A Fast Method to Segment Images with Additive Intensity Value

Master'sMASTER OF SCIENC

Asymptotically Optimal Sampling Policy for Quickest Change Detection with Observation-Switching Cost

We consider the problem of quickest change detection (QCD) in a signal where its observations are obtained using a set of actions, and switching from one action to another comes with a cost. The objective is to design a stopping rule consisting of a sampling policy to determine the sequence of actions used to observe the signal and a stopping time to quickly detect for the change, subject to a constraint on the average observation-switching cost. We propose an open-loop sampling policy of finite window size and a generalized likelihood ratio (GLR) Cumulative Sum (CuSum) stopping time for the QCD problem. We show that the GLR CuSum stopping time is asymptotically optimal with a properly designed sampling policy and formulate the design of this sampling policy as a quadratic programming problem. We prove that it is sufficient to consider policies of window size not more than one when designing policies of finite window size and propose several algorithms that solve this optimization problem with theoretical guarantees. For observation-dependent policies, we propose a $2$-threshold stopping time and an observation-dependent sampling policy. We present a method to design the observation-dependent sampling policy based on open-loop sampling policies. Finally, we apply our approach to the problem of QCD of a partially observed graph signal and empirically demonstrate the performance of our proposed stopping times

Quickest Change Detection in the Presence of a Nuisance Change

In the quickest change detection problem in which both nuisance and critical changes may occur, the objective is to detect the critical change as quickly as possible without raising an alarm when either there is no change or a nuisance change has occurred. A window-limited sequential change detection procedure based on the generalized likelihood ratio test statistic is proposed. A recursive update scheme for the proposed test statistic is developed and is shown to be asymptotically optimal under mild technical conditions. In the scenario where the post-change distribution belongs to a parametrized family, a generalized stopping time and a lower bound on its average run length are derived. The proposed stopping rule is compared with the FMA stopping time and the naive 2-stage procedure that detects the nuisance or critical change using separate CuSum stopping procedures for the nuisance and critical changes. Simulations demonstrate that the proposed rule outperforms the FMA stopping time and the 2-stage procedure, and experiments on a real dataset on bearing failure verify the performance of the proposed stopping time

A Binning Approach to Quickest Change Detection with Unknown Post-Change Distribution

The problem of quickest detection of a change in distribution is considered under the assumption that the pre-change distribution is known, and the post-change distribution is only known to belong to a family of distributions distinguishable from a discretized version of the pre-change distribution. A sequential change detection procedure is proposed that partitions the sample space into a finite number of bins, and monitors the number of samples falling into each of these bins to detect the change. A test statistic that approximates the generalized likelihood ratio test is developed. It is shown that the proposed test statistic can be efficiently computed using a recursive update scheme, and a procedure for choosing the number of bins in the scheme is provided. Various asymptotic properties of the test statistic are derived to offer insights into its performance trade-off between average detection delay and average run length to a false alarm. Testing on synthetic and real data demonstrates that our approach is comparable or better in performance to existing non-parametric change detection methods.Comment: Double-column 13-page version sent to IEEE. Transaction on Signal Processing. Supplementary material include

QUADRATIC FORMS OVER Q AND THE HASSE-MINKOWSKI THEOREM

Bachelor'sBACHELOR OF SCIENCE (HONOURS

Operationally constrained quickest change detection with multiple post-change distributions

Quickest change detection (QCD) is the problem of sequentially detecting a change in the statistical properties of a signal. As sensor and computing technology becomes increasingly pervasive and ubiquitous, QCD has found a wide spectrum of applications, from fraud detection to power system line outage detection. In many of these applications, rather than having one distribution, it is more likely that one of the multiple possible distributions generate the signal in the post-change regime. Furthermore, there are additional constraints due to operational requirements that need to be satisfied in addition to traditional QCD constraints. The research goal of this thesis is to study these problems and develop algorithms for QCD under some of these operational constraints. We first consider the problem of QCD when modeling or estimating the post-change distribution is impractical. A sequential change detection procedure that partitions the sample space into a finite number of bins and detects the change by observing the number of samples that fall into each of these bins is proposed. We developed an algorithm to update the test statistic recursively. Asymptotic properties of the test statistics are derived to offer intuition into its performance trade-off between average run length to a false alarm and the worse case average detection delay. Numerical experiments on synthetic and real data suggest that our proposed method is comparable or better in performance to existing non-parametric change detection methods. Next, we study the situation where the signal may undergo two types of change, nuisance and critical. We consider the problem where we are only interested in detecting the critical change as quickly as possible while not raising a false alarm when there is no change or when a nuisance has taken place. We develop a sequential change detection procedure based on the generalized likelihood ratio (GLR) test statistic and derive a recursive update scheme for this procedure. Our proposed stopping time is shown to be asymptotically optimal in the sense of Lorden, where it is not possible to improve the trade-off between the logarithm of the average run length and the worst-case average detection delay, under mild technical conditions. Furthermore, when the post-change distribution belongs to a parameterized family, we proposed a generalized stopping time and provided a lower bound on its average run length. We show that our proposed stopping time outperforms the finite moving average stopping time and the naive 2-stage stopping procedure via experiments on real and synthetic datasets. Another operational constraint that we study is sampling constraints. We consider the problem of QCD for a signal that is not fully observable and can only be observed using a finite set of actions. We propose a static sampling policy and a stopping rule based on the sampling policy. We show that the GLR CuSum achieves asymptotic optimality with a properly designed sampling policy and formulate an optimization problem for which the sampling policy that achieves asymptotic optimality is a solution. Finally, simulation results on partially observed graph signals show that our proposed approach achieves a much lower average detection delay, compared to a random uniform sampling policy, for large average run lengths. Finally, we consider the problem of QCD while taking privacy considerations into account. We formulate the privacy-aware QCD problem by including a privacy constraint to Lorden’s minimax formulation. We show that the GLR CuSum achieves asymptotic optimality with a properly designed sanitization channel and formulate the design of this sanitization channel as an optimization problem. We develop relaxations for the channel design problem to improve its computational tractability.Doctor of Philosoph

