{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline\n", "import pandas as pd\n", "\n", "import numpy as np\n", "from __future__ import division\n", "import itertools\n", "\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "plt.rcParams['axes.grid'] = False\n", "\n", "import logging\n", "logger = logging.getLogger()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "6 Frequent Itemsets\n", "===========" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "### 6.1 The Market-Basket Model\n", "Each **Basket** consists of a set of **items**(an itemset) \n", "\n", "+ The number of items in a basket is small.\n", "\n", "+ The number of baskets is usually very large.\n", "\n", "+ Basket are sets, and in priciple items can appear only once.\n", "\n", "\n", "##### Definition of Frequent Itemses\n", "a set of items that appears in many baskets is said to be \"frequent\".\n", "\n", "**support**: if ${I}$ is a set of items, the support of ${I}$ is the number of baskets for which I is a subset.\n", "\n", "Assume $s$ is the support threshold, then we say ${I}$ is frequent if its support is $s$ or more." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " training a and cat\n", "dog 4,6 2,3,7 1,2,7,8 1,2,3,6,7\n", "cat 5,6 2,3,7 1,2,5,7 NaN\n", "and 5 2,7 NaN NaN\n", "a NaN NaN NaN" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "logger.setLevel('WARN')\n", "\n", "data_raw = [\n", " ['Cat', 'and', 'dog', 'bites'],\n", " ['Yahoo', 'news', 'claims', 'a', 'cat', 'mated', 'with', 'a', 'dog', 'and', 'produced', 'viable', 'offspring'],\n", " ['Cat', 'killer', 'likely', 'is', 'a', 'big', 'dog'],\n", " ['Professional', 'free', 'advice', 'on', 'dog', 'training', 'puppy', 'training'],\n", " ['Cat', 'and', 'kitten', 'training', 'and', 'behavior'],\n", " ['Dog', '&', 'Cat', 'provides', 'dog', 'training', 'in', 'Eugene', 'Oregon'],\n", " ['Dog', 'and', 'cat', 'is', 'a', 'slang', 'term', 'used', 'by', 'police', 'officers', 'for', 'a', 'male-female', 'relationship'],\n", " ['Shop', 'for', 'your', 'show', 'dog', 'grooming', 'and', 'pet', 'supplies']\n", "]\n", "\n", "data = [set(map(str.lower, x)) for x in data_raw]\n", "data = pd.Series(data)\n", "\n", "def calc_occurrence_of_doubletons(df, data):\n", " logger.info('df: \\n{}\\n'.format(df))\n", " for i_ in df.index:\n", " for c_ in df.columns:\n", " if not np.isnan(df.loc[i_,c_]):\n", " key = {i_, c_}\n", " ind_ = [ind+1 for ind, is_in in enumerate(data.apply(lambda x: key.issubset(x))) if is_in]\n", " df.loc[i_,c_] = ','.join([str(x) for x in ind_]) \n", " return df\n", "\n", "mask = [\n", " [1, 1, 1, 1],\n", " [1, 1, 1, np.nan],\n", " [1, 1, np.nan, np.nan],\n", " [1, np.nan, np.nan, np.nan]\n", "]\n", "df = pd.DataFrame(mask, index=['dog', 'cat', 'and', 'a'], columns=['training', 'a', 'and', 'cat'])\n", "calc_occurrence_of_doubletons(df, data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### applications\n", "1. Related concepts\n", "\n", "2. Plagiarism\n", "\n", "3. Biomarkers" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 6.1.3 Associaton Rules\n", "an association rule $I \\to j$: \n", "if all of the items in $I$ appear in some basket, then $j$ is \"likely\" to appear in that basket as well.\n", "\n", "**confidence**: $$\\text{confidence}(I \\to j) = \\frac{\\text{support}(I \\cup \\{j\\})}{\\text{support}(I)}$$\n", "\n", "**interest**: $$\\text{interest}(I \\to j) = \\text{confience}(I \\to j) - \\frac{\\text{support}(j)}{m}$$ where $m$ is the number of all baskets.\n", "\n", "\n", "##### Finding Association Rules with High Confidence\n", "if $j$ is a set of $n$ items that is found to be frequent, then we have $n$ candidates: $J - \\{j\\} \\to j$ for each $j$ in $J$. Then their confidence can be calculated.\n", "\n", "cons: assumed that there are not too many frequent itemsets, since each one found must be acted upon. \n", "solution: adjust the support threshold $s$ so that we do not get too many frequent itemsets." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### 6.1.5 Exercise for Section 6.1\n", "略" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 6.2 Market Baskets and the A-Priori Algorithm\n", "#### 6.2.1 Representation of Market-Basket Data\n", "We assume that: \n", "+ market-basket data is stored in a file basket-by-basket. \n", "+ the size of the file of baskets is sufficiently large that it doesn't fit in main memory. \n", "+ a major cost of any algorithm is the time it takes to read the baskets from disk. \n", " Why we miss the time it takes to generate all the subsets of size $k$? \n", " 1. $k$ is usually small, never grows beyond 2 or 3. \n", " 2. It's possible to eliminate many of items in procession. \n", " \n", " Measure: only the number of passes taken by the algorithm matters." