# Multivariate Analysis

## You are here

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

## Competences

### Generic Technical Competences

#### Generic

• CG1 - Capability to apply the scientific method to study and analyse of phenomena and systems in any area of Computer Science, and in the conception, design and implementation of innovative and original solutions.
• CG3 - Capacity for mathematical modeling, calculation and experimental designing in technology and companies engineering centers, particularly in research and innovation in all areas of Computer Science.

### Transversal Competences

#### Information literacy

• CTR4 - Capability to manage the acquisition, structuring, analysis and visualization of data and information in the area of informatics engineering, and critically assess the results of this effort.

#### Reasoning

• CTR6 - Capacity for critical, logical and mathematical reasoning. Capability to solve problems in their area of study. Capacity for abstraction: the capability to create and use models that reflect real situations. Capability to design and implement simple experiments, and analyze and interpret their results. Capacity for analysis, synthesis and evaluation.

### Technical Competences of each Specialization

#### Specific

• CEC1 - Ability to apply scientific methodologies in the study and analysis of phenomena and systems in any field of Information Technology as well as in the conception, design and implementation of innovative and original computing solutions.
• CEC2 - Capacity for mathematical modelling, calculation and experimental design in engineering technology centres and business, particularly in research and innovation in all areas of Computer Science.

## Objectives

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

## 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

### Practice doubts

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

## 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%.