Evaluation and Selection of Classifiers – Lecture Notes

harmonic mean of precision and recall, \[F = \frac{2 \cdot \text{precision} \cdot \text{recall}}{\hphantom{2\cdot {}}\text{precision} \! +\! \text{recall}} = 2\Big/\left(\frac{1}{\text{precision}}+\frac{1} [...] \(f(x)\) \(C_1\) \(C_2\) \(C_3\) \(C_4\) \(\sum _j \mathit{c}_{ij}\) \(C_1\) \(\mathit{c}_{11}\) \(\mathit{c}_{12}\) \(\mathit{c}_{13}\) \(\mathit{c}_{14}\) \(\sum _j \mathit{c}_{1j}\) \(C_2\) \(\mathit{c}_{21}\) [...] \mathit{c}_{i1}\) \(\sum _i \mathit{c}_{i2}\) \(\sum _i \mathit{c}_{i3}\) \(\sum _i \mathit{c}_{i4}\) \(\sum _{i,j} \mathit{c}_{ij}\) \(y\) \  \(f(x)\) \(C_1\) \(C_2\) \(C_3\) \(C_4\) \(\sum _j \mathit{c}_{ij}\) …

Evaluation and Selection of Classifiers – Lecture Notes

harmonic mean of precision and recall, \[F = \frac{2 \cdot \text{precision} \cdot \text{recall}}{\hphantom{2\cdot {}}\text{precision} \! +\! \text{recall}} = 2\Big/\left(\frac{1}{\text{precision}}+\frac{1} [...] \(f(x)\) \(C_1\) \(C_2\) \(C_3\) \(C_4\) \(\sum _j \mathit{c}_{ij}\) \(C_1\) \(\mathit{c}_{11}\) \(\mathit{c}_{12}\) \(\mathit{c}_{13}\) \(\mathit{c}_{14}\) \(\sum _j \mathit{c}_{1j}\) \(C_2\) \(\mathit{c}_{21}\) [...] \mathit{c}_{i1}\) \(\sum _i \mathit{c}_{i2}\) \(\sum _i \mathit{c}_{i3}\) \(\sum _i \mathit{c}_{i4}\) \(\sum _{i,j} \mathit{c}_{ij}\) \(y\) \  \(f(x)\) \(C_1\) \(C_2\) \(C_3\) \(C_4\) \(\sum _j \mathit{c}_{ij}\) …

returns a new partitioning p′ satisfying: 1. ∀h1 ∈ H , p′(h) 6= p′(h1), and 2. ∀h1, h2 ∈ S, p(h1) 6= p(h2)⇒ p′(h1) 6= p′(h2). (In practice, condition 1 may be relaxed to separating at least one of the [...] A-state q ∈ QR,p with an L-state q2, after q has already been associated with an L-state q1 6= q2. As A is minimal, q1 and q2 cannot be equivalent. It follows that if w1, w2 ∈ Σ∗ are the BFS traversal paths [...] associated with q1, q2 ∈ QA, then there exists some differentiating sequence s ∈ Σ∗ for which fA(q1, s) 6= fA(q2, s), i.e., for which fA(w1·s) 6= fA(w2·s). Con- versely, the arrival of w1 and w2 at the same A-state …