Multivariate Analysis

Credits
6
Types
Compulsory
Requirements
This subject has not requirements , but it has got previous capacities
Department
EIO
Web
https://www.fib.upc.edu/en/studies/masters/master-data-science/curriculum/syllabus/MVA-MDS
The aim of the course is to introduce students to the fundamentals of multivariate data analysis methods and to provide them with the tools to deal with pre-processing, visualization, dimension reduction, classification and modelling of multivariate data.

Teachers

Person in charge

Others

Weekly hours

Theory
2
Problems
0
Laboratory
2
Guided learning
0
Autonomous learning
7.11

Competences

Transversal Competences

Information literacy

  • CT4 - Capacity for managing the acquisition, the structuring, analysis and visualization of data and information in the field of specialisation, and for critically assessing the results of this management.

    • Third language

  • CT5 - Achieving a level of spoken and written proficiency in a foreign language, preferably English, that meets the needs of the profession and the labour market.

    • Entrepreneurship and innovation

  • CT1 - Know and understand the organization of a company and the sciences that govern its activity; have the ability to understand labor standards and the relationships between planning, industrial and commercial strategies, quality and profit. Being aware of and understanding the mechanisms on which scientific research is based, as well as the mechanisms and instruments for transferring results among socio-economic agents involved in research, development and innovation processes.

    • Basic

  • CB6 - Ability to apply the acquired knowledge and capacity for solving problems in new or unknown environments within broader (or multidisciplinary) contexts related to their area of study.
  • CB7 - Ability to integrate knowledge and handle the complexity of making judgments based on information which, being incomplete or limited, includes considerations on social and ethical responsibilities linked to the application of their knowledge and judgments.
  • CB8 - Capability to communicate their conclusions, and the knowledge and rationale underpinning these, to both skilled and unskilled public in a clear and unambiguous way.
  • CB9 - Possession of the learning skills that enable the students to continue studying in a way that will be mainly self-directed or autonomous.
  • CB10 - Possess and understand knowledge that provides a basis or opportunity to be original in the development and/or application of ideas, often in a research context.

    • Generic Technical Competences

    Generic

  • CG2 - Identify and apply methods of data analysis, knowledge extraction and visualization for data collected in disparate formats
  • CG3 - Define, design and implement complex systems that cover all phases in data science projects

    • Technical Competences

    Especifics

  • CE5 - Model, design, and implement complex data systems, including data visualization
  • CE6 - Design the Data Science process and apply scientific methodologies to obtain conclusions about populations and make decisions accordingly, from both structured and unstructured data and potentially stored in heterogeneous formats.
  • CE7 - Identify the limitations imposed by data quality in a data science problem and apply techniques to smooth their impact
  • CE8 - Extract information from structured and unstructured data by considering their multivariate nature.
  • CE9 - Apply appropriate methods for the analysis of non-traditional data formats, such as processes and graphs, within the scope of data science
  • CE10 - Identify machine learning and statistical modeling methods to use and apply them rigorously in order to solve a specific data science problem
  • CE11 - Analyze and extract knowledge from unstructured information using natural language processing techniques, text and image mining
  • CE12 - Apply data science in multidisciplinary projects to solve problems in new or poorly explored domains from a data science perspective that are economically viable, socially acceptable, and in accordance with current legislation
  • CE13 - Identify the main threats related to ethics and data privacy in a data science project (both in terms of data management and analysis) and develop and implement appropriate measures to mitigate these threats

    • Objectives

    1. Data visualisation
      Related competences: CT4, CT5, CT1, CG2, CE5, CB8,
    2. Multivariate description of data
      Related competences: CT4, CE7, CE8, CE12, CE13, CB7, CB9, CB10,
    3. Dimension Reduction Methods
      Related competences: CT4, CT5, CG2, CE5, CE6, CE11, CE8, CE10, CB6, CB8, CB9, CB10,
    4. Multivariate inference
      Related competences: CT1, CG2, CG3, CE6, CE11, CE8, CE9, CE10, CB6, CB7, CB9,
    5. Classification of new individuals
      Related competences: CT1, CG3, CE6, CE10, CB6, CB7,

