Multivariate Techniques in Biomechanical Analysis

This work outlines the theoretical advantages of multivariate methods in biomechanical data, validates the proposed methods and outlines new clinical findings relating to knee osteoarthritis that were made possible by this approach. New techniques were based on existing multivariate approaches, Partial Least Squares (PLS) and Non-negative Matrix Factorization (NMF) and validated using existing data sets. The new techniques developed, PCA-PLS-LDA (Principal Component Analysis – Partial Least Squares – Linear Discriminant Analysis), PCA-PLS-MLR (Principal Component Analysis – Partial Least Squares –Multiple Linear Regression) and Waveform Similarity (based on NMF) were developed to address the challenging characteristics of biomechanical data, variability and correlation. As a result, these new structure-seeking technique revealed new clinical findings. The first new clinical finding relates to the relationship between pain, radiographic severity and mechanics. Simultaneous analysis of pain and radiographic severity outcomes, a first in biomechanics, revealed that the knee adduction moment’s relationship to radiographic features is mediated by pain in subjects with moderate osteoarthritis. The second clinical finding was quantifying the importance of neuromuscular patterns in brace effectiveness for patients with knee osteoarthritis. I found that brace effectiveness was more related to the patient’s unbraced neuromuscular patterns than it was to mechanics, and that these neuromuscular patterns were more complicated than simply increased overall muscle activity, as previously thought.

Linear Hyperspectral Unmixing Using L0-norm Approximations and Nonnegative Matrix Factorization

Spectral unmixing (SU) is a technique to characterize mixed pixels of the hyperspectral images measured by remote sensors. Most of the existing spectral unmixing algorithms are developed using the linear mixing models. Since the number of endmembers/materials present at each mixed pixel is normally scanty compared with the number of total endmembers (the dimension of spectral library), the problem becomes sparse. This thesis introduces sparse hyperspectral unmixing methods for the linear mixing model through two different scenarios. In the first scenario, the library of spectral signatures is assumed to be known and the main problem is to find the minimum number of endmembers under a reasonable small approximation error. Mathematically, the corresponding problem is called the $\ell_0$-norm problem which is NP-hard problem. Our main study for the first part of thesis is to find more accurate and reliable approximations of $\ell_0$-norm term and propose sparse unmixing methods via such approximations. The resulting methods are shown considerable improvements to reconstruct the fractional abundances of endmembers in comparison with state-of-the-art methods such as having lower reconstruction errors. In the second part of the thesis, the first scenario (i.e., dictionary-aided semiblind unmixing scheme) will be generalized as the blind unmixing scenario that the library of spectral signatures is also estimated. We apply the nonnegative matrix factorization (NMF) method for proposing new unmixing methods due to its noticeable supports such as considering the nonnegativity constraints of two decomposed matrices. Furthermore, we introduce new cost functions through some statistical and physical features of spectral signatures of materials (SSoM) and hyperspectral pixels such as the collaborative property of hyperspectral pixels and the mathematical representation of the concentrated energy of SSoM for the first few subbands. Finally, we introduce sparse unmixing methods for the blind scenario and evaluate the efficiency of the proposed methods via simulations over synthetic and real hyperspectral data sets. The results illustrate considerable enhancements to estimate the spectral library of materials and their fractional abundances such as smaller values of spectral angle distance (SAD) and abundance angle distance (AAD) as well.

The effects of the non-native invertebrate predator Bythotrephes longimanus and declining aqueous calcium on crustacean zooplankton communities in Canadian Shield lakes

Over the last several decades, human activities have resulted in environmental changes that have increased the number of stressors that can act on a single environment. In Canadian Shield lakes, two recent stressors, the invasion of Bythotrephes longimanus and calcium decline, have been documented. Widespread acidification of hundreds of North American lakes has resulted in the precipitous decline of lake water calcium concentration. Crustacean zooplankton with high calcium demands are likely to be vulnerable to calcium decline, especially <1.5 mg Ca/L, where survival and reproduction rates are reduced. These taxa are also vulnerable to predation by Bythotrephes that has been implicated in the loss of pelagic biodiversity in soft water lakes. Despite laboratory and field studies aimed at understanding the independent impact of these stressors, it is unclear how their co-occurrence will influence community response. Using a combination of data from a large regional lake survey and field experiments, I examined the individual and joint effects of Bythotrephes and calcium decline on native zooplankton community structure. Results demonstrated that much is known about Bythotrephes and our findings of reduced total zooplankton and species richness, due to the loss of Cladocera, are consistent with field surveys and other experimental studies. While we did not detect strong evidence for an effect of calcium on zooplankton using the lowest calcium concentration among invaded lakes (1.2 mg Ca/L), there is evidence that, as lake water calcium concentrations fall <1 mg Ca/L, per capita growth rates of a broad variety of taxa are expected to decline. At the regional scale, negative effects of Bythotrephes and calcium on abundances of small cladocerans and Daphnia pulicaria, respectively, were in agreement with my experimental observations. We also observed significant interactions between Bythotrephes and calcium for a broad variety of taxa. As Bythotrephes continues to spread and invade lakes that are also declining in aqueous calcium, both stressors are likely to amplify negative effects on Cladocera that appear the most vulnerable. Loss of these important zooplankton in response to both Bythotrephes and calcium decline, is likely to lower zooplankton productivity, with potential effects on phytoplankton and higher trophic levels.