Extended principal component analysis and its applications to image analysis

The objectives of this research are to analyze and develop a modified Principal Component Analysis (PCA) and to develop a two-dimensional PCA with applications in image processing. PCA is a classical multivariate technique where its mathematical treatment is purely based on the eigensystem of positive-definite symmetric matrices. Its main function is to statistically transform a set of correlated variables to a new set of uncorrelated variables over $\IR\sp{n}$ by retaining most of the variations present in the original variables.^ The variances of the Principal Components (PCs) obtained from the modified PCA form a correlation matrix of the original variables. The decomposition of this correlation matrix into a diagonal matrix produces a set of orthonormal basis that can be used to linearly transform the given PCs. It is this linear transformation that reproduces the original variables. The two-dimensional PCA can be devised as a two successive of one-dimensional PCA. It can be shown that, for an $m\times n$ matrix, the PCs obtained from the two-dimensional PCA are the singular values of that matrix.^ In this research, several applications for image analysis based on PCA are developed, i.e., edge detection, feature extraction, and multi-resolution PCA decomposition and reconstruction. ^

The relationship of student and teacher variables on academic achievement in Florida schools

Since 1995, Florida has been one of the leading states in the country initiating a high-stakes school accountability system. Public schools in Florida receive letter grades based on their performance on the Florida Comprehensive Assessment Test (FCAT). These school grades have significant effects on schools' reputations and funding. Consequently, the plan has been criticized for grading all schools in the same manner, without taking into account such variables as student poverty and mobility rates which are beyond the control of the school. ^ The purpose of this study was to examine the relationship of student variables (poverty and mobility rates) and teacher variables (average years of teacher experience and attained degree level) on FCAT math and reading performance. This research utilized an education production function model to examine which set of inputs (student or teacher) has a stronger influence on student academic output as measured by the FCAT. ^ The data collected for this study was from over 1500 public elementary schools in Florida that listed all pertinent information for 2 school years (1998/1999 & 1999/2000) on the Florida Department of Education's website. ^ It was concluded that student poverty, teacher average years of experience and student mobility taken together, provide a strong predictive measure of FCAT reading and math performance. However, the set of student inputs was significantly stronger than the teacher inputs. High student poverty was highly correlated with low FCAT scores. Teacher experience and student mobility rates were not nearly as strongly related to FCAT scores as was student poverty. The results of this study provide evidence for educators and other school stakeholders of the relative degree to which student and teacher variables are related to student academic achievement. The underlying reasons for these relationships will require further examination in future studies. These results raise questions for Florida's school policymakers about the educational equity of the state's accountability system and its implementation. ^

Cognitive and noncognitive variables that predict Florida community college radiography program graduates' success on the Registry

This study examined the predictive merits of selected cognitive and noncognitive variables on the national Registry exam pass rate using 2008 graduates (n = 175) from community college radiography programs in Florida. The independent variables included two GPAs, final grades in five radiography courses, self-efficacy, and social support. The dependent variable was the first-attempt results on the national Registry exam. The design was a retrospective predictive study that relied on academic data collected from participants using the self-report method and on perceptions of students' success on the national Registry exam collected through a questionnaire developed and piloted in the study. All independent variables except self-efficacy and social support correlated with success on the national Registry exam ( p < .01) using the Pearson Product-Moment Correlation analysis. The strongest predictor of the national Registry exam success was the end-of-program GPA, r = .550, p < .001. The GPAs and scores for self-efficacy and social support were entered into a logistic regression analysis to produce a prediction model. The end-of-program GPA (p = .015) emerged as a significant variable. This model predicted 44% of the students who failed the national Registry exam and 97.3% of those who passed, explaining 45.8% of the variance. A second model included the final grades for the radiography courses, self efficacy, and social support. Three courses significantly predicted national Registry exam success; Radiographic Exposures, p < .001; Radiologic Physics, p = .014; and Radiation Safety & Protection, p = .044, explaining 56.8% of the variance. This model predicted 64% of the students who failed the national Registry exam and 96% of those who passed. The findings support the use of in-program data as accurate predictors of success on the national Registry exam.

Tropical seagrass-associated macroalgae distributions and trends relative to water quality

Tropical coastal marine ecosystems including mangroves, seagrass beds and coral reef communities are undergoing intense degradation in response to natural and human disturbances, therefore, understanding the causes and mechanisms present challenges for scientist and managers. In order to protect our marine resources, determining the effects of nutrient loads on these coastal systems has become a key management goal. Data from monitoring programs were used to detect trends of macroalgae abundances and develop correlations with nutrient availability, as well as forecast potential responses of the communities monitored. Using eight years of data (1996–2003) from complementary but independent monitoring programs in seagrass beds and water quality of the Florida Keys National Marine Sanctuary (FKNMS), we: (1) described the distribution and abundance of macroalgae groups; (2) analyzed the status and spatiotemporal trends of macroalgae groups; and (3) explored the connection between water quality and the macroalgae distribution in the FKNMS. In the seagrass beds of the FKNMS calcareous green algae were the dominant macroalgae group followed by the red group; brown and calcareous red algae were present but in lower abundance. Spatiotemporal patterns of the macroalgae groups were analyzed with a non-linear regression model of the abundance data. For the period of record, all macroalgae groups increased in abundance (Abi) at most sites, with calcareous green algae increasing the most. Calcareous green algae and red algae exhibited seasonal pattern with peak abundances (Φi) mainly in summer for calcareous green and mainly in winter for red. Macroalgae Abi and long-term trend (mi) were correlated in a distinctive way with water quality parameters. Both the Abi and mi of calcareous green algae had positive correlations with NO3−, NO2−, total nitrogen (TN) and total organic carbon (TOC). Red algae Abi had a positive correlation with NO2−, TN, total phosphorus and TOC, and the mi in red algae was positively correlated with N:P. In contrast brown and calcareous red algae Abi had negative correlations with N:P. These results suggest that calcareous green algae and red algae are responding mainly to increases in N availability, a process that is happening in inshore sites. A combination of spatially variable factors such as local current patterns, nutrient sources, and habitat characteristics result in a complex array of the macroalgae community in the seagrass beds of the FKNMS.

Forecasting Responses of Seagrass Distributions to Changing Water Quality Using Monitoring Data

Extensive data sets on water quality and seagrass distributions in Florida Bay have been assembled under complementary, but independent, monitoring programs. This paper presents the landscape-scale results from these monitoring programs and outlines a method for exploring the relationships between two such data sets. Seagrass species occurrence and abundance data were used to define eight benthic habitat classes from 677 sampling locations in Florida Bay. Water quality data from 28 monitoring stations spread across the Bay were used to construct a discriminant function model that assigned a probability of a given benthic habitat class occurring for a given combination of water quality variables. Mean salinity, salinity variability, the amount of light reaching the benthos, sediment depth, and mean nutrient concentrations were important predictor variables in the discriminant function model. Using a cross-validated classification scheme, this discriminant function identified the most likely benthic habitat type as the actual habitat type in most cases. The model predicted that the distribution of benthic habitat types in Florida Bay would likely change if water quality and water delivery were changed by human engineering of freshwater discharge from the Everglades. Specifically, an increase in the seasonal delivery of freshwater to Florida Bay should cause an expansion of seagrass beds dominated by Ruppia maritima and Halodule wrightii at the expense of the Thalassia testudinum-dominated community that now occurs in northeast Florida Bay. These statistical techniques should prove useful for predicting landscape-scale changes in community composition in diverse systems where communities are in quasi-equilibrium with environmental drivers.