Understanding the user acceptance of gesture-based human-computer interactions

This study empirically evaluates how user perceptions and attitudes influence behavioral intention use of multi-touch gestures on a large multi-touch screen by using Technology Acceptance Model (TAM). In the study the researchers presented 20 novice users with an introduction and hands-on of multi-touch gestures on window, object and image manipulations. Following the hand-on session, data on user perceptions and attitudes about multi-touch gestures were gathered. The hierarchical multiple regression analyses were employed to test the hypothesized study model. The analysis results showed that both the user perceptions and attitudes have significant positive effects on user behavioral intention to use multi-touch gestures on computer applications. Suggestions for future research and conclusions for both researchers and practitioners are offered

Quickest change detection under a nuisance change

We consider the problem of quickest change detection (QCD) for a signal which may undergo both a nuisance and a critical change. Our goal is to detect the critical change without raising a false alarm over the nuisance change. An optimal sequential change detection procedure is proposed for the Bayesian formulation of our QCD problem. A sequential change detection procedure based on the generalized likelihood ratio test (GLRT) statistic is also proposed for the non-Bayesian formulation. We show that our proposed test statistics can be computed efficiently via respective recursive update schemes. We compare our proposed stopping rules with the naive 2-stage procedures, which attempt to detect the changes using separate optimal stopping procedures (i.e., the Shiryaev procedure in the Bayesian formulation, and the CuSum procedure in the non-Bayesian formulation) for the nuisance and critical changes. Simulations demonstrate that our proposed rules outperform the 2-stage procedures.NRF (Natl Research Foundation, S’pore)MOE (Min. of Education, S’pore)Accepted versio

Video Puzzle: A Visuospatial Based Tool To Evaluate Child-Multitouch Interaction Accuracy

We are now living in an ecosystem surrounding by interactive surface technology with its highly complex contents and applications. Pre-school children in Malaysia also face the same challenge in dealing with their edutainment which mainly resides on the multi-touch screen. This happened even more obvious when children playing game on multi-touch screen, gestures and objects are flashing fast from multiple angel within the screen, and children are moving their figure fast to ensure that that they can perform their task accurately. In this study, video puzzle had been employed as a metrics of evaluation to verify the level of accuracy at acquiring onscreen interactive and unstructured video puzzle pieces by pre-school children. Video puzzle is used to simulate the highly interactive, complexity, redundancies and repetitive child-computer interaction in today environment. The interactiveness, complexity, redundancy and repetitiveness in the interaction with video puzzle could be a significant challenge to pre-school children. Therefore, it’s an urgent call for us to understand the factors affecting the visuospatial skills and touch accuracy in child-computer interaction. The observation found that pre-school children tend to synthesis, evaluate and solve the unstructured video puzzle at their own efforts and this practice lay a foundation for children to become an effective problem solver in real world uncertain yet complex situation. In addition, this study also confirmed that the main reasons of missed numbers are due to the association of the pre-school children visuospatial motor’s abilities, size of the video puzzle piece and the complexity of the interaction. The touch accuracy on multi-touch surface for video puzzle is not really determined by age but size of the video puzzle and complexity does matter. The test indicated that less complexity with bigger size video puzzle leads to better touch accuracy on multi-touch screen. When the video puzzle testing moves into size 4 x 4, whereby the video puzzle piece size become smaller, the complexity and repetitiveness of interaction increased accordingly, pre-school children started to have difficulty to accurately tab on the piece of video puzzle