Carlos Ramos Carreo Grupo de Aprendizaje Automtico, Department of - - PowerPoint PPT Presentation

Carlos Ramos Carreño

Grupo de Aprendizaje Automático, Department of Computer Science , Universidad Autónoma de Madrid (UAM)

Who are we?

• Carlos Ramos Carreño (carlos.ramos@uam.es)¹
• José Luis Torrecilla Noguerales (joseluis.torrecilla@uam.es)²
• Alberto Suárez (alberto.suarez@uam.es)¹
• Miguel Carbajo Berrocal
• Pablo Marcos Manchón
• Amanda Hernando Bernabé
• Pablo Pérez Manso

¹ Department of Computer Science , Universidad Autónoma de Madrid (UAM) ² Department of Mathematics, Universidad Autónoma de Madrid (UAM)

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What is scikit-fda?

• A software package for Functional Data Analysis

(FDA)

• Preprocessing, exploration and machine learning

tools

• Fully integrated in the Python science ecosystem
• Efficient, flexible and easy to use

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Which other tools for FDA are available?

Mainly R software:

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• General purpose

○ fda ○ fda.usc ○ tidyfun

• Representation

○ funData

• Registration

○ fdasrvf

• Robust analysis

○ roahd

• FPCA

○ fdapace ○ MFPCA

• Regression

○ refund ○ refund.wave ○ fdaPDE ○ sparseFLMM ○ FDBoost

Which other tools for FDA are available?

Mainly R software:

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• Visualization

○ rainbow

• Variable selection

○ RFgroove

• Time series

○ fds ○ ftsa

• Clustering

○ Funclustering ○ funcy ○ funFEM ○ funHDDC

• Powerful, easy to use, generic purpose programming language
• The Scipy environment:

○ Numpy: N-dimensional arrays and linear algebra ○ SciPy: Utilities (statistics, integration, formats…) ○ Matplotlib: Plotting ○ Jupyter: Interactive notebooks ○ and much more...

Why Python?

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• Scipy Toolkits (SciKits)
• Specialized science packages:

Why scikit?

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exploratory analysis representation preprocessing statistical inference machine learning

scikit-fda

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representation

basis representation

regularly sampled irregularly sampled

discretized representation

Discretized representation

Each curve is evaluated at the same points

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Basis representation

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Expansion in a truncated basis of functions

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smoothing

preprocessing

registration dimensionality reduction

Registration

• Alignment of the curves, so that common features (peaks, valleys...) are

at the same points

• Typically, a warping function is used to transform the input
• Several methods

○ Shift registration ○ Landmark registration ○ Elastic registration ○ ...

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Shift registration

• Warpings are translations
• Try to minimize the least squares criterion

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Landmark registration

• Warping functions to move the predefined landmarks to fixed positions
• Landmarks should be specified by the user

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Elastic registration

• Uses the square root velocity framework (Srivastava et al., 2011

<arXiv:1103.3817> and Tucker et al., 2014 <doi:10.1016/j.csda.2012.12.001>)

• Available also in fdasrvf in R
• Unsupervised method

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descriptive statistics

exploratory analysis

• utliers

depth visualization

Functional data boxplot

• Similar to the boxplot of univariate data
• A depth function must be chosen

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statistical inference

estimation confidence intervals statistical hypothesis testing

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clustering

machine learning

regression classification

K-means clustering

• Predefined number of clusters
• Finds the best position of the centroids of the clusters
• A functional metric must be chosen

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Fuzzy K-means

• Fuzzy version of K-means
• Each observation does not necessary belong to only one of the clusters:

it has a degree of membership to each of them

• The degrees of membership add up to one

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Documentation

• Up to date and available online
• Easily searchable
• Cross referenced
• Detailed examples and interactive notebooks
• Examples downloadable as Python source files or

Jupyter notebook

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Where can I find more?

PyPI: https://pypi.org/project/scikit-fda/ Github page: https://github.com/GAA-UAM/scikit-fda/ Documentation: https://fda.readthedocs.io

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Thanks for your attention!!

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