Unsupervised Mining of Statistical Temporal Structures

in Video

Liu ze yuan

May 15,2011

What purpose does Markov Chain Monte-Carlo(MCMC) serve in this chapter?

Quiz of the Chapter

1 Introduction 1.1Keywords 1.2 Examples 1.3 Structure discovery problem 1.4 Characteristics of video structure 1.5 Approach

2 Methods Hierarchical Hidden Markov Models Learning HHMM parameters with EM Bayesian model adaptation Feature selection for unsupervised learning

3 Experiments & Results 4 Conclusion

Agenda

Algorithms for discovering statistical structures and finding informative features from videos in an unsupervised setting.

Effective solutions to video indexing require detection and recognition of structures and events.

We focus on temporal structures

1 Introduction

Hierarchical hidden Markov Model(HHMM) Hidden Markov model(HMM) Markov Chain Monte-Carlo(MCMC) Dynamic Bayesian network(DBN) Bayesian Information criteria(BIC) Maximum Likelihood(ML) Expectation Maximization(EM)

1.1 Introduction: keywords

General to various domains and applicable at different levels

At the lowest level, repeating color schemes in a video

At the mid level, seasonal trends in web traffics

At the highest level, genetic functional regions

1.2Introduction: examples

The problem of identifying structure consists of two parts: finding and locating.

The former is referred as training, while the latter is referred to as classification.

Hidden Markov Model(HMM) is a discrete state-space stochastic model with efficient learning algorithm that works well for temporally correlated data streams and successful application. However, due to domain restrictions, we propose a new algorithm that fully unsupervised statistical techniques.

1.3 Introduction: the structure discovery problem

Fixed domain: audio-visual streams The structures have the following properties:

* Video structure are in a discrete state-space* features are stochastic* sequences are correlated in time* Focus on dense structures

Assumptions Within events, states are discrete and Markov Observations are associated with states under Gaussian

1.4 Introduction: Characteristics of Video Structure

Model the temporal, dependencies in video and generic structure of events in a unified statistical framework

Model recurring events in each video as HMM and HHMM, where the state inference and parameter estimation learned using EM

Developed algorithms to address model selection and feature selection problems

Bayesian learning techniques for model complexity Bayesian Information Criteria as model posterior Filter-wrapper method for feature selection

1.5 Introduction: Approach

Use two-level hierarchical hidden Markov model

Higher- level elements correspond to semantic events and lower-levels elements represent variations

Special case of Dynamic Bayesian Network Could be extended to more levels and

feature distribution is not constrained to a mixture of Gaussians

2 Hierarchical Hidden Markov Models(HHMM)

2. Hierarchical Hidden Markov Models: Graphical Representation

Generalization to HMM with a hierarchical control structure.

Bottom-up structure

2 Hierarchical Hidden Markov Models: Structure of HHMM

(1) supervised learning

(2) unsupervised learning

(3) a mixture of the above

2 Hierarchical Hidden Markov Models: Structure of HHMM:

applications

Multi-level hidden state inference with HHMM is O(T3);however, not optimal due to some other algorithm with O(T).

A generalized forward-backward algorithm for hidden state inference

A generalized EM algorithm for parameter estimation with O(DT*|Q|2D).

2 Complexity of Inferencing and Learning with HHMM

Representations of states and parameter set of an HHMM

Scope of EM is the basic parameter estimation

Model size given and Learned over a per-defined feature set

2 Learning HHMM parameter with EM

2 Learning HHMM parameters with EM: representing an HHMM

The entire configuration of the hierarchical states from top to bottom with N-ary and D-digit integer.

Whole parameter set theta of an HHMM is represented by the followings:

2 Learning HHMM parameters with EM: Overview of EM algorithm

Parameter learning for HHMM using EM is known to converge to a local max and predefined model structures.

It has drawbacks, thus we adopt and Bayesian model.

use a Markov Chain Monte Carlo(MCMC) to maximize Bayesian information criterion

2 Bayesian Model adaptation

A class of algorithms designed to solve high dimensional optimization problems

MCMC iterates between two steps* new model sample based on current model and stat of

data* Decision step computes an acceptance probability based

on fitness of the proposed new model

Converge to global optimum

2 Overview of MCMC

Model adaptation for HHMM involves an iterative procedure.

Based on the current model, compute a probability profile involving EM, split(d),merge(d) and swap(d)

Certain formula to determine whether a proposed move is accepted

2 MCMC for HHMM

Select a relevant and compact feature subset that fits the HHMM model

Task of feature selection is divided into two aspect:

Eliminating irrelevant and redundant ones

2 Feature selection for unsupervised learning

Suppose the feature is a discrete set e.g F={ f1, …,fD}

Markov blanket filtering to eliminate

redundant features

A human operator needed to decide on whether to iterate

2 Feature selection for unsupervised learning: feature selection algorithm

2 Feature selection for unsupervised learning: evaluating information gain

After wrapping information gain criterion, we are left with possible redundancy.

Need to apply Markov blanket to solve this matter

Iterative algorithm with a threshold less than 5%

2 Feature selection for unsupervised learning: finding a Markov blanket

Computes a value that influences decision on whether to accept it.

Initialization and convergence issues exist, so randomization.

2 Feature selection for unsupervised learning: normalized BIC

3 Experiments & Results

Sports videos represent an interesting structure discovery

We compare the learning accuracy of four different learning schemes against the ground truth

Supervised HMM Supervised HHMM Unsupervised HHMM without model adaptation Unsupervised HHMM with model adaptation

* EM* MCMC

3 Experiments & Results: parameter and structure learning

3 Experiments & Results: parameter and structure learning

Run each of the four algorithm for 15 times with random starting points

Test the performance of the automatic feature selection method on the two video clips

For the Spain case, the evaluation has an accuracy of

74.8% and the Korea clip achieves an accuracy of 74.5%

3 Experiments & Results: feature selection

Conduct the baseball video clip on a different domain

HHMM learning with full model adaptation

Consistent results and agree with intuition

3 Experiments & Results: testing on a different domain

Simplified HHMM boils down to a sub-HMM but left to right model with skips

Fully connected general 2-level HHMM model Results show the constrained model is 2.3%

lower than the fully connected model, but more modeling power

3 Experiments & Results: comparing to HHMM with simplifying constraints

In this chapter, we proposed algorithms for unsupervised discovery of structure from video sequences.

We model video structures using HHMM with parameters learned using EM and MCMC.

We test them out on two different video clips and achieve results comparable to its supervised learning counterparts

Application to many other domains and simplified constraints.

4 Conclusion

It serves to solve high dimensional optimization problems

Solution to the Quiz

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