Table 4.
List of all 15 binary asymmetric similarity measures.
| Index | Name | Expression | Range |
|---|---|---|---|
| 1 | Jaccard | c/(a+b+c) | [0, 1) |
| 2 | Dice | 2c/(a+b+2c) | [0, 1) |
| 3 | 3W-Jaccard | 3c/(a+b+3c) | [0, 1) |
| 4 | Sokal–Sneath | c/(2a+2b+c) | [0, 1) |
| 5 | Cosine | c/√((a+c)·(b+c)) | [0, 1) |
| 6 | Mountford | 2c/(c(a+b)+2ab) | [0, 2] |
| 7 | McConnaughey | (c2−ab)/((a+c)·(b+c)) | [−1, 1) |
| 8 | Driver–Kroeber | c(a+b+2c)/(2(a+c)·(b+c)) | [0, 1) |
| 9 | Simpson | c/min(a+c,b+c) | [0, 1) |
| 10 | Braun–Banquet | c/max(a+c,b+c) | [0, 1) |
| 11 | Fager–McGowan | c/√((a+c)·(b+c)) − 1/(2·√(max(a+c,b+c))) | (−1/2, 1) |
| 12 | Kulczynski | c/(a+b) | [0, ∞) |
| 13 | Intersection | c | [0, ∞) |
| 14 | Hamming | 1/(a+b) | (0, 1] |
| 15 | Hellinger | 1 − √((1 − c/√((a+c)·(b+c)))) | [0, 1) |
1, Jaccard is also known as Tanimoto; 2, Dice is also known as Hodgkin index, Sorenson, Czekanowski, Nei–Li, and F1-score; 5, Cosine is equal to the square root of Sorgenfrei, and is also known as Carbo index, Ochiai, Otsuka, and Fowlkes–Mallows index; 8, Driver–Kroeber is equal to 0.5 times Johnson, and is also known as Kulczynski; 14, Hamming is also known as squared-Euclidean, Canberra, Manhattan, Cityblock, and Minkowski; a,b,c ≥ 0; a+b+c > 0.