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 6.2.2 Use of Main Memory for Itemset Counting\n", "Each algorithm has a limit on how many items it can deal with.\n", "\n", "##### Coding items as integers\n", "In general, we need a hash table that translates items as they appear in the file to integers.\n", "\n", "##### Count a pair $\\{i,j\\}$\n", "1. The Triangular-Matrix Method \n", " + Use the entry $a[i,j]$ in a two-dimensional array. \n", " make half the array __useless__. \n", " + Use a one-dimensional triangular array. \n", " We store in $a[k]$ the count for the pair $\\{i,j\\}$, where $k = (i-1)(n-\\frac{i}{2}) + (j-i), \\, 1 \\leq i < j \\leq n$.\n", "\n", "2. The Triples Method \n", "We can store counts as triples $[i,j,c]$. \n", "eg. a hash table with $i$ and $j$ as the search key.\n", "\n", "pros: don't store anything if a pair counts 0. \n", "cons: store 3 integers for every pair.\n", "\n", "###### comparison\n", "use the triangular matrix if at least 1/3 of the $C_n^2$ possible pairs actually appear in some basket. \n", "use the triples method if significatly fewer than 1/3 of the possible pairs occur.\n", "\n", "We might be better off using the triples method, because it would be normal to be a sufficiently uneven distribution of items even if the were ten or a hundred times as many baskets." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 6.2.3 Monotonicity of Itemsets\n", "__monotonicity__ for itemsets: \n", "If a set $I$ of items is frequent, then so it every subsets of $I$.\n", "\n", "If we are given a support threshold $s$, then we say an itemset is __maximal__ if no superset is frequent." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 6.2.4 Tyranny of Counting Pairs\n", "The number of items is rarely so large we cannot count all the singleton sets in main memory at the same time, while it would be impossible to count the larger sets - triples, quadruples, since $C_n^k$ - the number of them - is too large." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 6.2.5 The A-Priori Algorithm\n", "to avoid counting many triples or larger sets.\n", "\n", "1. The First Pass\n", " two tables: one is used to translate item names to integers, and another one is used to count.\n", " \n", "2. Between the Passes \n", " we get frequent sets after we set the threshold $s$.\n", " \n", "3. The Second Pass \n", " We count all pairs of the frequent sets as follows: \n", " 1. For each basket, identify its frequent items in frequent sets. \n", " 2. Generate all pairs. of its frequent items. \n", " 3. Add one for each pairs above." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 6.2.6 A-Priori for All Frequent Itemsets" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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U3RQqG9z+tWlRcGTTAhpPu8akflsYF7OJgSPeIvDF+Vo8kkJtg29YBP/sd27MvMGP6zbj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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(plt.imread('./res/fig6_4.png'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 6.2.7 Exercises for Section 6.2\n", "略" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 6.3 Handling Larger Datasets in Main Memory\n", "A-Priori Algorithm: the greatest requirement for main memory when counting of $C_2$. $\\to$ **idea**: cut down on the size of $C_2$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 6.3.1 The Algorithm of Park, Chen and Yu (PCY)\n", "1. 1st pass: \n", " + count single item $C_1$. \n", " + hash each pairs in the basket to the bucket, and add 1.\n", " \n", "2. during pass: \n", " + filter frequent items $L_1$. \n", " + filter frequent buckets. $to$ summaried as a *bitmap*. \n", " \n", "3. $C_2$, pairs ${i,j}$: \n", " 1. $i$ and $j$ are frequent items. \n", " 2. ${i,j}$ hashes to a frequent bucket. \n", " \n", "pros: $C_2 \\downarrow$. \n", "cons: cannot renumber $1,\\dotsc,m$ $\\to$ cannot use triangular matrix $\\to$ **ONLY use the triple method**." