Time Series Analysis In R

Using Hidden Markov Models
For Unsupervised Learning

Agoston Torok
@torokagoston


data scientist @SynetiqLab

Time series analysis


Time series:

A series of datapoints in time order

Methods of time series analysis:

  • Season trend decomposition (e.g. STL)
  • Autoregressive modeling (AR, ARMA, ARIMA)
  • State space models (e.g. HMM)

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A (very) short intro to hidden Markov models


We hypothesize latent states/regimes in the time series (for example past flow and tree rings [1])

\[ \begin{array} & X_{1}\overset{P_T}{\longrightarrow} & X_{2}\overset{P_T}{\longrightarrow} & \dots \overset{P_T}{\longrightarrow} & X_N\\ \downarrow P_O & \downarrow P_O & & \downarrow P_O \\ O_1 & O_2 & \dots & O_N\end{array} \]

  • We cannot directly observe the \( X \) time series, but we can infer it
  • We have a series of \( O \) observations resulting from \( X \) latent states
  • Based on the \( P_T \) transition probability matrix, and \( P_O \) probability matrix
  • Passes between \( O \), \( X \), and \( Model \)

. .

Human biosignals and HMM


Has been used to find patterns in:

  • EEG (sleep cycles) [3, 4]
  • Eye movements (face recognition) [5]
  • Heart rate (cardiac events) [6]

Can we use it to recognise emotional states?


  • Results show that emotions have different physiological correlates [7]
  • It is reasonable to say that the transition probabilities are not uniform
  • Some emotions lasts longer (fear), others fade rather fast (surprise)






“Emotions are just as easy to access as any Higgs boson.”

The dataset


Emotional reactions to Paperman (2012, dir: John Kahrs)