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Thursday, 27 November 2014

Data Mining and Frequent Datasets

I've been doing some work for my exams in a few days and I'm going through some past papers but unfortunately there are no corresponding answers. I've answered the question and I was wondering if someone could tell me if I am correct.

My question is

    (c) A transactional dataset, T, is given below:
    t1: Milk, Chicken, Beer
    t2: Chicken, Cheese
    t3: Cheese, Boots
    t4: Cheese, Chicken, Beer,
    t5: Chicken, Beer, Clothes, Cheese, Milk
    t6: Clothes, Beer, Milk
    t7: Beer, Milk, Clothes

    Assume that minimum support is 0.5 (minsup = 0.5).

    (i) Find all frequent itemsets.

Here is how I worked it out:

    Item : Amount
    Milk : 4
    Chicken : 4
    Beer : 5
    Cheese : 4
    Boots : 1
    Clothes : 3

Now because the minsup is 0.5 you eliminate boots and clothes and make a combo of the remaining giving:

    {items} : Amount
    {Milk, Chicken} : 2
    {Milk, Beer} : 4
    {Milk, Cheese} : 1
    {Chicken, Beer} : 3
    {Chicken, Cheese} : 3
    {Beer, Cheese} : 2

Which leaves milk and beer as the only frequent item set then as it is the only one above the minsup?

data mining


3 Answers

There are two ways to solve the problem:

    using Apriori algorithm
    Using FP counting

Assuming that you are using Apriori, the answer you got is correct.

The algorithm is simple:

First you count frequent 1-item sets and exclude the item-sets below minimum support.

Then count frequent 2-item sets by combining frequent items from previous iteration and exclude the item-sets below support threshold.

The algorithm can go on until no item-sets are greater than threshold.

In the problem given to you, you only get 1 set of 2 items greater than threshold so you can't move further.

There is a solved example of further steps on Wikipedia here.

You can refer "Data Mining Concepts and Techniques" by Han and Kamber for more examples.


There is more than two algorithms to solve this problem. I will just mention a few of them: Apriori, FPGrowth, Eclat, HMine, DCI, Relim, AIM, etc. –  Phil Mar 5 '13 at 7:18

OK to start, you must first understand, data mining (sometimes called data or knowledge discovery) is the process of analyzing data from different perspectives and summarizing it into useful information - information that can be used to increase revenue, cuts costs, or both. Data mining software is one of a number of analytical tools for analyzing data. It allows users to analyze data from many different dimensions or angles, categorize it, and summarize the relationships identified. Technically, data mining is the process of finding correlations or patterns among dozens of fields in large relational databases.

Now, the amount of raw data stored in corporate databases is exploding. From trillions of point-of-sale transactions and credit card purchases to pixel-by-pixel images of galaxies, databases are now measured in gigabytes and terabytes. (One terabyte = one trillion bytes. A terabyte is equivalent to about 2 million books!) For instance, every day, Wal-Mart uploads 20 million point-of-sale transactions to an A&T massively parallel system with 483 processors running a centralized database.

Raw data by itself, however, does not provide much information. In today's fiercely competitive business environment, companies need to rapidly turn these terabytes of raw data into significant insights into their customers and markets to guide their marketing, investment, and management strategies.

Now you must understand that association rule mining is an important model in data mining. Its mining algorithms discover all item associations (or rules) in the data that satisfy the user-specified minimum support (minsup) and minimum confidence (minconf) constraints. Minsup controls the minimum number of data cases that a rule must cover. Minconf controls the predictive strength of the rule.

Since only one minsup is used for the whole database, the model implicitly assumes that all items in the data are of the same nature and/or have similar frequencies in the data. This is, however, seldom the case in real- life applications. In many applications, some items appear very frequently in the data, while others rarely appear. If minsup is set too high, those rules that involve rare items will not be found. To find rules that involve both frequent and rare items, minsup has to be set very low.

This may cause combinatorial explosion because those frequent items will be associated with one another in all possible ways. This dilemma is called the rare item problem. This paper proposes a novel technique to solve this problem. The technique allows the user to specify multiple minimum supports to reflect the natures of the items and their varied frequencies in the database. In rule mining, different rules may need to satisfy different minimum supports depending on what items are in the rules.

Given a set of transactions T (the database), the problem of mining association rules is to discover all association rules that have support and confidence greater than the user-specified minimum support (called minsup) and minimum confidence (called minconf).

I hope that once you understand the very basics of data mining that the answer to this question shall become apparent.


The Apriori algorithm is based on the idea that for a pair o items to be frequent, each individual item should also be frequent. If the hamburguer-ketchup pair is frequent, the hamburger itself must also appear frequently in the baskets. The same can be said about the ketchup.

So for the algorithm, it is established a "threshold X" to define what is or it is not frequent. If an item appears more than X times, it is considered frequent.

The first step of the algorithm is to pass for each item in each basket, and calculate their frequency (count how many time it appears). This can be done with a hash of size N, where the position y of the hash, refers to the frequency of Y.

If item y has a frequency greater than X, it is said to be frequent.

In the second step of the algorithm, we iterate through the items again, computing the frequency of pairs in the baskets. The catch is that we compute only for items that are individually frequent. So if item y and item z are frequent on itselves, we then compute the frequency of the pair. This condition greatly reduces the pairs to compute, and the amount of memory taken.

Once this is calculated, the frequencies greater than the threshold are said frequent itemset.

Source: http://stackoverflow.com/questions/14164853/data-mining-and-frequent-datasets?rq=1

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