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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HibM3ZREDkSpFBN7gzLUHlg4jdfrDmVqr1aKzsgaeoMlelDp1alAqrwtXkhbO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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(plt.imread('./res/fig6_5.png'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 6.3.2 The Multistage Algorithm\n", "It improves upon PCA by using several *successive* hash tables to reduce further the number of candidate pairs. \n", "\n", "1. 1st pass is the same as of PCY.\n", "\n", "2. 2nd pass: \n", " We hash ${i,j}$ if and only if: \n", " + $i$ and $j$ are both frequent. \n", " + ${i,j}$ hashed to a frequent bucket of $B_1$ on the 1st pass. \n", " \n", " Then summarized as a bitmap $B_2$.\n", " \n", "3. $C_2$ pairs ${i,j}$: \n", " + $i$ and $j$ are both frequent items. \n", " + ${i,j}$ hashed to a frequent bucket in $B_1$.\n", " + ${i,j}$ hashed to a frequent bucket in $B_2$ as well.\n", " \n", "Attention: \n", "Each pass must store the bitmaps, eventually, there is not enough space left to count if used too many stages." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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YH+g2/HPWzxiOd9gYPiwewpBB45Hdm9K3tRWTxkznqPdhXCwM2NgWoaB9Fj0M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V+/cbFo/Rg/5XXGvLyVLP0YqrnaYSk4xsGTTanmf5Yr93opx3ewfn8sLYY9TVNNOsv+3ILGswaD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\nuHh4cuWTm9vt2kc1e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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(plt.imread('./res/fig6_6.png'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 6.3.3 The Multihash Algorithm\n", "use two hash functions and two seperate hash tables on the 1st pass.\n", "\n", "The danger of using two hash tables on one pass is that each hash table has half as many buckets as the one large hash table of PCY. $\\implies$ the average count of a bucket for PCY is much lower than the support threshold.\n", "\n", "$C_2$: $i$ and $j$ must both be frequent, and the pair must have hashed to a frequent bucket according to both hash tables.\n", "\n", "The **risk** is that should we use too many hash tables, the average count for a bucket will exceed the support threshold. \n", "$\\implies$ the probability an infrequent pair will be a candidate rises, rather than falls, if we add another hash table." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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oXw/4iosHmvDsXji/r5yHm6MN3ZvVoP6gxoTXrUrZojYEOz7j1JZlDN9vxDZw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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(plt.imread('./res/fig6_7.png'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 6.3.4 Exercises for Section 6.3\n", "#maybe" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 6.4 Limited-Pass Algorithms\n", "Main memory is too small. $to$ $k$ passes to compute. \n", "solution: it's not essential to discover every frequent itemset. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 6.4.1 The Simple, Randomized Algorithm\n", "to pick a random subset of the baskets and adjust the support thresold.\n", "\n", "The *safety* way: \n", "read the entire dataset one by one, \n", "and for each basket, select that basket for the sample with some fixed probility $p$.\n", "\n", "##### Avoiding Errors\n", "eliminate False Positives: making a pass through the full datasets and counting all the candidates to check. \n", "\n", "reduce False Negatives: \n", "use smaller threshold for the samples, such as $0.9ps$, and so push more itemsets to be checked. \n", "cons: need more main memory." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 6.4.3 The Algorithm of Savasere, Omiecinski, and Navathe(SON)\n", "Avoid both Fasle Negatives and False Positives, at the cost of making two full passes.\n", "\n", "1. 1st pass to find candidates. \n", " 1. Divide the input files into chunks. \n", " 2. Treat each chunks as sample, use $ps$ as the thresold. \n", " 3. *candidate* itemsets: the union of all the itemsets that have been found frequent for *one or more* chunks. \n", " idea: every itemset that's frequent in the whole is frequent in at least one chunk.\n", " \n", "2. 2nd pass to count all the candidates and check.