Categorical Time-Series Analysis
CategoricalTimeSeries.jl is a Julia package regrouping methods of categorical time-series analysis. The term categorical commonly refers to two types of data: nominal and ordinal.
Nominal, or labeled values represent discrete units that have no intrinsic order, like common types of pet:
Ordinal values on the other hand represent discrete and ordered units, like the size of a coffee cup:
When categorical data is layed out in function of time, one speaks of categorical time-series.
Often, especially when dealing with ordinal time-series, it is enough to map the different values to a set of integers to carry the analysis. However, when it is not sufficient CategoricalTimeSeries.jl is here to help.
The package lets you carry four main kind of analysis: Spectral analysis, Data clustering, correlations analysis and motif recognition. Other functionnalities are also avalaible (see misc.). These methods are agnostic to the type of data used (ordinal or nominal) as they do not rely on a pre-established ordering. Here is a quick overview of these methods, for more details go to the specific sections.
The standard approach to study spectral properties in categorical time-series is to map the different values to a set of numbers. While the overall shape of the spectrum is usually unaffected by this operation, peaks representing cyclic behaviors in the time-series can completely disappear depending on the choice of mapping. To tackle this issue, one can use the spectral envelope method. It was developed by David S. Stoffer in order to identify optimal mappings.
A categorical time-series might have many different possible values, but these values are rarely independant. Some categories can be loosely equivalent to one-another. For example, among the values
"car", it is evident that
"female" refer to similar concepts and could be grouped in one single category. Data clustering is the task of identifying such relationships in the time-series in order to reduce it to a more efficient representation. Here, an implementation of the information bottleneck concept is used to this end.
Time-series sometimes present repeating motifs (or patterns) that are worthwhile identifying. In categorical time-series, the lack of proper distance measurement complicates this task, nonetheless several methods have been developed to this end. An implementation using the concept of random projection is used here.
The notion of autocorrelation function is formally not defined for a categorical time-series. Yet, it might be of interest to know how inter-dependent the values of the time-series are. Efforts have been made to generalize the concept of linear correlations to categorical time-series. This package implements several of these methods.
The source code is available on GitHub, otherwise, CategoricalTimeSeries.jl can be installed with
using Pkg Pkg.add("CategoricalTimeSeries")
To use it, you need to import it: