Types of Datasets in Data Science

Types of Datasets

• Record Data
  • Relational records: Highly structured, often found in databases as tables.
  • Data matrix: Numerical or cross-tabulated data.
  • Transaction data: Records of events or transactions.
  • Document data: Text documents represented as term-frequency vectors (matrices).
• Graphs and Networks

Data in Data Science

• Entity: A specific individual or object of interest.
• Attribute: A measurable or observable property of an entity.
• Data: A measurement or observation of an attribute.

Data Categorization

• NOIR Topology: A framework for classifying data types based on their properties:
  • N: Nominal
  • O: Ordinal
  • I: Interval
  • R: Ratio

Nominal Scale

• Definition: A variable with mutually exclusive categories that have no logical order.
• Examples:
  • Gender: {M, F} or {1, 0}
  • Blood groups: {A, B, AB, O}
  • Country codes: 048, 040
• Note:
  • Nominal data uses labels for categorization, which can be numbers, letters, or strings.
  • Numerical values have no mathematical interpretation.
  • Labels from different attributes can be combined to create new nominal variables.
  • Examples: {A+, A-, AB+, etc.}

Binary Scale

• Definition: A nominal variable with exactly two mutually exclusive categories.
• Examples:
  • Switch: {ON, OFF}
  • Attendance: {True, False}
  • Entry: {Yes, No}
• Note:
  • A special case of nominal variables.

Symmetric and Asymmetric Binary Scale

• Symmetric: Both choices of a binary variable have equal importance.
  • Example: Gender = {male, female}
• Asymmetric: Both choices of a binary variable have unequal importance.
  • Example: Medical test (positive vs. negative)
  • Convention: Assign 1 to the most important outcome.

Ordinal Scale

• Definition: Ordered nominal data, where categories have a logical order.
• Example: Shirt size = {S, M, L, XL, XXL}
• Note:
  • Can be compared using relational operators (<, ≤, >, ≥).
  • Can be ranked.
  • Numerical variables can be transformed into ordinal variables with a loss of information.

Interval Scale

• Definition: Data measured on a numerical scale with equal intervals between adjacent values, but no true zero.
• Note:
  • Interval data has well-defined intervals.
  • 0 doesn't represent the absence of the attribute.
  • Example: Temperature in Celsius and Fahrenheit.

Operation on Interval Data

• Addition and subtraction are possible.
• Negation and multiplication by a constant are permitted.
• Affine transformations are permissible (adding a constant or multiplying by a constant).
• One-to-one non-linear transformations (log, exp, sin, etc.) can be applied.

Continuous and Discrete Data

• Discrete data: Can only take on specific, individual values.
• Continuous data: Can take on any value within a certain range.

Ratio Scale

• Definition: Data measured on a numerical scale with equal intervals between adjacent values and a true zero.
• Note:
  • Ratio data can be in linear or non-linear scales.
  • Operations like multiplication and division are meaningful.
  • Example: Height, weight, age.