scardenol/functional_data_analysis

A repository for the research of clustering methods for functional data analysis on high-dimensional data.

What is this?

A repository for the research of clustering methods for functional data analysis on high-dimensional data.

What is the problem?

Extending clustering methods on high-dimensional functional data is an active field of research in both real-world industry and academic applications. The problem is basically characterized by the nature of the data:

• The data space is high-dimensional (a non-trivial amount of rows and columns).
• The data is functional: the data is continuum as it comes from a continuum source (usually time-dependent).
• Clustering data of this nature implies that a cluster consist not of data points but by many observations of related data points usually known as "curves".

What do we do to solve this problem?

We develop both an extension and a new methodology to perform data analysis on this kind of data by taking two approaches:

• A distance-based traditional crisp (or hard) clustering where we compare our own custom functional PAM method with the functional version of the traditional k-means in both an euclidean and manhattan normed spaces.
• A density-based fuzzy (or soft) clustering where we introduce a new methodology by using the HDBSCAN (Hierarchical Density-Based Spatial Clustering of Applications with Noise) method to cluster the data with no hard assumptions like the distance-based methods.

What programming language do we use?

We develop everything in the programming language R 4.2.2 using both the traditional IDE RStudio 2023.06.1+524 and the popular IDE VS Code 1.82.

Why R?

The reasoning behind using this programming language is because the most serious research done on this subject is published in R code, as it already has peer-reviewed and cited libraries/packages on functional data analysis such as (fda.usc)[https://cran.r-project.org/web/packages/fda.usc/fda.usc.pdf].

Project structure

functional_data_analysis
├───data
└───src
    ├───images
    │   └───lib
    │   │   ├───crosstalk-1.2.0
    │   │   │   ├───css
    │   │   │   ├───js
    │   │   │   └───scss
    │   │   ├───htmlwidgets-1.6.2
    │   │   ├───jquery-3.5.1
    │   │   ├───plotly-binding-4.10.1
    │   │   ├───plotly-htmlwidgets-css-2.11.1
    │   │   ├───plotly-main-2.11.1
    │   │   └───typedarray-0.1
    │   └───plot_list.RDS
    └───modules
        ├───clustering
        ├───library_manager
        ├───numerical
        ├───preprocessing
        ├───read_data
        ├───unused
        ├───visualization
        └───write_data
    │ .Rhistory
    │ main.r