Due to the advance of storage technology in computers, matrix valued time series observations are collecting in many fields like finance, economics, weather forecasting, and many fields. The matrix valued data bring information along its row wise and column wise, and if they are collect over the time we have to treat the data as a time series. If we use classical dimension reduction by converting the matrix into a long vector, the structural information is lost. Here, we discuss two different ways of dimension reduction namely: PCA model for matrix valued time series data and the FA model for matrix valued time series data which keep the matrix structure and reduce the dimension of the observed data. The estimating procedure, theoretical properties and a simulation study are presented and demonstrated for both of these models.

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Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Master of Science / Department of Animal Sciences and Industry / Michael D. MacNeil / Jennifer M. Bormann / Genetic and phenotypic data are often provided to bull buyers at time of sale to aid producers in establishing economic value (pricing) of candidates for selection. This study evaluates the association between the information provided to bull buyers at time of sale and prices paid for bulls sold by two large seedstock operations located in Kansas (KS Ranch) and Colorado (CO Ranch). Data were gathered from 15 sale catalogs that documented bulls sold at auctions taking place from 2009 to 2013. In total, there were 39 potential predictor variables recorded for 2,601 Angus bulls for the KS Ranch; while 14 plausible predictor variables were recorded for 504 purebred and 1,399 Stabilizer bulls at the CO Ranch. Due to extensive multicollinearity between predictors, principal component (PC) analyses were conducted on the standardized predictors to reduce dimensionality within each ranch and genetic group. Eleven PC were considered to provide important meaningful information in summarizing the 39 predictors originally available to buyers at the KS Ranch. For both the purebred and Stabilizer bulls from each set of breed type data in the CO ranch, 6 principal components had eigenvalues greater than 1.0. Similar to the findings for the KS Ranch, these PCs also explained approximately 75% of the cumulative variability of the predictors. Sale prices were then regressed on the corresponding PC using a stepwise selection to identify the PC subset that most significantly explained the behavior of bull sale prices (P < 0.05). The final models explained approximately 63%, 37% and 58% of the variation in sale prices received for Angus, purebred and Stabilizer bulls, respectively. Interpretation of the eigenvectors for the PC having the greatest eigenvalues led to the conclusion that buyers put the most weight on growth traits followed by carcass characteristics and economic selection indices. However, no distinction of a specific variable’s numerical impact on price was determined.

We study the frequent problem of approximating a target matrix with a matrix of lower rank. We provide a simple and efficient (EM) algorithm for solving {\\em weighted} low rank approximation problems, which, unlike simple matrix factorization problems, do not admit a closed form solution in general. We analyze, in addition, the nature of locally optimal solutions that arise in this context, demonstrate the utility of accommodating the weights in reconstructing the underlying low rank representation, and extend the formulation to non-Gaussian noise models such as classification (collaborative filtering).

<p>This thesis covers the analysis of sparse and irregular fuel consumption data of long</p><p>distance haulage articulate trucks. It is shown that this kind of data is hard to analyse with multivariate as well as with functional methods. To be able to analyse the data, Principal Components Analysis through Conditional Expectation (PACE) is used, which enables the use of observations from many trucks to compensate for the sparsity of observations in order to get continuous results. The principal component scores generated by PACE, can then be used to get rough estimates of the trajectories for single trucks as well as to detect outliers. The data centric approach of PACE is very useful to enable functional analysis of sparse and irregular data. Functional analysis is desirable for this data to sidestep feature extraction and enabling a more natural view on the data.</p>

Estuary is an area with very complicated characteristics, which is mainly affected by tidal dynamics. The salinity of a tidal river is influenced by tidal characteristics where fresh water meets salty water and thus causing the complexity. The Love River in Kaohsiung, Taiwan, has been chosen as an study area for the researches describing in this thesis work. The four sampling stations cover the tidal zone of the Love River. Through frequent sampling, which corresponds to spring tides, neap tides and even during complete tidal cycles, the water quality and the variations of particle circulation in estuary area can be comprehended better. The distributions of the nutrients in the river are different during spring tides and neap tides. Nitrite and nitrate are mainly come from the upriver or generated by the nitrification within the river. In addition, the results from the whole tidal cycle experiments show that high flow rate occurs at the bottom during the period of turning tides, which caused higher SPM concentrations in the bottom layer. This is mainly due to the accumulated agitations at the river bottom were resuspended by the strong currents. Analytical results from a Pearson product-moment correlation has shown that the SPM concentrations in the bottom water partly come from the resuspension processes of bottom sediments. Nutrients accumulated in the bottom sediments were released into the water column by the SPM resuspensions. The result of PCA shows that the changes of tides affect the distribution of salinity has a strong negative correlation with turbidity and SPM. It also shows that tides not only have a quite obvious influence on suspended particle matters but also dominate the distribution of suspended particle matters through out the Love River.

