27:30Z

2013-08-13T19:27:21Z

@@ Line 7: / Line 7: @@
 Three-layer precision (<math>P_3</math>), three-layer recall (<math>R_3</math>), and three-layer <math>F_1</math> score (<math>F_3</math>) are defined as follows:
 :<math>
 F_3(\Pi, \Xi) = \frac{2 P_3(\Pi, \Xi) R_3(\Pi, \Xi)}{P_3(\Pi, \Xi) + R_3(\Pi, \Xi)},
 </math>
 where

@@ Line 7: / Line 7: @@
 Three-layer precision (<math>P_3</math>), three-layer recall (<math>R_3</math>), and three-layer <math>F_1</math> score (<math>F_3</math>) are defined as follows:
 :<math>
 F_3(\Pi, \Xi) = \frac{2 P_3(\Pi, \Xi) R_3(\Pi, \Xi)}{P_3(\Pi, \Xi) + R_3(\Pi, \Xi)},
 </math>
 where
 :<math>
 P_3(\Pi, \Xi) &=& \frac{1}{n_\mathcal{Q}} \sum_{j = 1}^{n_\mathcal{Q}}
 </math>

@@ Line 12: / Line 12: @@
 :<math>
 P_3(\Pi, \Xi) &=& \frac{1}{n_\mathcal{Q}} \sum_{j = 1}^{n_\mathcal{Q}}
 </math>

@@ Line 11: / Line 11: @@
 where
 :<math>
 P_3(\Pi, \Xi) &=& \frac{1}{n_\mathcal{Q}} \sum_{j = 1}^{n_\mathcal{Q}}
 \max \{ F_2(\mathcal{P}_i, \mathcal{Q}_j) \mid i = 1,\ldots, n_\mathcal{P} \},\\[.2cm]
@@ Line 25: / Line 24: @@
 P_1(P, Q) &=& |P \cap Q|/|Q|,\\[.2cm]
 R_1(P, Q) &=& |P \cap Q|/|P|.
 </math>

@@ Line 7: / Line 7: @@
 Three-layer precision (<math>P_3</math>), three-layer recall (<math>R_3</math>), and three-layer <math>F_1</math> score (<math>F_3</math>) are defined as follows:
 :<math>
 F_3(\Pi, \Xi) = \frac{2 P_3(\Pi, \Xi) R_3(\Pi, \Xi)}{P_3(\Pi, \Xi) + R_3(\Pi, \Xi)},
 </math>
 where

@@ Line 1: / Line 1: @@
-<math>
+====Three-Layer Precision, Three-Layer Recall, and Three-Layer F1 Score====
 F_3(\Pi, \Xi) = \frac{2 P_3(\Pi, \Xi) R_3(\Pi, \Xi)}{P_3(\Pi, \Xi) + R_3(\Pi, \Xi)},
 </math>

← Older revision		Revision as of 19:27, 13 August 2013
Line 4:		Line 4:

	<math>F_3</math>		<math>F_3</math>
−
−
−	~~Three-layer precision (<math>P_3</math>), three-layer recall (<math>R_3</math>), and three-layer <math>F_1</math> score (<math>F_3</math>) are defined as follows:~~
−	~~:<math>~~
−	~~\begin{equation}~~
−	~~F_3(\Pi, \Xi) = \frac{2 P_3(\Pi, \Xi) R_3(\Pi, \Xi)}{P_3(\Pi, \Xi) + R_3(\Pi, \Xi)},~~
−	~~\end{equation}~~
−	~~</math>~~
−	~~where~~
−	~~:<math>~~

← Older revision		Revision as of 19:27, 13 August 2013
Line 14:		Line 14:
	where		where
	:<math>		:<math>
−	~~\begin{eqnarray}~~
−	~~P_3(\Pi, \Xi) &=& \frac{1}{n_\mathcal{Q}} \sum_{j = 1}^{n_\mathcal{Q}}~~
−	~~\max \{ F_2(\mathcal{P}_i, \mathcal{Q}_j) \mid i = 1,\ldots, n_\mathcal{P} \},\\[.2cm]~~
−	~~R_3(\Pi, \Xi) &=& \frac{1}{n_\mathcal{P}} \sum_{i = 1}^{n_\mathcal{P}}~~
−	~~\max \{ F_2(\mathcal{P}_i, \mathcal{Q}_j) \mid j = 1,\ldots, n_\mathcal{Q} \},\\[.2cm]~~
−	~~F_2(\mathcal{P}, \mathcal{Q}) &=& \frac{2 P_2(\mathcal{P}, \mathcal{Q}) R_2(\mathcal{P}, \mathcal{Q})}~~
−	~~{P_2(\mathcal{P}, \mathcal{Q}) + R_2(\mathcal{P}, \mathcal{Q})},\\[.2cm]~~
−	~~P_2(\mathcal{P}, \mathcal{Q}) &=& \frac{1}{m_Q} \sum_{l = 1}^{m_Q}~~
−	~~\max \{ F_1(P_k, Q_l) \mid k = 1,\ldots, m_P \},\\[.2cm]~~
−	~~R_2(\mathcal{P}, \mathcal{Q}) &=& \frac{1}{m_P} \sum_{k = 1}^{n_P}~~
−	~~\max \{ F_1(P_k, Q_l) \mid l = 1,\ldots, m_Q \},\\[.2cm]~~
−	~~F_1(P, Q) &=& \frac{2 P_1(P, Q) R_1(P, Q)}{P_1(P, Q) + R_1(P, Q)},\\[.2cm]~~
−	~~P_1(P, Q) &=& \|P \cap Q\|/\|Q\|,\\[.2cm]~~
−	~~R_1(P, Q) &=& \|P \cap Q\|/\|P\|.~~
−	~~\end{eqnarray}~~
−	~~</math>~~