Repository: rasbt/mlxtend

Issue:
Adding more metrics for Association Rules
### Discussed in https://github.com/rasbt/mlxtend/discussions/1031

<div type='discussions-op-text'>

<sup>Originally posted by **Nachiket18** April 24, 2023</sup>
There are several metrics like lift, leverage, conviction etc are available for association rules. Wondering if it would be of help if we implement other metrics like Jaccard, Added Value, Certainty Factor etc. </div>

We are planning on implementing more Association Rules metrics from this resource: https://mhahsler.github.io/arules/docs/measures
Metrics we are currently considering are: Jaccard Coefficient, Certainty Factor, and Added Value.

![image](https://github.com/rasbt/mlxtend/assets/25268334/f69d0fa5-1ee0-490d-aa71-afb68ba0030a)
![image](https://github.com/rasbt/mlxtend/assets/25268334/90e83305-b23b-4b44-8eff-7ec03c6153d9)
![image](https://github.com/rasbt/mlxtend/assets/25268334/95b79e44-daa1-46df-81e8-d63d08a7081e)

Hints from issue comments:
@Nachiket18: 1. We were able to implement the _Jaccard_ similarity (https://github.com/UltraArceus3/mlxtend/blob/master/mlxtend/frequent_patterns/association_rules.py#L133)
2. We tested the code with an sample example (https://github.com/UltraArceus3/mlxtend/blob/master/mlxtend/frequent_patterns/tests/test_association_rules.py#L181)

@rasbt - Could you share your thoughts about this?  We have also implemented _Certainty Factor_ and _Centered Confidence_ for which we would be writing test cases.
@rasbt: H @UltraArceus3  and @Nachiket18 . Thanks for suggesting these and offering to help implementing these! On my end, I am currently very maxed out with other projects and wouldn't have the capacity to contribute anything at the moment. However, I could approve PRs etc in case you want to contribute these. (Sorry that I can't be more helpful at the moment, but my free time is mostly taken up by my LLM from Scratch book until mid July; but I am happy to approve PRs, and I actually really appreciate your willingness to contribute).

Solution patch:
diff --git a/docs/sources/CHANGELOG.md b/docs/sources/CHANGELOG.md
index aeb7c468..914cce35 100755
--- a/docs/sources/CHANGELOG.md
+++ b/docs/sources/CHANGELOG.md
@@ -6,6 +6,8 @@ The CHANGELOG for the current development version is available at
 [https://github.com/rasbt/mlxtend/blob/master/docs/sources/CHANGELOG.md](https://github.com/rasbt/mlxtend/blob/master/docs/sources/CHANGELOG.md).
 
 ---
+
+
 ### Version 0.23.2 (TBD)
 
 ##### Downloads
@@ -16,21 +18,13 @@ The CHANGELOG for the current development version is available at
 
 ##### New Features and Enhancements
 
+- [`mlxtend.frequent_patterns.association_rules`](https://rasbt.github.io/mlxtend/user_guide/frequent_patterns/association_rules/) Implemented three new metrics: Jaccard, Certainty, and Kulczynski. ([#1096](https://github.com/rasbt/mlxtend/issues/1096))
 - Integrated scikit-learn's `set_output` method into `TransactionEncoder` ([#1087](https://github.com/rasbt/mlxtend/issues/1087) via [it176131](https://github.com/it176131))
 
-
-
-
-### Version 0.23.2 (TBD)
-
-##### Downloads
-
-- [Source code (zip)](https://github.com/rasbt/mlxtend/archive/v0.23.2.zip)
-
-- [Source code (tar.gz)](https://github.com/rasbt/mlxtend/archive/v0.23.2.tar.gz)
-
 ##### Changes
 
+- [`mlxtend.frequent_patterns.association_rules`](https://rasbt.github.io/mlxtend/user_guide/frequent_patterns/association_rules/) Added optional parameter 'return_metrics' to only return a given list of metrics, rather than every possible metric.
+
 - Add `n_classes_` attribute to stacking classifiers for compatibility with scikit-learn 1.3 ([#1091](https://github.com/rasbt/mlxtend/issues/1091))
 - Use Scipy's instead of NumPy's decompositions in PCA for improved accuracy in edge cases ([#1080](https://github.com/rasbt/mlxtend/issues/1080) via [[fkdosilovic](https://github.com/rasbt/mlxtend/issues?q=is%3Apr+is%3Aopen+author%3Afkdosilovic)])
 
