198 lines
7.1 KiB
Python
198 lines
7.1 KiB
Python
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# Sebastian Raschka 2014-2020
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# mlxtend Machine Learning Library Extensions
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#
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# Function for generating association rules
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#
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# Author: Joshua Goerner <https://github.com/JoshuaGoerner>
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# Sebastian Raschka <sebastianraschka.com>
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#
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# License: BSD 3 clause
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from itertools import combinations
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import numpy as np
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import pandas as pd
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def association_rules(df, metric="confidence",
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min_threshold=0.8, support_only=False):
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"""Generates a DataFrame of association rules including the
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metrics 'score', 'confidence', and 'lift'
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Parameters
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-----------
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df : pandas DataFrame
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pandas DataFrame of frequent itemsets
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with columns ['support', 'itemsets']
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metric : string (default: 'confidence')
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Metric to evaluate if a rule is of interest.
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**Automatically set to 'support' if `support_only=True`.**
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Otherwise, supported metrics are 'support', 'confidence', 'lift',
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'leverage', and 'conviction'
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These metrics are computed as follows:
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- support(A->C) = support(A+C) [aka 'support'], range: [0, 1]\n
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- confidence(A->C) = support(A+C) / support(A), range: [0, 1]\n
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- lift(A->C) = confidence(A->C) / support(C), range: [0, inf]\n
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- leverage(A->C) = support(A->C) - support(A)*support(C),
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range: [-1, 1]\n
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- conviction = [1 - support(C)] / [1 - confidence(A->C)],
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range: [0, inf]\n
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min_threshold : float (default: 0.8)
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Minimal threshold for the evaluation metric,
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via the `metric` parameter,
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to decide whether a candidate rule is of interest.
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support_only : bool (default: False)
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Only computes the rule support and fills the other
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metric columns with NaNs. This is useful if:
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a) the input DataFrame is incomplete, e.g., does
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not contain support values for all rule antecedents
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and consequents
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b) you simply want to speed up the computation because
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you don't need the other metrics.
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Returns
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----------
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pandas DataFrame with columns "antecedents" and "consequents"
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that store itemsets, plus the scoring metric columns:
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"antecedent support", "consequent support",
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"support", "confidence", "lift",
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"leverage", "conviction"
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of all rules for which
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metric(rule) >= min_threshold.
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Each entry in the "antecedents" and "consequents" columns are
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of type `frozenset`, which is a Python built-in type that
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behaves similarly to sets except that it is immutable
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(For more info, see
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https://docs.python.org/3.6/library/stdtypes.html#frozenset).
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Examples
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-----------
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For usage examples, please see
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http://rasbt.github.io/mlxtend/user_guide/frequent_patterns/association_rules/
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"""
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# check for mandatory columns
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if not all(col in df.columns for col in ["support", "itemsets"]):
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raise ValueError("Dataframe needs to contain the\
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columns 'support' and 'itemsets'")
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def conviction_helper(sAC, sA, sC):
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confidence = sAC/sA
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conviction = np.empty(confidence.shape, dtype=float)
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if not len(conviction.shape):
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conviction = conviction[np.newaxis]
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confidence = confidence[np.newaxis]
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sAC = sAC[np.newaxis]
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sA = sA[np.newaxis]
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sC = sC[np.newaxis]
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conviction[:] = np.inf
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conviction[confidence < 1.] = ((1. - sC[confidence < 1.]) /
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(1. - confidence[confidence < 1.]))
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return conviction
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# metrics for association rules
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metric_dict = {
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"antecedent support": lambda _, sA, __: sA,
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"consequent support": lambda _, __, sC: sC,
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"support": lambda sAC, _, __: sAC,
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"confidence": lambda sAC, sA, _: sAC/sA,
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"lift": lambda sAC, sA, sC: metric_dict["confidence"](sAC, sA, sC)/sC,
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"leverage": lambda sAC, sA, sC: metric_dict["support"](
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sAC, sA, sC) - sA*sC,
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"conviction": lambda sAC, sA, sC: conviction_helper(sAC, sA, sC)
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}
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columns_ordered = ["antecedent support", "consequent support",
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"support",
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"confidence", "lift",
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"leverage", "conviction"]
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# check for metric compliance
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if support_only:
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metric = 'support'
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else:
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if metric not in metric_dict.keys():
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raise ValueError("Metric must be 'confidence' or 'lift', got '{}'"
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.format(metric))
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# get dict of {frequent itemset} -> support
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keys = df['itemsets'].values
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values = df['support'].values
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frozenset_vect = np.vectorize(lambda x: frozenset(x))
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frequent_items_dict = dict(zip(frozenset_vect(keys), values))
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# prepare buckets to collect frequent rules
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rule_antecedents = []
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rule_consequents = []
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rule_supports = []
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# iterate over all frequent itemsets
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for k in frequent_items_dict.keys():
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sAC = frequent_items_dict[k]
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# to find all possible combinations
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for idx in range(len(k)-1, 0, -1):
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# of antecedent and consequent
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for c in combinations(k, r=idx):
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antecedent = frozenset(c)
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consequent = k.difference(antecedent)
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if support_only:
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# support doesn't need these,
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# hence, placeholders should suffice
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sA = None
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sC = None
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else:
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try:
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sA = frequent_items_dict[antecedent]
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sC = frequent_items_dict[consequent]
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except KeyError as e:
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s = (str(e) + 'You are likely getting this error'
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' because the DataFrame is missing '
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' antecedent and/or consequent '
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' information.'
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' You can try using the '
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' `support_only=True` option')
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raise KeyError(s)
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# check for the threshold
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score = metric_dict[metric](sAC, sA, sC)
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if score >= min_threshold:
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rule_antecedents.append(antecedent)
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rule_consequents.append(consequent)
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rule_supports.append([sAC, sA, sC])
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# check if frequent rule was generated
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if not rule_supports:
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return pd.DataFrame(
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columns=["antecedents", "consequents"] + columns_ordered)
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else:
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# generate metrics
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rule_supports = np.array(rule_supports).T.astype(float)
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df_res = pd.DataFrame(
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data=list(zip(rule_antecedents, rule_consequents)),
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columns=["antecedents", "consequents"])
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if support_only:
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sAC = rule_supports[0]
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for m in columns_ordered:
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df_res[m] = np.nan
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df_res['support'] = sAC
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else:
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sAC = rule_supports[0]
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sA = rule_supports[1]
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sC = rule_supports[2]
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for m in columns_ordered:
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df_res[m] = metric_dict[m](sAC, sA, sC)
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return df_res
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