Fix formatting in README.md
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README.md
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@@ -37,17 +37,17 @@ The measure accounts for the hierarchical structure of the ISCO-08 classificatio
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2. The measure punishes distant errors more heavily:
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1. the measure gives higher evaluation for correctly classifying one level down compared to staying at the parent node, e.g. classification into node $E$ (ISCO minor group "111") is better than classification into its parent $C$ (ISCO sub-major group "11") since $E$ is closer to the correct category $G$; and
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2. the measure gives lower evaluation for incorrectly classifying one level down comparing to staying at the parent node, e.g. classification into node $F$ (ISCO unit group "1120") is worse than classification into its parent $C$ since $F$ is farther away from $G$.
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The features described are accomplished by pairing hierarchical variants of precision ($hP$) and recall ($hR$) to form a hierarchical F1 (hF_β) score where each sample belongs not only to its class (e.g., a unit group level code), but also to all ancestors of the class in a hierarchical graph (i.e., the minor, sub-major, and major group level codes)
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Hierarchical precision can be computed with
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$hP = \frac{| \v{C}_i ∩ \v{C}^′_i|} {|\v{C}^′_i |} = \frac{1}{2}
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Hierarchical recall can be computed with
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$hR = \frac{| \v{C}_i ∩ \v{C}^′_i|} {|\v{C}_i |} = \frac{1}{2}
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Combining the two values $hP$ and $hR$ into one hF-measure
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hF_β = \frac{(β^2 + 1) · hP · hR}{(β^2 · hP + hR)}, β ∈ [0, +∞)
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## How to Use
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*Give general statement of how to use the metric*
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2. The measure punishes distant errors more heavily:
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1. the measure gives higher evaluation for correctly classifying one level down compared to staying at the parent node, e.g. classification into node $E$ (ISCO minor group "111") is better than classification into its parent $C$ (ISCO sub-major group "11") since $E$ is closer to the correct category $G$; and
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2. the measure gives lower evaluation for incorrectly classifying one level down comparing to staying at the parent node, e.g. classification into node $F$ (ISCO unit group "1120") is worse than classification into its parent $C$ since $F$ is farther away from $G$.
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The features described are accomplished by pairing hierarchical variants of precision ($hP$) and recall ($hR$) to form a hierarchical F1 (hF_β) score where each sample belongs not only to its class (e.g., a unit group level code), but also to all ancestors of the class in a hierarchical graph (i.e., the minor, sub-major, and major group level codes).
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+
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Hierarchical precision can be computed with:
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+
$hP = \frac{| \v{C}_i ∩ \v{C}^′_i|} {|\v{C}^′_i |} = \frac{1}{2}$
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+
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+
Hierarchical recall can be computed with:
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+
$hR = \frac{| \v{C}_i ∩ \v{C}^′_i|} {|\v{C}_i |} = \frac{1}{2}$
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+
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+
Combining the two values $hP$ and $hR$ into one hF-measure:
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50 |
+
$hF_β = \frac{(β^2 + 1) · hP · hR}{(β^2 · hP + hR)}, β ∈ [0, +∞)$
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## How to Use
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*Give general statement of how to use the metric*
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