diff --git a/docs/sources/user_guide/frequent_patterns/association_rules.ipynb b/docs/sources/user_guide/frequent_patterns/association_rules.ipynb
index f81a8562..3f963b78 100644
--- a/docs/sources/user_guide/frequent_patterns/association_rules.ipynb
+++ b/docs/sources/user_guide/frequent_patterns/association_rules.ipynb
@@ -96,6 +96,29 @@
     "- introduced in [7]\n",
     "\n",
     "Measures both association and dissociation. Value ranges between -1 and 1. A positive value (>0) indicates Association and negative value indicated dissociation.\n",
+    "\n",
+    "#### 'jaccard':\n",
+    "\n",
+    "$$\\text{jaccard}(A\\rightarrow C) = \\frac{\\text{support}(A\\rightarrow C)}{\\text{support}(A) + \\text{support}(C) - \\text{support}(A\\rightarrow C)}, \\;\\;\\; \\text{range: } [0, 1]$$\n",
+    "\n",
+    "- introduced in [8]\n",
+    "\n",
+    "Measures similarity between A and C. Value ranges between 0 and 1. A value of 0 indicates complete dissimilarity, and a value of 1 indicates complete similarity.\n",
+    " \n",
+    "#### 'certainty':\n",
+    " $$\\text{certainty}(A\\rightarrow C) = \\frac{\\text{confidence}(A\\rightarrow C) - \\text{support}(C)}{1 - \\text{support}(C)}, \\;\\;\\; \\text{range: } [-1, 1]$$ \n",
+    "\n",
+    " - introduced in [9]\n",
+    " \n",
+    " Measures\n",
+    "the certainty between A and C. Value ranges from -1 and 1, where 0 indicates independence. \n",
+    "\n",
+    "#### 'kulczynski':\n",
+    " $$\\text{Kulczynski}(A\\rightarrow C) = \\frac{1}{2}\\left(\\frac{\\text{support}(A\\rightarrow C)}{\\text{support}(A)} + \\frac{\\text{support}(A\\rightarrow C)}{\\text{support}(C)}\\right), \\;\\;\\; \\text{range: } [0, 1]$$\n",
+    "\n",
+    " - introduced in [10]\n",
+    "\n",
+    " Measures the association between A and C. Value ranges from 0 to 1. Rules near 0 or 1 are considered negatively or positively associated, respectively. Rules near 0.5 are considered to be unintresting.\n",
     " "
    ]
   },
@@ -122,7 +145,13 @@
     "\n",
     "[6] Sergey Brin, Rajeev Motwani, Jeffrey D. Ullman, and Shalom Turk. Dynamic itemset counting and implication rules for market basket data. In SIGMOD 1997, Proceedings ACM SIGMOD International Conference on Management of Data, pages 255-264, Tucson, Arizona, USA, May 1997\n",
     "\n",
-    "[7]  Xiaowei Yan , Chengqi Zhang & Shichao Zhang (2009) CONFIDENCE METRICS FOR ASSOCIATION RULE MINING, Applied Artificial Intelligence, 23:8, 713-737 https://www.tandfonline.com/doi/pdf/10.1080/08839510903208062.\n"
+    "[7]  Xiaowei Yan , Chengqi Zhang & Shichao Zhang (2009) CONFIDENCE METRICS FOR ASSOCIATION RULE MINING, Applied Artificial Intelligence, 23:8, 713-737 https://www.tandfonline.com/doi/pdf/10.1080/08839510903208062.\n",
+    "\n",
+    "[8] Pang-Ning Tan, Vipin Kumar, Jaideep Srivastava. Selecting the right objective measure for association analysis. Information Systems, Volume 29, Issue 4, 2004, Pages 293-313.\n",
+    "\n",
+    "[9] Berzal Fernando, Blanco Ignacio, Sánchez Daniel, Vila, María-Amparo. Measuring the accuracy and interest of association rules: A new framework. Intelligent Data Analysis, Volume 6, no. 3, 2002, Pages 221-235.\n",
+    "\n",
+    "[10] Wu, T., Chen, Y., Han, J. Re-examination of interestingness measures in pattern mining: a unified framework. Data Min Knowl Disc 21, 371–397 (2010). https://doi.org/10.1007/s10618-009-0161-2."
    ]
   },
   {
@@ -141,114 +170,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": null,
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<div>\n",
-       "<style scoped>\n",
-       "    .dataframe tbody tr th:only-of-type {\n",
-       "        vertical-align: middle;\n",
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-       "\n",
-       "    .dataframe tbody tr th {\n",
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-       "\n",
-       "    .dataframe thead th {\n",
-       "        text-align: right;\n",
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-       "</style>\n",
-       "<table border=\"1\" class=\"dataframe\">\n",
-       "  <thead>\n",
-       "    <tr style=\"text-align: right;\">\n",
-       "      <th></th>\n",
-       "      <th>support</th>\n",
-       "      <th>itemsets</th>\n",
-       "    </tr>\n",
-       "  </thead>\n",
-       "  <tbody>\n",
-       "    <tr>\n",
-       "      <th>0</th>\n",
-       "      <td>1.0</td>\n",
-       "      <td>(Kidney Beans)</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>1</th>\n",
-       "      <td>0.8</td>\n",
-       "      <td>(Eggs)</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2</th>\n",
-       "      <td>0.6</td>\n",
-       "      <td>(Yogurt)</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>3</th>\n",
-       "      <td>0.6</td>\n",
-       "      <td>(Onion)</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>4</th>\n",
-       "      <td>0.6</td>\n",
-       "      <td>(Milk)</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>5</th>\n",
-       "      <td>0.8</td>\n",
-       "      <td>(Kidney Beans, Eggs)</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>6</th>\n",
-       "      <td>0.6</td>\n",
-       "      <td>(Kidney Beans, Yogurt)</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>7</th>\n",
-       "      <td>0.6</td>\n",
-       "      <td>(Eggs, Onion)</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>8</th>\n",
-       "      <td>0.6</td>\n",
-       "      <td>(Kidney Beans, Onion)</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>9</th>\n",
-       "      <td>0.6</td>\n",
-       "      <td>(Eggs, Kidney Beans, Onion)</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>10</th>\n",
-       "      <td>0.6</td>\n",
-       "      <td>(Kidney Beans, Milk)</td>\n",
-       "    </tr>\n",
-       "  </tbody>\n",
-       "</table>\n",
-       "</div>"
-      ],
-      "text/plain": [
-       "    support                     itemsets\n",
-       "0       1.0               (Kidney Beans)\n",
-       "1       0.8                       (Eggs)\n",
-       "2       0.6                     (Yogurt)\n",
-       "3       0.6                      (Onion)\n",
-       "4       0.6                       (Milk)\n",
-       "5       0.8         (Kidney Beans, Eggs)\n",
-       "6       0.6       (Kidney Beans, Yogurt)\n",
-       "7       0.6                (Eggs, Onion)\n",
-       "8       0.6        (Kidney Beans, Onion)\n",
-       "9       0.6  (Eggs, Kidney Beans, Onion)\n",
-       "10      0.6         (Kidney Beans, Milk)"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import pandas as pd\n",
     "from mlxtend.preprocessing import TransactionEncoder\n",
@@ -282,252 +206,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": null,
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<div>\n",
-       "<style scoped>\n",
-       "    .dataframe tbody tr th:only-of-type {\n",
-       "        vertical-align: middle;\n",
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-       "\n",
-       "    .dataframe tbody tr th {\n",
-       "        vertical-align: top;\n",
-       "    }\n",
-       "\n",
-       "    .dataframe thead th {\n",
-       "        text-align: right;\n",
-       "    }\n",
-       "</style>\n",
-       "<table border=\"1\" class=\"dataframe\">\n",
-       "  <thead>\n",
-       "    <tr style=\"text-align: right;\">\n",
-       "      <th></th>\n",
-       "      <th>antecedents</th>\n",
-       "      <th>consequents</th>\n",
-       "      <th>antecedent support</th>\n",
-       "      <th>consequent support</th>\n",
-       "      <th>support</th>\n",
-       "      <th>confidence</th>\n",
-       "      <th>lift</th>\n",
-       "      <th>leverage</th>\n",
-       "      <th>conviction</th>\n",
-       "      <th>zhangs_metric</th>\n",
-       "    </tr>\n",
-       "  </thead>\n",
-       "  <tbody>\n",
-       "    <tr>\n",
-       "      <th>0</th>\n",
-       "      <td>(Kidney Beans)</td>\n",
-       "      <td>(Eggs)</td>\n",
-       "      <td>1.0</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.80</td>\n",
-       "      <td>1.00</td>\n",
-       "      <td>0.00</td>\n",
-       "      <td>1.0</td>\n",
-       "      <td>0.0</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>1</th>\n",
-       "      <td>(Eggs)</td>\n",
-       "      <td>(Kidney Beans)</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>1.0</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>1.00</td>\n",
-       "      <td>1.00</td>\n",
-       "      <td>0.00</td>\n",
-       "      <td>inf</td>\n",
-       "      <td>0.0</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2</th>\n",
-       "      <td>(Yogurt)</td>\n",
-       "      <td>(Kidney Beans)</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>1.0</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>1.00</td>\n",
-       "      <td>1.00</td>\n",
-       "      <td>0.00</td>\n",
-       "      <td>inf</td>\n",
-       "      <td>0.0</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>3</th>\n",
-       "      <td>(Eggs)</td>\n",
-       "      <td>(Onion)</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.75</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>1.6</td>\n",
-       "      <td>1.0</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>4</th>\n",
-       "      <td>(Onion)</td>\n",
-       "      <td>(Eggs)</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>1.00</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>inf</td>\n",
-       "      <td>0.5</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>5</th>\n",
-       "      <td>(Onion)</td>\n",
-       "      <td>(Kidney Beans)</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>1.0</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>1.00</td>\n",
-       "      <td>1.00</td>\n",
-       "      <td>0.00</td>\n",
-       "      <td>inf</td>\n",
-       "      <td>0.0</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>6</th>\n",
-       "      <td>(Kidney Beans, Eggs)</td>\n",
-       "      <td>(Onion)</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.75</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>1.6</td>\n",
-       "      <td>1.0</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>7</th>\n",
-       "      <td>(Onion, Eggs)</td>\n",
-       "      <td>(Kidney Beans)</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>1.0</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>1.00</td>\n",
-       "      <td>1.00</td>\n",
-       "      <td>0.00</td>\n",
-       "      <td>inf</td>\n",
-       "      <td>0.0</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>8</th>\n",
-       "      <td>(Kidney Beans, Onion)</td>\n",
-       "      <td>(Eggs)</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>1.00</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>inf</td>\n",
-       "      <td>0.5</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>9</th>\n",
-       "      <td>(Eggs)</td>\n",
-       "      <td>(Kidney Beans, Onion)</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.75</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>1.6</td>\n",
-       "      <td>1.0</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>10</th>\n",
-       "      <td>(Onion)</td>\n",
-       "      <td>(Kidney Beans, Eggs)</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>1.00</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>inf</td>\n",
-       "      <td>0.5</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>11</th>\n",
-       "      <td>(Milk)</td>\n",
-       "      <td>(Kidney Beans)</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>1.0</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>1.00</td>\n",
-       "      <td>1.00</td>\n",
-       "      <td>0.00</td>\n",
-       "      <td>inf</td>\n",
-       "      <td>0.0</td>\n",
-       "    </tr>\n",
-       "  </tbody>\n",
-       "</table>\n",
-       "</div>"
-      ],
-      "text/plain": [
-       "              antecedents            consequents  antecedent support  \\\n",
-       "0          (Kidney Beans)                 (Eggs)                 1.0   \n",
-       "1                  (Eggs)         (Kidney Beans)                 0.8   \n",
-       "2                (Yogurt)         (Kidney Beans)                 0.6   \n",
-       "3                  (Eggs)                (Onion)                 0.8   \n",
-       "4                 (Onion)                 (Eggs)                 0.6   \n",
-       "5                 (Onion)         (Kidney Beans)                 0.6   \n",
-       "6    (Kidney Beans, Eggs)                (Onion)                 0.8   \n",
-       "7           (Onion, Eggs)         (Kidney Beans)                 0.6   \n",
-       "8   (Kidney Beans, Onion)                 (Eggs)                 0.6   \n",
-       "9                  (Eggs)  (Kidney Beans, Onion)                 0.8   \n",
-       "10                (Onion)   (Kidney Beans, Eggs)                 0.6   \n",
-       "11                 (Milk)         (Kidney Beans)                 0.6   \n",
-       "\n",
-       "    consequent support  support  confidence  lift  leverage  conviction  \\\n",
-       "0                  0.8      0.8        0.80  1.00      0.00         1.0   \n",
-       "1                  1.0      0.8        1.00  1.00      0.00         inf   \n",
-       "2                  1.0      0.6        1.00  1.00      0.00         inf   \n",
-       "3                  0.6      0.6        0.75  1.25      0.12         1.6   \n",
-       "4                  0.8      0.6        1.00  1.25      0.12         inf   \n",
-       "5                  1.0      0.6        1.00  1.00      0.00         inf   \n",
-       "6                  0.6      0.6        0.75  1.25      0.12         1.6   \n",
-       "7                  1.0      0.6        1.00  1.00      0.00         inf   \n",
-       "8                  0.8      0.6        1.00  1.25      0.12         inf   \n",
-       "9                  0.6      0.6        0.75  1.25      0.12         1.6   \n",
-       "10                 0.8      0.6        1.00  1.25      0.12         inf   \n",
-       "11                 1.0      0.6        1.00  1.00      0.00         inf   \n",
-       "\n",
-       "    zhangs_metric  \n",
-       "0             0.0  \n",
-       "1             0.0  \n",
-       "2             0.0  \n",
-       "3             1.0  \n",
-       "4             0.5  \n",
-       "5             0.0  \n",
-       "6             1.0  \n",
-       "7             0.0  \n",
-       "8             0.5  \n",
-       "9             1.0  \n",
-       "10            0.5  \n",
-       "11            0.0  "
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "from mlxtend.frequent_patterns import association_rules\n",
     "\n",
@@ -550,156 +231,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": null,
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<div>\n",
-       "<style scoped>\n",
-       "    .dataframe tbody tr th:only-of-type {\n",
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-       "    }\n",
-       "\n",
-       "    .dataframe tbody tr th {\n",
-       "        vertical-align: top;\n",
-       "    }\n",
-       "\n",
-       "    .dataframe thead th {\n",
-       "        text-align: right;\n",
-       "    }\n",
-       "</style>\n",
-       "<table border=\"1\" class=\"dataframe\">\n",
-       "  <thead>\n",
-       "    <tr style=\"text-align: right;\">\n",
-       "      <th></th>\n",
-       "      <th>antecedents</th>\n",
-       "      <th>consequents</th>\n",
-       "      <th>antecedent support</th>\n",
-       "      <th>consequent support</th>\n",
-       "      <th>support</th>\n",
-       "      <th>confidence</th>\n",
-       "      <th>lift</th>\n",
-       "      <th>leverage</th>\n",
-       "      <th>conviction</th>\n",
-       "      <th>zhangs_metric</th>\n",
-       "    </tr>\n",
-       "  </thead>\n",
-       "  <tbody>\n",
-       "    <tr>\n",
-       "      <th>0</th>\n",
-       "      <td>(Eggs)</td>\n",
-       "      <td>(Onion)</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.75</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>1.6</td>\n",
-       "      <td>1.0</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>1</th>\n",
-       "      <td>(Onion)</td>\n",
-       "      <td>(Eggs)</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>1.00</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>inf</td>\n",
-       "      <td>0.5</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2</th>\n",
-       "      <td>(Kidney Beans, Eggs)</td>\n",
-       "      <td>(Onion)</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.75</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>1.6</td>\n",
-       "      <td>1.0</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>3</th>\n",
-       "      <td>(Kidney Beans, Onion)</td>\n",
-       "      <td>(Eggs)</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>1.00</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>inf</td>\n",
-       "      <td>0.5</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>4</th>\n",
-       "      <td>(Eggs)</td>\n",
-       "      <td>(Kidney Beans, Onion)</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.75</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>1.6</td>\n",
-       "      <td>1.0</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>5</th>\n",
-       "      <td>(Onion)</td>\n",
-       "      <td>(Kidney Beans, Eggs)</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>1.00</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>inf</td>\n",
-       "      <td>0.5</td>\n",
-       "    </tr>\n",
-       "  </tbody>\n",
-       "</table>\n",
-       "</div>"
-      ],
-      "text/plain": [
-       "             antecedents            consequents  antecedent support  \\\n",
-       "0                 (Eggs)                (Onion)                 0.8   \n",
-       "1                (Onion)                 (Eggs)                 0.6   \n",
-       "2   (Kidney Beans, Eggs)                (Onion)                 0.8   \n",
-       "3  (Kidney Beans, Onion)                 (Eggs)                 0.6   \n",
-       "4                 (Eggs)  (Kidney Beans, Onion)                 0.8   \n",
-       "5                (Onion)   (Kidney Beans, Eggs)                 0.6   \n",
-       "\n",
-       "   consequent support  support  confidence  lift  leverage  conviction  \\\n",
-       "0                 0.6      0.6        0.75  1.25      0.12         1.6   \n",
-       "1                 0.8      0.6        1.00  1.25      0.12         inf   \n",
-       "2                 0.6      0.6        0.75  1.25      0.12         1.6   \n",
-       "3                 0.8      0.6        1.00  1.25      0.12         inf   \n",
-       "4                 0.6      0.6        0.75  1.25      0.12         1.6   \n",
-       "5                 0.8      0.6        1.00  1.25      0.12         inf   \n",
-       "\n",
-       "   zhangs_metric  \n",
-       "0            1.0  \n",
-       "1            0.5  \n",
-       "2            1.0  \n",
-       "3            0.5  \n",
-       "4            1.0  \n",
-       "5            0.5  "
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "rules = association_rules(frequent_itemsets, metric=\"lift\", min_threshold=1.2)\n",
     "rules"
@@ -720,163 +254,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": null,
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<div>\n",
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-       "</style>\n",
-       "<table border=\"1\" class=\"dataframe\">\n",
-       "  <thead>\n",
-       "    <tr style=\"text-align: right;\">\n",
-       "      <th></th>\n",
-       "      <th>antecedents</th>\n",
-       "      <th>consequents</th>\n",
-       "      <th>antecedent support</th>\n",
-       "      <th>consequent support</th>\n",
-       "      <th>support</th>\n",
-       "      <th>confidence</th>\n",
-       "      <th>lift</th>\n",
-       "      <th>leverage</th>\n",
-       "      <th>conviction</th>\n",
-       "      <th>zhangs_metric</th>\n",
-       "      <th>antecedent_len</th>\n",
-       "    </tr>\n",
-       "  </thead>\n",
-       "  <tbody>\n",
-       "    <tr>\n",
-       "      <th>0</th>\n",
-       "      <td>(Eggs)</td>\n",
-       "      <td>(Onion)</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.75</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>1.6</td>\n",
-       "      <td>1.0</td>\n",
-       "      <td>1</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>1</th>\n",
-       "      <td>(Onion)</td>\n",
-       "      <td>(Eggs)</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>1.00</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>inf</td>\n",
-       "      <td>0.5</td>\n",
-       "      <td>1</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2</th>\n",
-       "      <td>(Kidney Beans, Eggs)</td>\n",
-       "      <td>(Onion)</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.75</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>1.6</td>\n",
-       "      <td>1.0</td>\n",
-       "      <td>2</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>3</th>\n",
-       "      <td>(Kidney Beans, Onion)</td>\n",
-       "      <td>(Eggs)</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>1.00</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>inf</td>\n",
-       "      <td>0.5</td>\n",
-       "      <td>2</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>4</th>\n",
-       "      <td>(Eggs)</td>\n",
-       "      <td>(Kidney Beans, Onion)</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.75</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>1.6</td>\n",
-       "      <td>1.0</td>\n",
-       "      <td>1</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>5</th>\n",
-       "      <td>(Onion)</td>\n",
-       "      <td>(Kidney Beans, Eggs)</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>1.00</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>inf</td>\n",
-       "      <td>0.5</td>\n",
-       "      <td>1</td>\n",
-       "    </tr>\n",
-       "  </tbody>\n",
-       "</table>\n",
-       "</div>"
-      ],
-      "text/plain": [
-       "             antecedents            consequents  antecedent support  \\\n",
-       "0                 (Eggs)                (Onion)                 0.8   \n",
-       "1                (Onion)                 (Eggs)                 0.6   \n",
-       "2   (Kidney Beans, Eggs)                (Onion)                 0.8   \n",
-       "3  (Kidney Beans, Onion)                 (Eggs)                 0.6   \n",
-       "4                 (Eggs)  (Kidney Beans, Onion)                 0.8   \n",
-       "5                (Onion)   (Kidney Beans, Eggs)                 0.6   \n",
-       "\n",
-       "   consequent support  support  confidence  lift  leverage  conviction  \\\n",
-       "0                 0.6      0.6        0.75  1.25      0.12         1.6   \n",
-       "1                 0.8      0.6        1.00  1.25      0.12         inf   \n",
-       "2                 0.6      0.6        0.75  1.25      0.12         1.6   \n",
-       "3                 0.8      0.6        1.00  1.25      0.12         inf   \n",
-       "4                 0.6      0.6        0.75  1.25      0.12         1.6   \n",
-       "5                 0.8      0.6        1.00  1.25      0.12         inf   \n",
-       "\n",
-       "   zhangs_metric  antecedent_len  \n",
-       "0            1.0               1  \n",
-       "1            0.5               1  \n",
-       "2            1.0               2  \n",
-       "3            0.5               2  \n",
-       "4            1.0               1  \n",
-       "5            0.5               1  "
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "rules[\"antecedent_len\"] = rules[\"antecedents\"].apply(lambda x: len(x))\n",
     "rules"
@@ -891,78 +271,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": null,
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<div>\n",
-       "<style scoped>\n",
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-       "</style>\n",
-       "<table border=\"1\" class=\"dataframe\">\n",
-       "  <thead>\n",
-       "    <tr style=\"text-align: right;\">\n",
-       "      <th></th>\n",
-       "      <th>antecedents</th>\n",
-       "      <th>consequents</th>\n",
-       "      <th>antecedent support</th>\n",
-       "      <th>consequent support</th>\n",
-       "      <th>support</th>\n",
-       "      <th>confidence</th>\n",
-       "      <th>lift</th>\n",
-       "      <th>leverage</th>\n",
-       "      <th>conviction</th>\n",
-       "      <th>zhangs_metric</th>\n",
-       "      <th>antecedent_len</th>\n",
-       "    </tr>\n",
-       "  </thead>\n",
-       "  <tbody>\n",
-       "    <tr>\n",
-       "      <th>3</th>\n",
-       "      <td>(Kidney Beans, Onion)</td>\n",
-       "      <td>(Eggs)</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>1.0</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>inf</td>\n",
-       "      <td>0.5</td>\n",
-       "      <td>2</td>\n",
-       "    </tr>\n",
-       "  </tbody>\n",
-       "</table>\n",
-       "</div>"
-      ],
-      "text/plain": [
-       "             antecedents consequents  antecedent support  consequent support  \\\n",
-       "3  (Kidney Beans, Onion)      (Eggs)                 0.6                 0.8   \n",
-       "\n",
-       "   support  confidence  lift  leverage  conviction  zhangs_metric  \\\n",
-       "3      0.6         1.0  1.25      0.12         inf            0.5   \n",
-       "\n",
-       "   antecedent_len  \n",
-       "3               2  "
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "rules[ (rules['antecedent_len'] >= 2) &\n",
