Data Mining_ Concepts and Techniques - Jiawei Han [38]
In our presentation, we have organized attributes into nominal, binary, ordinal, and numeric types. There are many ways to organize attribute types. The types are not mutually exclusive.
Classification algorithms developed from the field of machine learning often talk of attributes as being either discrete or continuous. Each type may be processed differently. A discrete attribute has a finite or countably infinite set of values, which may or may not be represented as integers. The attributes hair_color, smoker, medical_test, and drink_size each have a finite number of values, and so are discrete. Note that discrete attributes may have numeric values, such as 0 and 1 for binary attributes or, the values 0 to 110 for the attribute age. An attribute is countably infinite if the set of possible values is infinite but the values can be put in a one-to-one correspondence with natural numbers. For example, the attribute customer_ID is countably infinite. The number of customers can grow to infinity, but in reality, the actual set of values is countable (where the values can be put in one-to-one correspondence with the set of integers). Zip codes are another example.
If an attribute is not discrete, it is continuous. The terms numeric attribute and continuous attribute are often used interchangeably in the literature. (This can be confusing because, in the classic sense, continuous values are real numbers, whereas numeric values can be either integers or real numbers.) In practice, real values are represented using a finite number of digits. Continuous attributes are typically represented as floating-point variables.
2.2. Basic Statistical Descriptions of Data
For data preprocessing to be successful, it is essential to have an overall picture of your data. Basic statistical descriptions can be used to identify properties of the data and highlight which data values should be treated as noise or outliers.
This section discusses three areas of basic statistical descriptions. We start with measures of central tendency (Section 2.2.1), which measure the location of the middle or center of a data distribution. Intuitively speaking, given an attribute, where do most of its values fall? In particular, we discuss the mean, median, mode, and midrange.
In addition to assessing the central tendency of our data set, we also would like to have an idea of the dispersion of the data. That is, how are the data spread out? The most common data dispersion measures are the range, quartiles, and interquartile range; the five-number summary and boxplots; and the variance and standard deviation of the data These measures are useful for identifying outliers and are described in Section 2.2.2.
Finally, we can use many graphic displays of basic statistical descriptions to visually inspect our data (Section 2.2.3). Most statistical or graphical data presentation software packages include bar charts, pie charts, and line graphs. Other popular displays of data summaries and distributions include quantile plots, quantile–quantile plots, histograms, and scatter plots.
2.2.1. Measuring the Central Tendency: Mean, Median, and Mode
In this section, we look at various ways to measure the central tendency of data. Suppose that we have some attribute X, like salary, which has been recorded for a set of objects. Let be the set of N observed values or observations for X. Here, these values may also be referred to as the data set (for X). If we were to plot the observations for salary, where would most of the values fall? This gives us an idea of the central tendency of the data. Measures of central tendency include the mean, median, mode, and midrange.
The most common and effective numeric measure of the “center” of a set of data is the (arithmetic) mean. Let be a set of N values or observations, such as for some numeric attribute X, like salary. The mean of this set of values is
(2.1)
This corresponds to the built-in aggregate function, average (avg() in SQL), provided in relational database systems.
Mean
Suppose we have the following values