1.1. WHAT IS DATA MINING?
3
2. Extracting the most prominent features of the data and ignoring the rest.
We shall explore these two approaches in the following sections.
1.1.4
Summarization
One of the most interesting forms of summarization is the PageRank idea, which
made Google successful and which we shall cover in Chapter 5. In this form
of Web mining, the entire complex structure of the Web is summarized by a
single number for each page. This number, the “PageRank” of the page, is
(oversimplifying somewhat) the probability that a random walker on the graph
would be at that page at any given time. The remarkable property this ranking
has is that it reflects very well the “importance” of the page – the degree to
which typical searchers would like that page returned as an answer to their
search query.
Another important form of summary – clustering – will be covered in Chap-
ter 7. Here, data is viewed as points in a multidimensional space. Points
that are “close” in this space are assigned to the same cluster. The clusters
themselves are summarized, perhaps by giving the centroid of the cluster and
the average distance from the centroid of points in the cluster. These cluster
summaries become the summary of the entire data set.
Example 1.2 :
A famous instance of clustering to solve a problem took place
long ago in London, and it was done entirely without computers.
2
The physician
John Snow, dealing with a Cholera outbreak plotted the cases on a map of the
city. A small illustration suggesting the process is shown in Fig. 1.1.
Figure 1.1: Plotting cholera cases on a map of London
2
See http://en.wikipedia.org/wiki/1854 Broad Street cholera outbreak.
4
CHAPTER 1. DATA MINING
The cases clustered around some of the intersections of roads. These inter-
sections were the locations of wells that had become contaminated; people who
lived nearest these wells got sick, while people who lived nearer to wells that
had not been contaminated did not get sick. Without the ability to cluster the
data, the cause of Cholera would not have been discovered.
✷
1.1.5
Feature Extraction
The typical feature-based model looks for the most extreme examples of a phe-
nomenon and represents the data by these examples. If you are familiar with
Bayes nets, a branch of machine learning and a topic we do not cover in this
book, you know how a complex relationship between objects is represented by
finding the strongest statistical dependencies among these objects and using
only those in representing all statistical connections. Some of the important
kinds of feature extraction from large-scale data that we shall study are:
1. Frequent Itemsets. This model makes sense for data that consists of “bas-
kets” of small sets of items, as in the market-basket problem that we shall
discuss in Chapter 6. We look for small sets of items that appear together
in many baskets, and these “frequent itemsets” are the characterization of
the data that we seek. The original application of this sort of mining was
true market baskets: the sets of items, such as hamburger and ketchup,
that people tend to buy together when checking out at the cash register
of a store or super market.
2. Similar Items. Often, your data looks like a collection of sets, and the
objective is to find pairs of sets that have a relatively large fraction of
their elements in common. An example is treating customers at an on-
line store like Amazon as the set of items they have bought. In order
for Amazon to recommend something else they might like, Amazon can
look for “similar” customers and recommend something many of these
customers have bought. This process is called “collaborative filtering.”
If customers were single-minded, that is, they bought only one kind of
thing, then clustering customers might work. However, since customers
tend to have interests in many different things, it is more useful to find,
for each customer, a small number of other customers who are similar
in their tastes, and represent the data by these connections. We discuss
similarity in Chapter 3.
1.2
Statistical Limits on Data Mining
A common sort of data-mining problem involves discovering unusual events
hidden within massive amounts of data. This section is a discussion of the
problem, including “Bonferroni’s Principle,” a warning against overzealous use
of data mining.
1.2. STATISTICAL LIMITS ON DATA MINING
5
1.2.1
Total Information Awareness
In 2002, the Bush administration put forward a plan to mine all the data it could
find, including credit-card receipts, hotel records, travel data, and many other
kinds of information in order to track terrorist activity. This idea naturally
caused great concern among privacy advocates, and the project, called TIA,
or Total Information Awareness, was eventually killed by Congress, although
it is unclear whether the project in fact exists under another name. It is not
the purpose of this book to discuss the difficult issue of the privacy-security
tradeoff. However, the prospect of TIA or a system like it does raise technical
questions about its feasibility and the realism of its assumptions.
The concern raised by many is that if you look at so much data, and you try
to find within it activities that look like terrorist behavior, are you not going to
find many innocent activities – or even illicit activities that are not terrorism –
that will result in visits from the police and maybe worse than just a visit? The
answer is that it all depends on how narrowly you define the activities that you
look for. Statisticians have seen this problem in many guises and have a theory,
which we introduce in the next section.
1.2.2
Bonferroni’s Principle
Suppose you have a certain amount of data, and you look for events of a cer-
tain type within that data. You can expect events of this type to occur, even if
the data is completely random, and the number of occurrences of these events
will grow as the size of the data grows. These occurrences are “bogus,” in the
sense that they have no cause other than that random data will always have
some number of unusual features that look significant but aren’t. A theorem
of statistics, known as the Bonferroni correction gives a statistically sound way
to avoid most of these bogus positive responses to a search through the data.
Without going into the statistical details, we offer an informal version, Bon-
ferroni’s principle, that helps us avoid treating random occurrences as if they
were real. Calculate the expected number of occurrences of the events you are
looking for, on the assumption that data is random. If this number is signifi-
cantly larger than the number of real instances you hope to find, then you must
expect almost anything you find to be bogus, i.e., a statistical artifact rather
than evidence of what you are looking for. This observation is the informal
statement of Bonferroni’s principle.
In a situation like searching for terrorists, where we expect that there are
few terrorists operating at any one time, Bonferroni’s principle says that we
may only detect terrorists by looking for events that are so rare that they are
unlikely to occur in random data. We shall give an extended example in the
next section.
Dostları ilə paylaş: |