     "       (rules['confidence'] > 0.75) &\n",
@@ -978,78 +289,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": null,
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<div>\n",
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-       "</style>\n",
-       "<table border=\"1\" class=\"dataframe\">\n",
-       "  <thead>\n",
-       "    <tr style=\"text-align: right;\">\n",
-       "      <th></th>\n",
-       "      <th>antecedents</th>\n",
-       "      <th>consequents</th>\n",
-       "      <th>antecedent support</th>\n",
-       "      <th>consequent support</th>\n",
-       "      <th>support</th>\n",
-       "      <th>confidence</th>\n",
-       "      <th>lift</th>\n",
-       "      <th>leverage</th>\n",
-       "      <th>conviction</th>\n",
-       "      <th>zhangs_metric</th>\n",
-       "      <th>antecedent_len</th>\n",
-       "    </tr>\n",
-       "  </thead>\n",
-       "  <tbody>\n",
-       "    <tr>\n",
-       "      <th>2</th>\n",
-       "      <td>(Kidney Beans, Eggs)</td>\n",
-       "      <td>(Onion)</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.75</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>1.6</td>\n",
-       "      <td>1.0</td>\n",
-       "      <td>2</td>\n",
-       "    </tr>\n",
-       "  </tbody>\n",
-       "</table>\n",
-       "</div>"
-      ],
-      "text/plain": [
-       "            antecedents consequents  antecedent support  consequent support  \\\n",
-       "2  (Kidney Beans, Eggs)     (Onion)                 0.8                 0.6   \n",
-       "\n",
-       "   support  confidence  lift  leverage  conviction  zhangs_metric  \\\n",
-       "2      0.6        0.75  1.25      0.12         1.6            1.0   \n",
-       "\n",
-       "   antecedent_len  \n",
-       "2               2  "
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "rules[rules['antecedents'] == {'Eggs', 'Kidney Beans'}]"
    ]
@@ -1089,90 +331,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": null,
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<div>\n",
-       "<style scoped>\n",
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-       "\n",
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-       "        text-align: right;\n",
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-       "</style>\n",
-       "<table border=\"1\" class=\"dataframe\">\n",
-       "  <thead>\n",
-       "    <tr style=\"text-align: right;\">\n",
-       "      <th></th>\n",
-       "      <th>itemsets</th>\n",
-       "      <th>support</th>\n",
-       "    </tr>\n",
-       "  </thead>\n",
-       "  <tbody>\n",
-       "    <tr>\n",
-       "      <th>0</th>\n",
-       "      <td>[177, 176]</td>\n",
-       "      <td>0.253623</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>1</th>\n",
-       "      <td>[177, 179]</td>\n",
-       "      <td>0.253623</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2</th>\n",
-       "      <td>[176, 178]</td>\n",
-       "      <td>0.217391</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>3</th>\n",
-       "      <td>[176, 179]</td>\n",
-       "      <td>0.217391</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>4</th>\n",
-       "      <td>[93, 100]</td>\n",
-       "      <td>0.181159</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>5</th>\n",
-       "      <td>[177, 178]</td>\n",
-       "      <td>0.108696</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>6</th>\n",
-       "      <td>[177, 176, 178]</td>\n",
-       "      <td>0.108696</td>\n",
-       "    </tr>\n",
-       "  </tbody>\n",
-       "</table>\n",
-       "</div>"
-      ],
-      "text/plain": [
-       "          itemsets   support\n",
-       "0       [177, 176]  0.253623\n",
-       "1       [177, 179]  0.253623\n",
-       "2       [176, 178]  0.217391\n",
-       "3       [176, 179]  0.217391\n",
-       "4        [93, 100]  0.181159\n",
-       "5       [177, 178]  0.108696\n",
-       "6  [177, 176, 178]  0.108696"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import pandas as pd\n",
     "\n",
@@ -1209,328 +370,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": null,
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
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-       "</style>\n",
-       "<table border=\"1\" class=\"dataframe\">\n",
-       "  <thead>\n",
-       "    <tr style=\"text-align: right;\">\n",
-       "      <th></th>\n",
-       "      <th>antecedents</th>\n",
-       "      <th>consequents</th>\n",
-       "      <th>antecedent support</th>\n",
-       "      <th>consequent support</th>\n",
-       "      <th>support</th>\n",
-       "      <th>confidence</th>\n",
-       "      <th>lift</th>\n",
-       "      <th>leverage</th>\n",
-       "      <th>conviction</th>\n",
-       "      <th>zhangs_metric</th>\n",
-       "    </tr>\n",
-       "  </thead>\n",
-       "  <tbody>\n",
-       "    <tr>\n",
-       "      <th>0</th>\n",
-       "      <td>(176)</td>\n",
-       "      <td>(177)</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>0.253623</td>\n",
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-       "      <td>NaN</td>\n",
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-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
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-       "      <th>1</th>\n",
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-       "      <td>0.253623</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2</th>\n",
-       "      <td>(179)</td>\n",
-       "      <td>(177)</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>0.253623</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>3</th>\n",
-       "      <td>(177)</td>\n",
-       "      <td>(179)</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>0.253623</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>4</th>\n",
-       "      <td>(178)</td>\n",
-       "      <td>(176)</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>0.217391</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>5</th>\n",
-       "      <td>(176)</td>\n",
-       "      <td>(178)</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>0.217391</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>6</th>\n",
-       "      <td>(179)</td>\n",
-       "      <td>(176)</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>0.217391</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>7</th>\n",
-       "      <td>(176)</td>\n",
-       "      <td>(179)</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>0.217391</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>8</th>\n",
-       "      <td>(100)</td>\n",
-       "      <td>(93)</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>0.181159</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>9</th>\n",
-       "      <td>(93)</td>\n",
-       "      <td>(100)</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>0.181159</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>10</th>\n",
-       "      <td>(178)</td>\n",
-       "      <td>(177)</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>0.108696</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>11</th>\n",
-       "      <td>(177)</td>\n",
-       "      <td>(178)</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>0.108696</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>12</th>\n",
-       "      <td>(178, 176)</td>\n",
-       "      <td>(177)</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>0.108696</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>13</th>\n",
-       "      <td>(178, 177)</td>\n",
-       "      <td>(176)</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>0.108696</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>14</th>\n",
-       "      <td>(177, 176)</td>\n",
-       "      <td>(178)</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>0.108696</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>15</th>\n",
-       "      <td>(178)</td>\n",
-       "      <td>(177, 176)</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>0.108696</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>16</th>\n",
-       "      <td>(176)</td>\n",
-       "      <td>(178, 177)</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>0.108696</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>17</th>\n",
-       "      <td>(177)</td>\n",
-       "      <td>(178, 176)</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>0.108696</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "    </tr>\n",
-       "  </tbody>\n",
-       "</table>\n",
-       "</div>"
-      ],
-      "text/plain": [
-       "   antecedents consequents  antecedent support  consequent support   support  \\\n",
-       "0        (176)       (177)                 NaN                 NaN  0.253623   \n",
-       "1        (177)       (176)                 NaN                 NaN  0.253623   \n",
-       "2        (179)       (177)                 NaN                 NaN  0.253623   \n",
-       "3        (177)       (179)                 NaN                 NaN  0.253623   \n",
-       "4        (178)       (176)                 NaN                 NaN  0.217391   \n",
-       "5        (176)       (178)                 NaN                 NaN  0.217391   \n",
-       "6        (179)       (176)                 NaN                 NaN  0.217391   \n",
-       "7        (176)       (179)                 NaN                 NaN  0.217391   \n",
-       "8        (100)        (93)                 NaN                 NaN  0.181159   \n",
-       "9         (93)       (100)                 NaN                 NaN  0.181159   \n",
-       "10       (178)       (177)                 NaN                 NaN  0.108696   \n",
-       "11       (177)       (178)                 NaN                 NaN  0.108696   \n",
-       "12  (178, 176)       (177)                 NaN                 NaN  0.108696   \n",
-       "13  (178, 177)       (176)                 NaN                 NaN  0.108696   \n",
-       "14  (177, 176)       (178)                 NaN                 NaN  0.108696   \n",
-       "15       (178)  (177, 176)                 NaN                 NaN  0.108696   \n",
-       "16       (176)  (178, 177)                 NaN                 NaN  0.108696   \n",
-       "17       (177)  (178, 176)                 NaN                 NaN  0.108696   \n",
-       "\n",
-       "    confidence  lift  leverage  conviction  zhangs_metric  \n",
-       "0          NaN   NaN       NaN         NaN            NaN  \n",
-       "1          NaN   NaN       NaN         NaN            NaN  \n",
-       "2          NaN   NaN       NaN         NaN            NaN  \n",
-       "3          NaN   NaN       NaN         NaN            NaN  \n",
-       "4          NaN   NaN       NaN         NaN            NaN  \n",
-       "5          NaN   NaN       NaN         NaN            NaN  \n",
-       "6          NaN   NaN       NaN         NaN            NaN  \n",
-       "7          NaN   NaN       NaN         NaN            NaN  \n",
-       "8          NaN   NaN       NaN         NaN            NaN  \n",
-       "9          NaN   NaN       NaN         NaN            NaN  \n",
-       "10         NaN   NaN       NaN         NaN            NaN  \n",
-       "11         NaN   NaN       NaN         NaN            NaN  \n",
-       "12         NaN   NaN       NaN         NaN            NaN  \n",
-       "13         NaN   NaN       NaN         NaN            NaN  \n",
-       "14         NaN   NaN       NaN         NaN            NaN  \n",
-       "15         NaN   NaN       NaN         NaN            NaN  \n",
-       "16         NaN   NaN       NaN         NaN            NaN  \n",
-       "17         NaN   NaN       NaN         NaN            NaN  "
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "from mlxtend.frequent_patterns import association_rules\n",
     "\n",
@@ -1547,175 +389,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": null,
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<div>\n",
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-       "\n",
-       "    .dataframe thead th {\n",
-       "        text-align: right;\n",
-       "    }\n",
-       "</style>\n",
-       "<table border=\"1\" class=\"dataframe\">\n",
-       "  <thead>\n",
-       "    <tr style=\"text-align: right;\">\n",
-       "      <th></th>\n",
-       "      <th>antecedents</th>\n",
-       "      <th>consequents</th>\n",
-       "      <th>support</th>\n",
-       "    </tr>\n",
-       "  </thead>\n",
-       "  <tbody>\n",
-       "    <tr>\n",
-       "      <th>0</th>\n",
-       "      <td>(176)</td>\n",
-       "      <td>(177)</td>\n",
-       "      <td>0.253623</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>1</th>\n",
-       "      <td>(177)</td>\n",
-       "      <td>(176)</td>\n",