This thesis covers the analysis of sparse and irregular fuel consumption data of long distance haulage articulate trucks. It is shown that this kind of data is hard to analyse with multivariate as well as with functional methods. To be able to analyse the data, Principal Components Analysis through Conditional Expectation (PACE) is used, which enables the use of observations from many trucks to compensate for the sparsity of observations in order to get continuous results. The principal component scores generated by PACE, can then be used to get rough estimates of the trajectories for single trucks as well as to detect outliers. The data centric approach of PACE is very useful to enable functional analysis of sparse and irregular data. Functional analysis is desirable for this data to sidestep feature extraction and enabling a more natural view on the data.

The protection of assets is an important part of daily life. Currently this is done using a combination of passive security cameras and security officers actively patrolling the premises. However, security officers, being human, are subject to a number of limitations both physical and mental. A security robot would not suffer from these limitations, however currently there are a number of challenges to implementing such a robot. These challenges include navigation in a complex real-world environment, fast and accurate threat detection and threat tracking. Overcoming these challenges is the focus of my research. To that end a small security robot, the CuWITH or Curious WITH,has been developed and is presented in this thesis. The CuWITH utilises a programmable navigation system, curiosity-based threat detection and curiosity-driven threat tracking curiosity to protect a real office environment. In this thesis we will first discuss the CuWITH's system design in detail, with a particular focus on the components and the architectural strategies employed. We then move to a more detailed examination of the mathematical underpinnings of the CuWITHs curiosity based threat detection and curiosity driven threat tracking. The details of the CuWITH's navigation will also be explained. We will then present a number of experiments which demonstrate the effectiveness of the CuWITH. We show that the programmable navigation of the CuWITH, although simple, allows for easy modification of the patrol path without risk to the stability of the system. We will then present the results of both offline and online testing of the CuWITH's curiosity based threat detection. The reaction time and accuracy of the CuWITHs curiosity driven threat tracking will also be illustrated. As a final test the CuWITH is instructed to execute a patrol in a real office environment, with threatening and non-threatening persons present. The results of this test demonstrate all major systems of the CuWITH working together very well and successfully executing the patrol even when moved to a different environment.

The protection of assets is an important part of daily life. Currently this is done using a combination of passive security cameras and security officers actively patrolling the premises. However, security officers, being human, are subject to a number of limitations both physical and mental. A security robot would not suffer from these limitations, however currently there are a number of challenges to implementing such a robot. These challenges include navigation in a complex real-world environment, fast and accurate threat detection and threat tracking. Overcoming these challenges is the focus of my research. To that end a small security robot, the CuWITH or Curious WITH,has been developed and is presented in this thesis. The CuWITH utilises a programmable navigation system, curiosity-based threat detection and curiosity-driven threat tracking curiosity to protect a real office environment. In this thesis we will first discuss the CuWITH's system design in detail, with a particular focus on the components and the architectural strategies employed. We then move to a more detailed examination of the mathematical underpinnings of the CuWITHs curiosity based threat detection and curiosity driven threat tracking. The details of the CuWITH's navigation will also be explained. We will then present a number of experiments which demonstrate the effectiveness of the CuWITH. We show that the programmable navigation of the CuWITH, although simple, allows for easy modification of the patrol path without risk to the stability of the system. We will then present the results of both offline and online testing of the CuWITH's curiosity based threat detection. The reaction time and accuracy of the CuWITHs curiosity driven threat tracking will also be illustrated. As a final test the CuWITH is instructed to execute a patrol in a real office environment, with threatening and non-threatening persons present. The results of this test demonstrate all major systems of the CuWITH working together very well and successfully executing the patrol even when moved to a different environment.