Sequential Inference for Evolving Groups of Objects 이범진 Biointelligence Lab Seoul National University

What are we going to do? Think about dynamically evolving groups of objects  Ex)  flocks of birds  Schools of fish  Group of aircraft

However... Difficulties on this research  1. recognizing groups are hard  2. incorporating new members into the groups,  Ex) splitting and merging of groups How many groups? Merging Spliting

Proposed solution Implementation rule  1. Targets themselves are dynamic  2. Targets’ grouping can change overtime  3. Assignment of a target to a group affects the probabilistic properties of the target dynamics  4. Group statistics belong to a second hidden layer, target statistics belong to the first hidden layer and the observation process usually depends only on the targets  5. Number of targets is typically unknown

Framework (1) Dynamic group tracking model G1G1 X1X1 Z1Z1 G2G2 X2X2 Z2Z2 GtGt XtXt ZtZt G t+1 X t+1 Z t+1

Framework (2) Main components of the group tracking model  1. group dynamical model :  Describes motion of members in a group   2. group structure transition model  Describes the way the group membership or group matic states X t  Markovian assumption

How do we inference? Proposed MCMC-particle algorithm

Why is it better!? No resampling is required  Particle filters use MCMC to rejuvenate degenerate samples after resampling Less computationally intensive than the MCMC- based particle filter  Because avoids numerical integration of the predictive density at every MCMC iteration Consider the general joint distribution of S t and S t-1 

How good is it?

Framework (2) Main components of the group tracking model  1. group dynamical model :  Describes motion of members in a group   2. group structure transition model  Describes the way the group membership or group matic states X t  Markovian assumption

Experiments(1) Ground target tracking  For group dynamical model(with repulsive force, virtual leader)  Use stochastic differential equations (SDEs) and Itô stochastic calculus –Using velocity, position, acceleration, restoring force, etc.  For state-dependent group structure transition model  For observation model  Using single discretized sensor model which scans a fixed rectangular region, and track-before-detect approach(TBD) otherwise

Experiments(1)

Experiments(1) result MCMC-particles algorithm is used to detect and track the group targets N burn = 1000 iteration for burn-in

Experiments(1) result cont.

Experiments(2)

Experiments(2) cont.

Experiments(2) result MCMC-particles algorithm is used to inference {G t, π t } These models can identify groupings of stock based only on their stock price behaviour

Thank you