Multivariate Analysis

• Teachers
• Weekly hours
• Competences
• Objectives
• Contents
• Activities
• Teaching methodology
• Evaluation methodology
• Bibliography
• Web links
• Previous capacities

Teachers

Person in charge

• Nihan Acar Denizli ( )

Others

• Ariel Duarte López ( )
• Belchin Adriyanov Kostov ( )
• Dante Conti ( )
• Karina Gibert Oliveras ( )
• Sergi Ramirez Mitjans ( )

Weekly hours

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

Teaching methodology

Evaluation methodology

Bibliography

Basic:

• Applied multivariate statistical analysis - Johnson, Richard A.; Wichern, Dean W, Pearson Education Limited, [2014]. ISBN: 9781292024943
  http://cataleg.upc.edu/record=b1520493~S1*cat
• Exploratory multivariate analysis by example using R - Husson, François; Lê, Sébastien; Pagès, Jérôme, CRC Press, Taylor & Francis Group, 2017. ISBN: 9781315301860
  http://cataleg.upc.edu/record=b1496325~S1*cat
• Multivariate statistical methods : a primer - Manly, Bryan F. J, CRC Press, Taylor & Francis Group, [2017]. ISBN: 9781498728966
  http://cataleg.upc.edu/record=b1521931~S1*cat

Complementary:

• Análisis de datos multivariantes - Peña, Daniel, McGraw-Hill/Interamericana de España, S.L , [2010]. ISBN: 9788448136109
  http://cataleg.upc.edu/record=b1222351~S1*cat

Web links

• Homepage of R https://cran.r-project.org/
• Rstudio homepage https://rstudio.com/

Previous capacities