What is data? Explain the different types of data most commonly found in cluster analysis.

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 TYPES OF DATA IN CLUSTER ANALYSIS

A data set can often be viewed as a collection of data objects (record, data point, event, case, sample, observation, or entity). Each data object is described by a number of attributes that capture the basic characteristics (variable, characteristic field, feature, or dimension) of an object. There are many types of data sets, and as the field of data mining develops and matures, a greater variety of data sets become available for cluster analysis. The type of data determines which proximity measure can be used to cluster the data. For each type of data in cluster analysis there exists a specific method for proximity computation. Improper use of proximity computation methods can lead to misleading clustering results. Therefore, knowing the data type is an important aspect in choosing the proximity calculation methods in cluster analysis. Some of the most common types of data in cluster analysis are described below.

1. Nominal (categorical) attributes: Nominal is one that has two or more categories, but there is no agreed way to order these from highest to lowest. A nominal attribute cannot be counted. For r example, gender is a nominal attribute having two categories male and female and there is no intrinsic ordering to the categories. You can assign a numerical value (e.g., "Male" = 1, "Female" =2) but you cannot rank the data from highest to lowest. Similarly, hair color is also a nominal attribute having a number of categories (blonde, brown, brunette, red, etc.). If the attribute has a clear way to be ordered or sorted from highest to lowest, then that attribute would be an ordinal variable, as described below. For Example, gender (M/F), color (yellow, red, blue, etc.), compass orientation (North, South,East, West), animals (dogs, cats, birds, etc.), marital status (married/single/divorced/widow)


2. Binary attributes: A binary attribute is a nominal attribute with only two possible states: 0 or 1, where 0 means that the y attributes are absent and 1 means that it is present. Given the attribute attendance describing a student, for instance, indicates that the student is present, while 0 indicates that the student is absent. Binary variable further can be of two types: 

a. Symmetric binary: both outcomes are equally important for example, gender

b Asymmetric binary: outcomes not equally important. For example, medical test (positive vs. negative)

3. Ordinal attributes: Just like a categorical attribute, an "ordinal" variable also has two or more categories but these categories can be "ordered" from high to low. You can therefore assign a value to those categories and sort them. However, these categories are not equally spaced. For example, the difference between "rich" and "middle class" might be greater in $ amount than between "middle-class" and "poor". If the categories are equally spaced, then the variable is an interval attribute.

For Example, economic status (rich, middle-class, poor), IQ (high, medium, low), education (college graduate, some college, high school, elementary school), ratings of perception (pleasure, pain, etc.), speed (fast/slow), school grades (AF), cost of living (expensive, moderate, low), air quality (good, bad).

4. Interval-scaled attributes: Just like an ordinal attribute, an interval attribute also has two or more categories which can also be ordered from high to low, but the intervals between the values of the interval attribute are equally spaced. For example, suppose you have attributes such as annual income that is measured in dollars, and we have three people who make $10,000, $15,000, and $20,000. The second person makes $5,000 more than the first person and $5,000 less than the third person, and the size of these intervals is the same. If there were two other people who make $90,000 and $95,000, the size of that interval between these two people is also the same ($5,000). Also, an interval attribute does not really have a true zero: a value of "zero" just means "no value": an income of "zero dollars" just means "no income. A temperature of 0 kelvins means "no temperature measurable". An interval value with a true and attainable value of zero is a ratio attribute.

For example, annual income in S, temperatures, time of day, elevation 

5. Ratio-scaled attributes: Just like an interval attribute, a ratio variable can be sorted from high to low, and the intervals are equally spaced, BUT the ratio variable has a real and attainable value of zero. For example, weight, height, speed in km/h, age

6. Attributes of mixed types: Multiple attributes with various types.

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