-       "      <td>0.253623</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2</th>\n",
-       "      <td>(179)</td>\n",
-       "      <td>(177)</td>\n",
-       "      <td>0.253623</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>3</th>\n",
-       "      <td>(177)</td>\n",
-       "      <td>(179)</td>\n",
-       "      <td>0.253623</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>4</th>\n",
-       "      <td>(178)</td>\n",
-       "      <td>(176)</td>\n",
-       "      <td>0.217391</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>5</th>\n",
-       "      <td>(176)</td>\n",
-       "      <td>(178)</td>\n",
-       "      <td>0.217391</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>6</th>\n",
-       "      <td>(179)</td>\n",
-       "      <td>(176)</td>\n",
-       "      <td>0.217391</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>7</th>\n",
-       "      <td>(176)</td>\n",
-       "      <td>(179)</td>\n",
-       "      <td>0.217391</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>8</th>\n",
-       "      <td>(100)</td>\n",
-       "      <td>(93)</td>\n",
-       "      <td>0.181159</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>9</th>\n",
-       "      <td>(93)</td>\n",
-       "      <td>(100)</td>\n",
-       "      <td>0.181159</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>10</th>\n",
-       "      <td>(178)</td>\n",
-       "      <td>(177)</td>\n",
-       "      <td>0.108696</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>11</th>\n",
-       "      <td>(177)</td>\n",
-       "      <td>(178)</td>\n",
-       "      <td>0.108696</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>12</th>\n",
-       "      <td>(178, 176)</td>\n",
-       "      <td>(177)</td>\n",
-       "      <td>0.108696</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>13</th>\n",
-       "      <td>(178, 177)</td>\n",
-       "      <td>(176)</td>\n",
-       "      <td>0.108696</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>14</th>\n",
-       "      <td>(177, 176)</td>\n",
-       "      <td>(178)</td>\n",
-       "      <td>0.108696</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>15</th>\n",
-       "      <td>(178)</td>\n",
-       "      <td>(177, 176)</td>\n",
-       "      <td>0.108696</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>16</th>\n",
-       "      <td>(176)</td>\n",
-       "      <td>(178, 177)</td>\n",
-       "      <td>0.108696</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>17</th>\n",
-       "      <td>(177)</td>\n",
-       "      <td>(178, 176)</td>\n",
-       "      <td>0.108696</td>\n",
-       "    </tr>\n",
-       "  </tbody>\n",
-       "</table>\n",
-       "</div>"
-      ],
-      "text/plain": [
-       "   antecedents consequents   support\n",
-       "0        (176)       (177)  0.253623\n",
-       "1        (177)       (176)  0.253623\n",
-       "2        (179)       (177)  0.253623\n",
-       "3        (177)       (179)  0.253623\n",
-       "4        (178)       (176)  0.217391\n",
-       "5        (176)       (178)  0.217391\n",
-       "6        (179)       (176)  0.217391\n",
-       "7        (176)       (179)  0.217391\n",
-       "8        (100)        (93)  0.181159\n",
-       "9         (93)       (100)  0.181159\n",
-       "10       (178)       (177)  0.108696\n",
-       "11       (177)       (178)  0.108696\n",
-       "12  (178, 176)       (177)  0.108696\n",
-       "13  (178, 177)       (176)  0.108696\n",
-       "14  (177, 176)       (178)  0.108696\n",
-       "15       (178)  (177, 176)  0.108696\n",
-       "16       (176)  (178, 177)  0.108696\n",
-       "17       (177)  (178, 176)  0.108696"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "res = res[['antecedents', 'consequents', 'support']]\n",
     "res"
@@ -1738,156 +414,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": null,
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<div>\n",
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-       "\n",
-       "    .dataframe thead th {\n",
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-       "</style>\n",
-       "<table border=\"1\" class=\"dataframe\">\n",
-       "  <thead>\n",
-       "    <tr style=\"text-align: right;\">\n",
-       "      <th></th>\n",
-       "      <th>antecedents</th>\n",
-       "      <th>consequents</th>\n",
-       "      <th>antecedent support</th>\n",
-       "      <th>consequent support</th>\n",
-       "      <th>support</th>\n",
-       "      <th>confidence</th>\n",
-       "      <th>lift</th>\n",
-       "      <th>leverage</th>\n",
-       "      <th>conviction</th>\n",
-       "      <th>zhangs_metric</th>\n",
-       "    </tr>\n",
-       "  </thead>\n",
-       "  <tbody>\n",
-       "    <tr>\n",
-       "      <th>0</th>\n",
-       "      <td>(Eggs)</td>\n",
-       "      <td>(Onion)</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.75</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>1.6</td>\n",
-       "      <td>1.0</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>1</th>\n",
-       "      <td>(Onion)</td>\n",
-       "      <td>(Eggs)</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>1.00</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>inf</td>\n",
-       "      <td>0.5</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2</th>\n",
-       "      <td>(Kidney Beans, Eggs)</td>\n",
-       "      <td>(Onion)</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.75</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>1.6</td>\n",
-       "      <td>1.0</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>3</th>\n",
-       "      <td>(Kidney Beans, Onion)</td>\n",
-       "      <td>(Eggs)</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>1.00</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>inf</td>\n",
-       "      <td>0.5</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>4</th>\n",
-       "      <td>(Eggs)</td>\n",
-       "      <td>(Kidney Beans, Onion)</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.75</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>1.6</td>\n",
-       "      <td>1.0</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>5</th>\n",
-       "      <td>(Onion)</td>\n",
-       "      <td>(Kidney Beans, Eggs)</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>1.00</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>inf</td>\n",
-       "      <td>0.5</td>\n",
-       "    </tr>\n",
-       "  </tbody>\n",
-       "</table>\n",
-       "</div>"
-      ],
-      "text/plain": [
-       "             antecedents            consequents  antecedent support  \\\n",
-       "0                 (Eggs)                (Onion)                 0.8   \n",
-       "1                (Onion)                 (Eggs)                 0.6   \n",
-       "2   (Kidney Beans, Eggs)                (Onion)                 0.8   \n",
-       "3  (Kidney Beans, Onion)                 (Eggs)                 0.6   \n",
-       "4                 (Eggs)  (Kidney Beans, Onion)                 0.8   \n",
-       "5                (Onion)   (Kidney Beans, Eggs)                 0.6   \n",
-       "\n",
-       "   consequent support  support  confidence  lift  leverage  conviction  \\\n",
-       "0                 0.6      0.6        0.75  1.25      0.12         1.6   \n",
-       "1                 0.8      0.6        1.00  1.25      0.12         inf   \n",
-       "2                 0.6      0.6        0.75  1.25      0.12         1.6   \n",
-       "3                 0.8      0.6        1.00  1.25      0.12         inf   \n",
-       "4                 0.6      0.6        0.75  1.25      0.12         1.6   \n",
-       "5                 0.8      0.6        1.00  1.25      0.12         inf   \n",
-       "\n",
-       "   zhangs_metric  \n",
-       "0            1.0  \n",
-       "1            0.5  \n",
-       "2            1.0  \n",
-       "3            0.5  \n",
-       "4            1.0  \n",
-       "5            0.5  "
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import pandas as pd\n",
     "from mlxtend.preprocessing import TransactionEncoder\n",
@@ -1919,140 +448,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": null,
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<div>\n",
-       "<style scoped>\n",
-       "    .dataframe tbody tr th:only-of-type {\n",
-       "        vertical-align: middle;\n",
-       "    }\n",
-       "\n",
-       "    .dataframe tbody tr th {\n",
-       "        vertical-align: top;\n",
-       "    }\n",
-       "\n",
-       "    .dataframe thead th {\n",
-       "        text-align: right;\n",
-       "    }\n",
-       "</style>\n",
-       "<table border=\"1\" class=\"dataframe\">\n",
-       "  <thead>\n",
-       "    <tr style=\"text-align: right;\">\n",
-       "      <th></th>\n",
-       "      <th>antecedents</th>\n",
-       "      <th>consequents</th>\n",
-       "      <th>antecedent support</th>\n",
-       "      <th>consequent support</th>\n",
-       "      <th>support</th>\n",
-       "      <th>confidence</th>\n",
-       "      <th>lift</th>\n",
-       "      <th>leverage</th>\n",
-       "      <th>conviction</th>\n",
-       "      <th>zhangs_metric</th>\n",
-       "    </tr>\n",
-       "  </thead>\n",
-       "  <tbody>\n",
-       "    <tr>\n",
-       "      <th>0</th>\n",
-       "      <td>(Eggs)</td>\n",
-       "      <td>(Onion)</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.75</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>1.6</td>\n",
-       "      <td>1.0</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>1</th>\n",
-       "      <td>(Onion)</td>\n",
-       "      <td>(Eggs)</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>1.00</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>inf</td>\n",
-       "      <td>0.5</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2</th>\n",
-       "      <td>(Kidney Beans, Eggs)</td>\n",
-       "      <td>(Onion)</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.75</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>1.6</td>\n",
-       "      <td>1.0</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>4</th>\n",
-       "      <td>(Eggs)</td>\n",
-       "      <td>(Kidney Beans, Onion)</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.75</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>1.6</td>\n",
-       "      <td>1.0</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>5</th>\n",
-       "      <td>(Onion)</td>\n",
-       "      <td>(Kidney Beans, Eggs)</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>0.8</td>\n",
-       "      <td>0.6</td>\n",
-       "      <td>1.00</td>\n",
-       "      <td>1.25</td>\n",
-       "      <td>0.12</td>\n",
-       "      <td>inf</td>\n",
-       "      <td>0.5</td>\n",
-       "    </tr>\n",
-       "  </tbody>\n",
-       "</table>\n",
-       "</div>"
-      ],
-      "text/plain": [
-       "            antecedents            consequents  antecedent support  \\\n",
-       "0                (Eggs)                (Onion)                 0.8   \n",
-       "1               (Onion)                 (Eggs)                 0.6   \n",
-       "2  (Kidney Beans, Eggs)                (Onion)                 0.8   \n",
-       "4                (Eggs)  (Kidney Beans, Onion)                 0.8   \n",
-       "5               (Onion)   (Kidney Beans, Eggs)                 0.6   \n",
-       "\n",
-       "   consequent support  support  confidence  lift  leverage  conviction  \\\n",
-       "0                 0.6      0.6        0.75  1.25      0.12         1.6   \n",
-       "1                 0.8      0.6        1.00  1.25      0.12         inf   \n",
-       "2                 0.6      0.6        0.75  1.25      0.12         1.6   \n",
-       "4                 0.6      0.6        0.75  1.25      0.12         1.6   \n",
-       "5                 0.8      0.6        1.00  1.25      0.12         inf   \n",
-       "\n",
-       "   zhangs_metric  \n",
-       "0            1.0  \n",
-       "1            0.5  \n",
-       "2            1.0  \n",
-       "4            1.0  \n",
-       "5            0.5  "
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "antecedent_sele = rules['antecedents'] == frozenset({'Onion', 'Kidney Beans'}) # or  frozenset({'Kidney Beans', 'Onion'})\n",
     "consequent_sele = rules['consequents'] == frozenset({'Eggs'})\n",
@@ -2096,7 +494,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.6"
+   "version": "3.11.9"
   },
   "toc": {
    "nav_menu": {},
diff --git a/mlxtend/frequent_patterns/association_rules.py b/mlxtend/frequent_patterns/association_rules.py
index bcd24348..16cba9b3 100644
--- a/mlxtend/frequent_patterns/association_rules.py
+++ b/mlxtend/frequent_patterns/association_rules.py
@@ -13,8 +13,28 @@ from itertools import combinations
 import numpy as np
 import pandas as pd
 
