Statistical Methods in Data Mining

Data mining refers to extracting or mining knowledge from large amounts of data. In other words, data mining is the science, art, and technology of discovering large and complex bodies of data in order to discover useful patterns. Theoreticians and practitioners are continually seeking improved techniques to make the process more efficient, cost-effective, and accurate. Any situation can be analyzed in two ways in data mining:

• Statistical Analysis: In statistics, data is collected, analyzed, explored, and presented to identify patterns and trends. Alternatively, it is referred to as quantitative analysis.
• Non-statistical Analysis: This analysis provides generalized information and includes sound, still images, and moving images.

In statistics, there are two main categories:

• Descriptive Statistics: The purpose of descriptive statistics is to organize data and identify the main characteristics of that data. Graphs or numbers summarize the data. Average, Mode, SD(Standard Deviation), and Correlation are some of the commonly used descriptive statistical methods.
• Inferential Statistics: The process of drawing conclusions based on probability theory and generalizing the data. By analyzing sample statistics, you can infer parameters about populations and make models of relationships within data.

There are various statistical terms that one should be aware of while dealing with statistics. Some of these are:

• Population
• Sample
• Variable
• Quantitative Variable
• Qualitative Variable
• Discrete Variable
• Continuous Variable

Now, let’s start discussing statistical methods. This is the analysis of raw data using mathematical formulas, models, and techniques. Through the use of statistical methods, information is extracted from research data, and different ways are available to judge the robustness of research outputs.

As a matter of fact, today’s statistical methods used in the data mining field typically are derived from the vast statistical toolkit developed to answer problems arising in other fields. These techniques are taught in science curriculums. It is necessary to check and test several hypotheses. The hypotheses described above help us assess the validity of our data mining endeavor when attempting to infer any inferences from the data under study. When using more complex and sophisticated statistical estimators and tests, these issues become more pronounced.

For extracting knowledge from databases containing different types of observations, a variety of statistical methods are available in Data Mining and some of these are:

• Logistic regression analysis
• Correlation analysis
• Regression analysis
• Discriminate analysis
• Linear discriminant analysis (LDA)
• Classification
• Clustering
• Outlier detection
• Classification and regression trees,
• Correspondence analysis
• Nonparametric regression,
• Statistical pattern recognition,
• Categorical data analysis,
• Time-series methods for trends and periodicity
• Artificial neural networks

Now, let’s try to understand some of the important statistical methods which are used in data mining:

• Linear Regression: The linear regression method uses the best linear relationship between the independent and dependent variables to predict the target variable. In order to achieve the best fit, make sure that all the distances between the shape and the actual observations at each point are as small as possible. A good fit can be determined by determining that no other position would produce fewer errors given the shape chosen. Simple linear regression and multiple linear regression are the two major types of linear regression. By fitting a linear relationship to the independent variable, the simple linear regression predicts the dependent variable. Using multiple independent variables, multiple linear regression fits the best linear relationship with the dependent variable. For more details, you can refer linear regression.
• Classification: This is a method of data mining in which a collection of data is categorized so that a greater degree of accuracy can be predicted and analyzed. An effective way to analyze very large datasets is to classify them. Classification is one of several methods aimed at improving the efficiency of the analysis process. A Logistic Regression and a Discriminant Analysis stand out as two major classification techniques.
  • Logistic Regression: It can also be applied to machine learning applications and predictive analytics. In this approach, the dependent variable is either binary (binary regression) or multinomial (multinomial regression): either one of the two or a set of one, two, three, or four options. With a logistic regression equation, one can estimate probabilities regarding the relationship between the independent variable and the dependent variable. For understanding logistic regression analysis in detail, you can refer to logistic regression.
  • Discriminant Analysis: A Discriminant Analysis is a statistical method of analyzing data based on the measurements of categories or clusters and categorizing new observations into one or more populations that were identified a priori. The discriminant analysis models each response class independently then uses Bayes’s theorem to flip these projections around to estimate the likelihood of each response category given the value of X. These models can be either linear or quadratic.
    • Linear Discriminant Analysis:  According to Linear Discriminant Analysis, each observation is assigned a discriminant score to classify it into a response variable class. By combining the independent variables in a linear fashion, these scores can be obtained. Based on this model, observations are drawn from a Gaussian distribution, and the predictor variables are correlated across all k levels of the response variable, Y. and for further details linear discriminant analysis
    • Quadratic Discriminant Analysis:  An alternative approach is provided by Quadratic Discriminant Analysis. LDA and QDA both assume Gaussian distributions for the observations of the Y classes. Unlike LDA, QDA considers each class to have its own covariance matrix. As a result, the predictor variables have different variances across the k levels in Y.
  • Correlation Analysis: In statistical terms, correlation analysis captures the relationship between variables in a pair. The value of such variables is usually stored in a column or rows of a database table and represents a property of an object. 
  • Regression Analysis: Based on a set of numeric data, regression is a data mining method that predicts a range of numerical values (also known as continuous values). You could, for instance, use regression to predict the cost of goods and services based on other variables. A regression model is used across numerous industries for forecasting financial data, modeling environmental conditions, and analyzing trends.

The first step in creating good statistics is having good data that was derived with an aim in mind. There are two main types of data: an input (independent or predictor) variable, which we control or are able to measure, and an output (dependent or response) variable which is observed. A few will be quantitative measurements, but others may be qualitative or categorical variables (called factors).