PP: Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data

From: Stanford University; Jure Leskovec, citation 6w+;

Problem:

subsequence clustering.

Challenging:

discover patterns is challenging because it requires simultaneous segmentation and clustering of the time series + interpreting the cluster results is difficult.

Why discover time series patterns is a challenge?? thinking by yourself!! there are already so many distance measures(DTW, manifold distance) and clustering methods(knn,k-means etc.). But I admit the interpretation is difficult.

Introduction:

long time series ----breakdown-----> a sequence of states/patterns ------> so time series can be expressed as a sequential timeline of a few key states. -------> discover repeated patterns/ understand trends/ detect anomalies/ better interpret large and high-dimensional datasets.

Key steps: simultaneously segment and cluster the time series.

Unsupervised learning: hard to interpretation, after clustering, you have to view data itself.

how to discover interpretable structure in the data?

Traditional clustering methods are not particularly well-suited to discover interpretable structure in the data. This is because they typically rely on distance-based metrics

distance-based metrics, DTW.

距离式的算法，在处理multivariate time series上有劣势，看不到细微的数据结构相似性。

Propose a new method for multivariate time series clustering TICC:

• define each cluster as a dependency network showing the relationships between the different sensors in a short subsequence.
• each cluster is a markov random field.
• In thes MRFs, an edge represents a partial correlation between two variables.
• learn each cluster's MRF by estimating a sparse Gaussian inverse covariance matrix.
• This network has multiple layers.
• the number of layers corresponds to the window size of a short subsequence.
• 逆协方差矩阵定义了MRF dependency network 的adjaccency matrix.

Related work:

time series clustering and convex optimization;

variations of dtw; symbolic representations; rule-based motif discovery;

However, these methods generally rely on distance-based metrics.

TICC ------ a model-based clustering method, like ARMA, Gaussian mixture or hidden markov models.

• define each cluster by a Gaussian inverse covariance.
• so the Gaussian inverse covariance defines a Markov random field encoding the structural representation.
• K clusters/ inverse covariances.

selecting the number of clusters: cross-validation; mornalized mutual information; BIC or silhouette score.

看不懂哇 T T

Supplementary knowledge:

1. 对于unsupervised learning, 目前对结果的解释或者中间参数的选取，全是靠经验。

2. Aarhus data, Martin, 做多变量time series 预测。

3. Toeplitz Matrices: 常对角矩阵。

4. ticc code

Reference:

1. 如何用简单易懂的例子解释条件随机场（CRF）模型？