    Contents

    1. Introduction to Multivariate Data Analysis
      Pre-processing and visualization of multivariate data.
    2. Principal Component Analysis
      Analysis of individuals. Analysis of variables. Visual representation of the information. Dimensionality reduction. Supplementary information. Singular value and spectral value decomposition.
    3. Multidimensional Scaling
      Dimension reduction based on similarity or distance matrices with applications.
    4. Correspondence Analysis
      Dimension reduction of two categorical variables and visualization of relationships between categories.
    5. Multiple Correspondence Analysis
      The analysis and visualization of relationships among categories of more than two categorical variables by using dimension reduction.
    6. Cluster Analysis
      The use of hierarchical and non-hierarchical clustering methods to classify observations into groups based on multivariate data.
    7. Profiling methods
      Profiling methods help to understand the common characteristics of clusters.
    8. Multivariate normal distribution
      The probability density function of multivariate normal distribution and hypothesis tests of mean for multivariate data.
    9. Discriminant Analysis
      Classification of observations into given groups by using linear discriminant analysis, quadratic discriminant analysis and Naive Bayes methods.
    10. 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
    4h
    Guided learning
    0h
    Autonomous learning
    5.5h

    Principal Component Analysis


    Objectives: 2 1 3
    Theory
    4h
    Problems
    0h
    Laboratory
    2h
    Guided learning
    0h
    Autonomous learning
    5.5h

    Multidimensional Scaling


    Objectives: 2 1 3
    Contents:
    Theory
    2h
    Problems
    0h
    Laboratory
    2h
    Guided learning
    0h
    Autonomous learning
    5.5h

    Correspondence Analysis and Multiple Correspondence Analysis


    Objectives: 2 1 3
    Theory
    4h
    Problems
    0h
    Laboratory
    4h
    Guided learning
    0h
    Autonomous learning
    10h

    Cluster Analysis and Profiling


    Objectives: 2 5 3
    Theory
    4h
    Problems
    0h
    Laboratory
    4h
    Guided learning
    0h
    Autonomous learning
    10h

    Multivariate Normal Distribution and Hypothesis Tests of Mean for Multivariate Data


    Objectives: 2 4
    Theory
    4h
    Problems
    0h
    Laboratory
    4h
    Guided learning
    0h
    Autonomous learning
    5.5h

    Discriminant Analysis


    Objectives: 4 5 1
    Theory
    2h
    Problems
    0h
    Laboratory
    2h
    Guided learning
    0h
    Autonomous learning
    5.5h

    Association Rules


    Objectives: 2 4
    Theory
    2h
    Problems
    0h
    Laboratory
    2h
    Guided learning
    0h
    Autonomous learning
    5.5h

    Session of Doubts



    Theory
    2h
    Problems
    0h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    0h

    Practics


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

    Task 1

    The application and interpretation of dimension reduction methods seen through the first part of the course on a case study.
    Objectives: 2 1 3
    Week: 8 (Outside class hours)
    Theory
    0h
    Problems
    0h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    0h

    Task 2

    In this task students should apply the methods of classification on a case study and interpret the results. This task is done in groups of three students.
    Objectives: 4 5 3
    Week: 13 (Outside class hours)
    Theory
    0h
    Problems
    0h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    0h

    Final Exam

    In the final exam students will be responsible for all the methods they have seen throughout the semester. There will be both theoretical questions and interpretation questions based on R outputs in the exam.
    Objectives: 2 4 5 1 3
    Week: 15 (Outside class hours)
    Theory
    0h
    Problems
    0h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    0h

    Final Project

    The final project includes application and interpretation of the multivariate data analysis methods on a real data set that could be selected based on students' interests. It should be done in groups of three students.
    Objectives: 2 4 5 1 3
    Week: 14 (Outside class hours)
    Theory
    0h
    Problems
    0h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    0h

    Teaching methodology

    This course aims to give theoretical explanation of different methods for multivariate data analysis and their applications on real data sets. In tehory classes the fundamentals and theoratical structure of the methods will be explained while in the lab sessions the application of considered methods will be done on different data sets in R. The projects and the homeworks of the course will be done in groups which allows students to colloborate to construct a team work.

    Evaluation methodology

    During the course students should submit two homeworks (tasks) and a final project which should be done in groups of three students. The first homework focus on the application of dimension reduction methods while the second homework focuses on classification methods.In the final project of the course students should work on a real data set that they download or webscrapped and apply the methods seen during the course on the chosen data sets. The results should be presented in a report written in pdf format.

    The overall grade of the students will be weighted 15% by the first task, 15% by the second task, %40 by the final project and 30% by the final exam.

    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:
    - Descriptive Statistical Analysis
    - Hypothesis Tests
    - Matrix algebra, eigenvalues ¿¿and eigenvectors.
    - Programing algorithms.
    - Multiple linear-regression.