Time Varying Graphical Lasso
Clustering of time series data using Toeplitz Inverse Covariance based Clustering
There are applications in various domains ranging from protein interactions to complex machine working like car , aeroplanes to social media to financial markets like crash or boom to wearable sensors to biological interactions generates huge amounts of continuous time-series data these datasets can often be decompose down into a series of states for example electronic sensor data from a wearable fitness tracking gadget can be interpreted as a temporal sequence of actions like some running related activities like walking for 12 minutes then running for 35 minutes then sitting for one hour then running again for 50 minutes which affect the working and sates of organs like heart for blood circulation , lungs for inhalation , leg muscles or dehydration or using automobile data the car driving session can be modeled as a series of timeline of a few key states and actions like starting, turning, speeding up ,slowing down, stopping at a red light, going straight and so on which compels the changes in states and working of car engine, brakes , its acceleration , deacceleration, if we attach sensor to the car for capturing these data we can predict the state and condition and working actions of car. Learning these sequential series can help us draw interpretable conclusions from the data and can help in understanding in its working however in general these states are not enough predefined and we do not know what they are or what they refer to, therefore we need to learn both the states itself and also how the time series splits into these states however achieving both goals simultaneously.
Various problems can be defined as a dynamic of system of interconnected nodes , where each node(entity)is recording time dependent sequential observations or actions. In order to find trends, find anomalies, and understand the temporal dynamics of such data, it is needed to understand the relationships between the different nodes and how these relationships evolve over time period .
Graphical Models-
Graphical networks are used to represent the relationship between various entities ,in graph, each vertices represents a random variables which can change its relationship with other nodes according to various states . The absence of an edge between two vertices means the corresponding random variables are conditionally independent, given other variables. Penalized regression methods for inducing sparsity in precision matrix are prime to the construction of gaussian graphical model.
In finance , many industries and companies are interconnected with each other through various contracts of works and depends on each other for their businesses , some are competitors, some gets vanished . New industry like social media emerges with Facebook and becomes one of the biggest company. economic condition of a market of particular country has impact on many countries directly or indirectly.
Programming tools/packages-
It can be implemented in advance analytical platforms like Python , R Matlab. In Python ‘TICC’ library can be used , its made by Standford University.
Brief working summary-
In short its graphical model which is unsupervised model which takes takes into consideration interdependencies and big event’s/action’s causality & effects on other entities , whether its financial or biological or sensor data. Raw Data is feeded and its covariance correlation matrix is acquired and then the model tries to understand the interdependencies between time varying multivariate series of data and tries to do prediction on the basis of that. But it is very important to define the graphical network of interdependence in correct way which is difficult relatively.