tsseg.algorithms.ticc package

TICC — Toeplitz Inverse Covariance-based Clustering.

Description

TICC simultaneously segments and clusters multivariate time series by modelling each cluster as a Markov Random Field (MRF) defined over a short window of length window_size. The MRF is characterised by a block-Toeplitz inverse covariance matrix that captures temporal and cross-variable partial correlations.

The algorithm alternates between:

1. Assignment step — dynamic programming assigns each time step to the cluster maximising a log-likelihood + switching penalty \(\beta\).

2. Update step — ADMM updates the Toeplitz inverse covariance of each cluster subject to a sparsity penalty \(\lambda\).

Type: state detection

Supervision: semi-supervised (n_states required)

Scope: multivariate (transductive)

Parameters

Name	Type	Default	Description
window_size	int	10	Sliding window size.
n_states	int	5	Number of states (clusters).
lambda_parameter	float	0.11	Sparsity parameter for the inverse covariance.
beta	float	400	Switching penalty (temporal consistency).
maxIters	int	100	Maximum EM iterations.
threshold	float	2e-5	Convergence threshold.
num_proc	int	1	Number of parallel processes.
axis	int	0	Time axis.

Usage

from tsseg.algorithms import TiccDetector

detector = TiccDetector(n_states=4, window_size=10, beta=200)
states = detector.fit_predict(X)

Implementation: Adapted from the original TICC code by Hallac et al.

Reference: Hallac, Vare, Boyd & Leskovec (2017), Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data, KDD.

Submodules

tsseg.algorithms.ticc.detector module

tsseg.algorithms.ticc.ticc module

Module contents