-
-def association_rules(df, metric="confidence", min_threshold=0.8, support_only=False):
+_metrics = [
+    "antecedent support",
+    "consequent support",
+    "support",
+    "confidence",
+    "lift",
+    "leverage",
+    "conviction",
+    "zhangs_metric",
+    "jaccard",
+    "certainty",
+    "kulczynski",
+]
+
+
+def association_rules(
+    df: pd.DataFrame,
+    metric="confidence",
+    min_threshold=0.8,
+    support_only=False,
+    return_metrics: list = _metrics,
+) -> pd.DataFrame:
     """Generates a DataFrame of association rules including the
     metrics 'score', 'confidence', and 'lift'
 
@@ -91,6 +111,12 @@ def association_rules(df, metric="confidence", min_threshold=0.8, support_only=F
                          columns 'support' and 'itemsets'"
         )
 
+    def kulczynski_helper(sAC, sA, sC):
+        conf_AC = sAC / sA
+        conf_CA = sAC / sC
+        kulczynski = (conf_AC + conf_CA) / 2
+        return kulczynski
+
     def conviction_helper(sAC, sA, sC):
         confidence = sAC / sA
         conviction = np.empty(confidence.shape, dtype=float)
@@ -117,6 +143,20 @@ def association_rules(df, metric="confidence", min_threshold=0.8, support_only=F
 
