Functional Regression

Functional data analysis (FDA) involves the analysis of data whose ideal units of observation are functions defined on some continuous domain, and the observed data consist of a sample of functions taken from some population, sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the development of this field, which has accelerated in the past 10 years to become one of the fastest growing areas of statistics, fueled by the growing number of applications yielding this type of data. One unique characteristic of FDA is the need to combine information both across and within functions, which Ramsay and Silverman called replication and regularization, respectively. This article will focus on functional regression, the area of FDA that has received the most attention in applications and methodological development. First will be an introduction to basis functions, key building blocks for regularization in functional regression methods, followed by an overview of functional regression methods, split into three types: [1] functional predictor regression (scalar-on-function), [2] functional response regression (function-on-scalar) and [3] function-on-function regression. For each, the role of replication and regularization will be discussed and the methodological development described in a roughly chronological manner, at times deviating from the historical timeline to group together similar methods. The primary focus is on modeling and methodology, highlighting the modeling structures that have been developed and the various regularization approaches employed. At the end is a brief discussion describing potential areas of future development in this field

Forensic Face Recognition: A Survey

Beside a few papers which focus on the forensic aspects of automatic face recognition, there is not much published about it in contrast to the literature on developing new techniques and methodologies for biometric face recognition. In this report, we review forensic facial identification which is the forensic experts‟ way of manual facial comparison. Then we review famous works in the domain of forensic face recognition. Some of these papers describe general trends in forensics [1], guidelines for manual forensic facial comparison and training of face examiners who will be required to verify the outcome of automatic forensic face recognition system [2]. Some proposes theoretical framework for application of face recognition technology in forensics [3] and automatic forensic facial comparison [4, 5]. Bayesian framework is discussed in detail and it is elaborated how it can be adapted to forensic face recognition. Several issues related with court admissibility and reliability of system are also discussed. \ud Until now, there is no operational system available which automatically compare image of a suspect with mugshot database and provide result usable in court. The fact that biometric face recognition can in most cases be used for forensic purpose is true but the issues related to integration of technology with legal system of court still remain to be solved. There is a great need for research which is multi-disciplinary in nature and which will integrate the face recognition technology with existing legal systems. In this report we present a review of the existing literature in this domain and discuss various aspects and requirements for forensic face recognition systems particularly focusing on Bayesian framework