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" }, { "__type": "FootnoteReference", "__tag": 4066, "label": "2" } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "If a (non-negative) weight vector " }, { "__type": "InlineMath", "__tag": 4057, "value": "w \\equiv (w_1, \\cdots, w_n)" }, { "__type": "Text", "__tag": 4046, "value": " is supplied, the " }, { "__type": "Emphasis", "__tag": 4047, "children": [ { "__type": "Text", "__tag": 4046, "value": "weighted Jaccard dissimilarity" } ] }, { "__type": "Text", "__tag": 4046, "value": " is defined similarly but with " }, { "__type": "InlineMath", "__tag": 4057, "value": "c_{ij}" }, { "__type": "Text", "__tag": 4046, "value": " replaced by" } ] }, { "__type": "Math", "__tag": 4058, "value": "\\tilde{c}_{ij} := \\sum_{1 \\le k \\le n, u_k=i, v_k=j} w_k" } ], "title": [], "level": 0, "target": null }, "Other Parameters": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null } }, "_ordered_sections": [ "Summary", "Extended Summary", "Parameters", "Attributes", "Methods", "Returns", "Yields", "Receives", "Other Parameters", "Raises", "Warns", "Warnings", "Notes" ], "item_file": "/scipy/spatial/distance.py", "item_line": 778, "item_type": "function", "aliases": [ "scipy.spatial.distance.jaccard" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Code", "__tag": 4050, "value": "from scipy.spatial import distance\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nNon-zero vectors with no matching 1s have dissimilarity of 1.0:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "distance.jaccard([1, 0, 0], [0, 1, 0])\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\nVectors with some matching 1s have dissimilarity less than 1.0:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "distance.jaccard([1, 0, 0, 0], [1, 1, 1, 0])\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\nIdentical vectors, including zero vectors, have dissimilarity of 0.0:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "distance.jaccard([1, 0, 0], [1, 0, 0])\ndistance.jaccard([0, 0, 0], [0, 0, 0])\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\nThe following example computes the dissimilarity from a confusion matrix\ndirectly by setting the weight vector to the frequency of True Positive,\nFalse Negative, False Positive, and True Negative:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "distance.jaccard([1, 1, 0, 0], [1, 0, 1, 0], [31, 41, 59, 26])\n", "execution_status": "failure" } ], "title": [], "level": 0, "target": null }, "see_also": [], "signature": { "__type": "SignatureNode", "__tag": 4029, "kind": "function", "parameters": [ { "__type": "SigParam", "__tag": 4030, "name": "u", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "v", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "w", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "jaccard" }, "references": [ ".. [1] Kaufman, L. and Rousseeuw, P. J. (1990). \"Finding Groups in Data:", " An Introduction to Cluster Analysis.\" John Wiley & Sons, Inc.", ".. [2] Kosub, S. (2019). \"A note on the triangle inequality for the", " Jaccard distance.\" *Pattern Recognition Letters*, 120:36-38.", ".. [3] https://en.wikipedia.org/wiki/Jaccard_index" ], "qa": "scipy.spatial.distance:jaccard", "arbitrary": [], "local_refs": [ "jaccard", "u", "v", "w" ] }