         return zhangs_metric
 
+    def jaccard_metric_helper(sAC, sA, sC):
+        numerator = metric_dict["support"](sAC, sA, sC)
+        denominator = sA + sC - numerator
+
+        jaccard_metric = numerator / denominator
+        return jaccard_metric
+
+    def certainty_metric_helper(sAC, sA, sC):
+        certainty_num = metric_dict["confidence"](sAC, sA, sC) - sC
+        certainty_denom = 1 - sC
+
+        cert_metric = np.where(certainty_denom == 0, 0, certainty_num / certainty_denom)
+        return cert_metric
+
     # metrics for association rules
     metric_dict = {
         "antecedent support": lambda _, sA, __: sA,
@@ -127,19 +167,11 @@ def association_rules(df, metric="confidence", min_threshold=0.8, support_only=F
         "leverage": lambda sAC, sA, sC: metric_dict["support"](sAC, sA, sC) - sA * sC,
         "conviction": lambda sAC, sA, sC: conviction_helper(sAC, sA, sC),
         "zhangs_metric": lambda sAC, sA, sC: zhangs_metric_helper(sAC, sA, sC),
+        "jaccard": lambda sAC, sA, sC: jaccard_metric_helper(sAC, sA, sC),
+        "certainty": lambda sAC, sA, sC: certainty_metric_helper(sAC, sA, sC),
+        "kulczynski": lambda sAC, sA, sC: kulczynski_helper(sAC, sA, sC),
     }
 