\n", "\n", "\n", "##### The SON Algorithm and MapReduces\n", "1. First Map Function: $(F,1)$, where $F$ is a frequent itemset from the sample. \n", "\n", "2. First Reduce Function: combine all the $F$ to construct the candidate itemsets.\n", "\n", "3. Second Map Function: $(C,v)$, where $C$ is one of the candidate sets and $v$ is the support.\n", "\n", "4. Second Reduce Function: Sum and filter out the frequent itemsets." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 6.4.5 Toivonen's Algorithm\n", "pass over a small sample and one full pass over the data. \n", "avoid both FN and FP, but there is a small probability that it will fail to produce any answer at all.\n", "\n", "1. 1st pass: candidates \n", " 1. select a small sample. \n", " 2. use a smaller threshold, such as $0.9ps$, to find candidate frequent itemsets $F$. \n", " 3. construct the *negative border*($N$): \n", " They are not frequent in the sample, but all of their *immediate subsets*(subsets constructed by deleting exactly one item) are frequent in the sample.\n", " \n", "2. 2nd pass: check, counting all $F$ and $N$. \n", " + if no member of $N$ is frequent in the whole datasets. $to$ output the $F$. \n", " + otherwise, give no answer and resample again.\n", " \n", "##### Why it works.\n", "1. eliminate FP $gets$ check in the full datasets. \n", "\n", "2. eliminate FN(namely, find all *real* frequent itemset in the *sample*): \n", " Proof: \n", " When no member of the $N$ is frequent in the whole, \n", " there can be no itemset $S$ whatsoever that is:\n", " 1. Frequent in the whole, but \n", " 2. In neither $N$ or $F$.\n", " \n", " Proof by Contradiction: \n", " Suppose $S$ exist, but the algorithm gives OUTPUT when no member of the $N$ is frequent in the whole. \n", " \n", " Let $T$ be a subset of $S$ that is of the smallest possible size among all subsets of $S$ that are not frequent in the sample. \n", " + smallest $to$ all of its immediate subsets are frequent. \n", " + $T$ is not frequent. \n", " So, $T \\in N$. \n", " While $T$ is frequent in the whold datasets, $\\to$ fail to answer. CONTRATY with output." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### 6.4.7 Exercises for Section 6.4\n", "略" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 6.5 Counting Frequent Items in a Stream\n", "For stream, we must think of the support threshold $s$ as a fraction of the baskets in which an itemset must appear in order to be considered frequent." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 6.5.1 Sampling Methods for Streams\n", "When the frquent-itemsets algorithm finishes, we have an estimate of the frequent itemsets in the stream. \n", "Then we have several options:\n", "\n", "1. Use the collection at handy, but start running another iteration immediately.\n", "\n", "2. Continue to count the frequent itemsets, and \n", " + drop someone when they reach below $s$, \n", " + add new frequent itemsets. \n", " eg: \n", " + Periodically gather. \n", " + Add negative border.(most potential itemsets)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 6.5.2 Frequent Itemsets in Decaying Windows\n", "a decaying window on a stream: \n", "1. picking a small constant $c$. \n", "2. giving the $i$th element the weight $(1-c)^i \\approx e^{-ci}$.\n", "\n", "record all items whose score was at least $1/2$.\n", "\n", "##### baskets $\\to$ items\n", "1. unfold directly. $\\{a,b\\}, \\{c,d\\} \\to a, b, c, d$ \n", " cons: We want to find all frequent itemsets, not just singleton itemsets.\n", "\n", "2. Start scoring certain itemsets as soon as we see one instance, but be conservative about which itemsets we start. $gets$ too many counts. \n", " eg: Only start an itemset $I$ if all its immediate subsets are already being scored." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 6.5.3 Hybird Methods\n", "The big disadvantage of decaying window is: \n", "It requires us to maintain scores for each itemset with a score of at least $1/2$, \n", "while limiting by $c$ will force us to accept information that tracks the local fluctuations in frequency too closely.\n", "\n", "Solution: \n", "1. Use sampling method to find candidates and give them initial scores. \n", "2. When the score of an candidate reach upper $s$, then it's collected as frequent-itemsets." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 6.5.4 Exercises for Section 6.5\n", "略" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }