Multivariate Analysis

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Credits
6
Types
Specialization compulsory (Data Science)
Requirements
This subject has not requirements, but it has got previous capacities
Department
EIO
The objective of MVA is to provide the students with the knowledge of the statistical concepts of multivariate data analysis and their most basic methodologies and techniques, which constitute a core mainstream for Data Mining.

Weekly hours

Theory
2
Problems
0
Laboratory
2
Guided learning
0.15
Autonomous learning
7.39

Objectives

  1. Multivariate description of data
    Related competences: CG1, CG3, CEC1, CEC2, CTR4, CTR6,
  2. Data visualisation
    Related competences: CG3, CTR4,
  3. Multivariate inference
    Related competences: CG3, CEC1, CEC2, CTR6,
  4. Classification of new individuals
    Related competences: CG1, CG3, CEC1, CEC2, CTR6,

Contents

  1. Introduction to Multivariate Data Analysis
    Advantages of the multivariate treatment. Examples of multivariate data. Probabilistic and distribution free methods. Exploratory versus modeling approach.
  2. Principal Component Analysis
    Analysis of individuals. Analysis of variables. Visual representation of the information. Dimensionality reduction. Supplementary information
  3. Correspondence Analysis
    Correspondence analysis, also called reciprocal averaging, is a useful data science visualization technique for finding out and displaying the relationship between categories. It uses a graph that plots data, visually showing the outcome of two or more data points.
  4. Factor Analysis
    Dimension reduction method.
  5. Multidimensional Scaling
    This method deals with data relating to distances between elements. Usually uses data from distances or similarities. The method reveals a common structure of all the elements and the specificity of each of them, evidencing what makes them close or distant.
  6. Hierarchical and Partitioning Clustering
    Two approaches to clustering methods used to classify observations, within a data set, into multiple groups based on their similarity.
  7. Model-based Clustering
    Model-based clustering assumes that the data were generated by a model and tries to recover the original model from the data. The model that we recover from the data then defines clusters and an assignment of documents to clusters. A commonly used criterion for estimating the model parameters is maximum likelihood.
  8. Multivariate normal distribution
    Particularities of the normal distribution in the general case of multivariate approaches, where the points are distributed in several dimensions. This topic is not done specifically but transversally to all the contents of the course.
  9. Discriminant Analysis and beyond
    Discriminant Analysis (DA) is a classification method. DA classifies observations into non-overlapping groups, based on scores on one or more quantitative predictor variables. We will look at different techniques based on different discrimination algorithms
  10. Classification and Regression Trees
    This method can predict or classify. Explains how the values ​​of a result variable can be predicted or classified based on other values. It has a very useful graphic structure.
  11. Association rules
    Find common patterns, associations, correlations, or causal structures between sets of items or objects in transaction databases, relational databases, and other information repositories.

Activities

Activity Evaluation act


Introduction to the course + Multivariate Data Analysis


Objectives: 2 1
Contents:
Theory
2h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
5h

Principal Component Analysis


Objectives: 2 1
Contents:
Theory
2h
Problems
0h
Laboratory
2h
Guided learning
0h
Autonomous learning
5h

Correspondence Analysis


Objectives: 2 1
Contents:
Theory
2h
Problems
0h
Laboratory
2h
Guided learning
0h
Autonomous learning
5h

Model-based Clustering


Objectives: 2 1
Contents:
Theory
2h
Problems
0h
Laboratory
2h
Guided learning
0h
Autonomous learning
5h

Factor Analysis


Objectives: 2 1
Contents:
Theory
2h
Problems
0h
Laboratory
2h
Guided learning
0h
Autonomous learning
5h

Factor Analysis


Objectives: 2 4
Contents:
Theory
2h
Problems
0h
Laboratory
2h
Guided learning
0h
Autonomous learning
5h

Multidimensional Scaling


Objectives: 2 1
Contents:
Theory
2h
Problems
0h
Laboratory
2h
Guided learning
0h
Autonomous learning
5h

Discriminant Analysis


Objectives: 3 4
Contents:
Theory
2h
Problems
0h
Laboratory
2h
Guided learning
0h
Autonomous learning
5h

Classification and Regression Trees


Objectives: 2 3 4
Contents:
Theory
2h
Problems
0h
Laboratory
2h
Guided learning
0h
Autonomous learning
5h

Hierarchical and Partitioning Clustering


Objectives: 2 4
Contents:
Theory
2h
Problems
0h
Laboratory
2h
Guided learning
0h
Autonomous learning
5h

Multivariate normal distribution


Objectives: 2 4
Contents:
Theory
2h
Problems
0h
Laboratory
2h
Guided learning
0h
Autonomous learning
5h

Association rules


Objectives: 4
Contents:
Theory
2h
Problems
0h
Laboratory
2h
Guided learning
0h
Autonomous learning
5h

Final Practical Work



Week: 18
Theory
0h
Problems
0h
Laboratory
0h
Guided learning
1.9h
Autonomous learning
13h

Quiz



Week: 14
Theory
0h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
13.1h

Summary and Practice. 1st part


Objectives: 2 1 3 4
Contents:
Theory
0h
Problems
0h
Laboratory
2h
Guided learning
0h
Autonomous learning
5h

Summary and Practice. 2nd part


Objectives: 2 1 3 4
Contents:
Theory
0h
Problems
0h
Laboratory
2h
Guided learning
0h
Autonomous learning
5h


Teaching methodology

The course aims to give the statistical foundations for data mining. Learning is done through a combination of theoretical explanation and its application to a real case. The lectures will develop the necessary scientific knowledge, while lab classes will be its application to solving problems of data mining. The implementation of practices fosters generic skills related to teamwork and presentation of results and serve to integrate different knowledge of the subject. The software used will be primarily R & RStudio.

Evaluation methodology

The course evaluation will be based on the marks obtained in practical exercises conducted during the course, a theory grade, and the grade obtained in the final practice.
Each practice will lead to the drafting of the relevant report writing and may be made jointly, up to a maximum of four students per group.
The exercises conducted throughout the course aim to consolidate the learning of multivariate techniques.
The final practice is that students show their maturity to solve a real problem using multivariate visualisation techniques, clustering interpretation, and prediction. Students will choose between different alternatives to solve the problem. This practice will be presented and publicly defended, in which the student must answer any questions about the theoretical models and methods used in the solution. Practices are conducted using the software R.
The written tests will evaluate the assimilation of the basic concepts of the subject. There will be three tests during the curse, in theory class. While the presentation of the practice will be done during the examination period.

The exercises performed during the course have a weighting of 30%, the theory of 30%, and the final practice of 40%.

Bibliography

Basic:

Complementary:

Web links

Previous capacities

The course implies having previously done a basic course in statistics, programming and mathematics; in particular having adquired the following concepts:
- Average, covariance and correlation matrix.
- Hypothesis Test
- Matrix algebra, eigenvalues ​​and eigenvectors.,
- programing algorithms.
- multiple linear-regression