-    columns_ordered = [
-        "antecedent support",
-        "consequent support",
-        "support",
-        "confidence",
-        "lift",
-        "leverage",
-        "conviction",
-        "zhangs_metric",
-    ]
-
     # check for metric compliance
     if support_only:
         metric = "support"
@@ -200,7 +232,7 @@ def association_rules(df, metric="confidence", min_threshold=0.8, support_only=F
 
     # check if frequent rule was generated
     if not rule_supports:
-        return pd.DataFrame(columns=["antecedents", "consequents"] + columns_ordered)
+        return pd.DataFrame(columns=["antecedents", "consequents"] + return_metrics)
 
     else:
         # generate metrics
@@ -212,7 +244,7 @@ def association_rules(df, metric="confidence", min_threshold=0.8, support_only=F
 
         if support_only:
             sAC = rule_supports[0]
-            for m in columns_ordered:
+            for m in return_metrics:
                 df_res[m] = np.nan
             df_res["support"] = sAC
 
@@ -220,7 +252,7 @@ def association_rules(df, metric="confidence", min_threshold=0.8, support_only=F
             sAC = rule_supports[0]
             sA = rule_supports[1]
             sC = rule_supports[2]
-            for m in columns_ordered:
+            for m in return_metrics:
                 df_res[m] = metric_dict[m](sAC, sA, sC)
 
         return df_res


Test patch:
diff --git a/mlxtend/frequent_patterns/tests/test_association_rules.py b/mlxtend/frequent_patterns/tests/test_association_rules.py
index c2850924..1035183c 100644
--- a/mlxtend/frequent_patterns/tests/test_association_rules.py
+++ b/mlxtend/frequent_patterns/tests/test_association_rules.py
@@ -46,9 +46,13 @@ columns_ordered = [
     "leverage",
     "conviction",
     "zhangs_metric",
+    "jaccard",
+    "certainty",
+    "kulczynski",
 ]
 
 
+# fmt: off
 def test_default():
     res_df = association_rules(df_freq_items)
     res_df["antecedents"] = res_df["antecedents"].apply(lambda x: str(frozenset(x)))
@@ -58,16 +62,17 @@ def test_default():
 
     expect = pd.DataFrame(
         [
-            [(8,), (5,), 0.6, 1.0, 0.6, 1.0, 1.0, 0.0, np.inf, 0],
-            [(6,), (5,), 0.6, 1.0, 0.6, 1.0, 1.0, 0.0, np.inf, 0],
-            [(8, 3), (5,), 0.6, 1.0, 0.6, 1.0, 1.0, 0.0, np.inf, 0],
-            [(8, 5), (3,), 0.6, 0.8, 0.6, 1.0, 1.25, 0.12, np.inf, 0.5],
-            [(8,), (3, 5), 0.6, 0.8, 0.6, 1.0, 1.25, 0.12, np.inf, 0.5],
-            [(3,), (5,), 0.8, 1.0, 0.8, 1.0, 1.0, 0.0, np.inf, 0],
-            [(5,), (3,), 1.0, 0.8, 0.8, 0.8, 1.0, 0.0, 1.0, 0],
-            [(10,), (5,), 0.6, 1.0, 0.6, 1.0, 1.0, 0.0, np.inf, 0],
-            [(8,), (3,), 0.6, 0.8, 0.6, 1.0, 1.25, 0.12, np.inf, 0.5],
+            [(8,), (5,), 0.6, 1.0, 0.6, 1.0, 1.0, 0.0, np.inf, 0, 0.6, 0.0, 0.8],
+            [(6,), (5,), 0.6, 1.0, 0.6, 1.0, 1.0, 0.0, np.inf, 0, 0.6, 0.0, 0.8],
+            [(8, 3), (5,), 0.6, 1.0, 0.6, 1.0, 1.0, 0.0, np.inf, 0, 0.6, 0.0, 0.8],
+            [(8, 5), (3,), 0.6, 0.8, 0.6, 1.0, 1.25, 0.12, np.inf, 0.5, 0.75, 1.0, 0.875],
+            [(8,), (3, 5), 0.6, 0.8, 0.6, 1.0, 1.25, 0.12, np.inf, 0.5, 0.75, 1.0, 0.875],
+            [(3,), (5,), 0.8, 1.0, 0.8, 1.0, 1.0, 0.0, np.inf, 0, 0.8, 0.0, 0.9],
+            [(5,), (3,), 1.0, 0.8, 0.8, 0.8, 1.0, 0.0, 1.0, 0.0, 0.8, 0.0, 0.9],
+            [(10,), (5,), 0.6, 1.0, 0.6, 1.0, 1.0, 0.0, np.inf, 0, 0.6, 0.0, 0.8],
+            [(8,), (3,), 0.6, 0.8, 0.6, 1.0, 1.25, 0.12, np.inf, 0.5, 0.75, 1.0, 0.875],
         ],
+
         columns=columns_ordered,
     )
 
@@ -75,8 +80,8 @@ def test_default():
     expect["consequents"] = expect["consequents"].apply(lambda x: str(frozenset(x)))
     expect.sort_values(columns_ordered, inplace=True)
     expect.reset_index(inplace=True, drop=True)
-
     assert res_df.equals(expect), res_df
+# fmt: on
 
 
 def test_datatypes():
@@ -130,6 +135,9 @@ def test_empty_result():
             "leverage",
             "conviction",
             "zhangs_metric",
+            "jaccard",
+            "certainty",
+            "kulczynski",
         ]
     )
     res_df = association_rules(df_freq_items, min_threshold=2)
@@ -176,6 +184,36 @@ def test_confidence():
     assert res_df.values.shape[0] == 9
 
 
+def test_jaccard():
+    res_df = association_rules(df_freq_items, min_threshold=0.7, metric="jaccard")
+    assert res_df.values.shape[0] == 8
+
+    res_df = association_rules(
+        df_freq_items_with_colnames, min_threshold=0.7, metric="jaccard"
+    )
+    assert res_df.values.shape[0] == 8
+
+
+def test_certainty():
+    res_df = association_rules(df_freq_items, metric="certainty", min_threshold=0.6)
+    assert res_df.values.shape[0] == 3
+
+    res_df = association_rules(
+        df_freq_items_with_colnames, metric="certainty", min_threshold=0.6
+    )
+    assert res_df.values.shape[0] == 3
+
+
+def test_kulczynski():
+    res_df = association_rules(df_freq_items, metric="kulczynski", min_threshold=0.9)
+    assert res_df.values.shape[0] == 2
+
+    res_df = association_rules(
+        df_freq_items_with_colnames, metric="kulczynski", min_threshold=0.6
+    )
+    assert res_df.values.shape[0] == 16
+
+
 def test_frozenset_selection():
     res_df = association_rules(df_freq_items)