<p dir="ltr">This study introduces a methodology wherein daily values are linearly interpolated to achieve uniform temporal resolution across various data sets, including spectral and environmental information. This approach facilitates further analysis using machine learning techniques to estimate biomass. The proposed Best Friend Frame (B.F.F.) data set integrates Unmanned Aerial Systems (UAS) data, weather data, weather indices, soil hydrological group classifications, and topographic information. Two different biomass estimations were created to enhance versatility: one averaged per management practice and another averaged per physical experimental plot size. Additionally, SuperDove satellite data were combined with identical environmental data as that of the UAS.</p><p dir="ltr">UAS flights were conducted at the ACRE field in 2022 and 2023. The UAS data were captured at a height of 30 meters, yielding a ground sample distance of 2 cm/pixel per flight. Satellite data were sourced from the Planet SuperDove product. The images were processed using Crop Image Extraction (CIE) and calibrated with Vegetation Index Derivation (VID). Spatial resolution was defined as the experimental plot size per year per crop type (soybean or corn). Topographic data were derived from Indiana LiDAR data, and soil information was obtained from the USDA SSURGO dataset.</p><p dir="ltr">The B.F.F. framework can be utilized with various models to identify which environmental inputs influence biomass accumulation throughout the growing season.</p>

<p dir="ltr">In the dynamic and ever-evolving landscape of Artificial Intelligence (AI), the domain of deep learning has emerged as a pivotal force, propelling advancements across a broad spectrum of applications, notably in the intricate field of image classification. Image classification, a critical task that involves categorizing images into predefined classes, serves as the backbone for numerous cutting-edge technologies, including but not limited to, automated surveillance, facial recognition systems, and advanced diagnostics in healthcare. Despite the significant strides made in the area, the quest for models that not only excel in accuracy but also demonstrate robust generalization across varied datasets, and maintain resilience against the pitfalls of overfitting, remains a formidable challenge.</p><p dir="ltr">EfficientNetB0, a model celebrated for its optimized balance between computational efficiency and accuracy, stands at the forefront of solutions addressing these challenges. However, the nuanced complexities of datasets such as CIFAR-10, characterized by its diverse array of images spanning ten distinct categories, call for specialized adaptations to harness the full potential of such sophisticated architectures. In response, this thesis introduces an optimized version of the EffciientNetB0 architecture, meticulously enhanced with strategic architectural modifications, including the incorporation of an additional Dense layer endowed with 512 units and the strategic use of Dropout regularization. These adjustments are designed to amplify the model's capacity for learning and interpreting complex patterns inherent in the data.</p><p dir="ltr">Complimenting these architectural refinements, a nuanced two-phase training methodology is also adopted in the proposed model. This approach commences with the initial phase of training where the base model's pre-trained weights are frozen, thus leveraging the power of transfer learning to secure a solid foundational understanding. The subsequent phase of fine-tuning, characterized by the selective unfreezing of layers, meticulously calibrates the model to the intricacies of the CIFAR-10 dataset. This is further bolstered by the implementation of adaptive learning rate adjustments, ensuring the model’s training process is both efficient and responsive to the nuances of the learning curve.</p><p><br></p>

<p dir="ltr">Since graphs are natural representations for encoding relational data, the problem of graph matching is an emerging task and has attracted increasing attention, which could potentially impact various domains such as social network de-anonymization and computer vision. Our main interest is designing polynomial-time algorithms for seeded graph matching problems where a subset of pre-matched vertex-pairs (seeds) is revealed. </p><p dir="ltr">However, the existing work does not fully investigate the pivotal role of seeds and falls short of making the most use of the seeds. Notably, the majority of existing hand-crafted algorithms only focus on using ``witnesses'' in the 1-hop neighborhood. Although some advanced algorithms are proposed to use multi-hop witnesses, their theoretical analysis applies only to \ER random graphs and requires seeds to be all correct, which often do not hold in real applications. Furthermore, a parallel line of research, Graph Neural Network (GNN) approaches, typically employs a semi-supervised approach, which requires a large number of seeds and lacks the capacity to distill knowledge transferable to unseen graphs.</p><p dir="ltr">In my dissertation, I have taken two approaches to address these limitations. In the first approach, we study to design hand-crafted algorithms that can properly use multi-hop witnesses to match graphs. We first study graph matching using multi-hop neighborhoods when partially-correct seeds are provided. Specifically, consider two correlated graphs whose edges are sampled independently from a parent \ER graph $\mathcal{G}(n,p)$. A mapping between the vertices of the two graphs is provided as seeds, of which an unknown fraction is correct. We first analyze a simple algorithm that matches vertices based on the number of common seeds in the $1$-hop neighborhoods, and then further propose a new algorithm that uses seeds in the $D$-hop neighborhoods. We establish non-asymptotic performance guarantees of perfect matching for both $1$-hop and $2$-hop algorithms, showing that our new $2$-hop algorithm requires substantially fewer correct seeds than the $1$-hop algorithm when graphs are sparse. Moreover, by combining our new performance guarantees for the $1$-hop and $2$-hop algorithms, we attain the best-known results (in terms of the required fraction of correct seeds) across the entire range of graph sparsity and significantly improve the previous results. We then study the role of multi-hop neighborhoods in matching power-law graphs. Assume that two edge-correlated graphs are independently edge-sampled from a common parent graph with a power-law degree distribution. A set of correctly matched vertex-pairs is chosen at random and revealed as initial seeds. Our goal is to use the seeds to recover the remaining latent vertex correspondence between the two graphs. Departing from the existing approaches that focus on the use of high-degree seeds in $1$-hop neighborhoods, we develop an efficient algorithm that exploits the low-degree seeds in suitably-defined $D$-hop neighborhoods. Our result achieves an exponential reduction in the seed size requirement compared to the best previously known results.</p><p dir="ltr">In the second approach, we study GNNs for seeded graph matching. We propose a new supervised approach that can learn from a training set how to match unseen graphs with only a few seeds. Our SeedGNN architecture incorporates several novel designs, inspired by our theoretical studies of seeded graph matching: 1) it can learn to compute and use witness-like information from different hops, in a way that can be generalized to graphs of different sizes; 2) it can use easily-matched node-pairs as new seeds to improve the matching in subsequent layers. We evaluate SeedGNN on synthetic and real-world graphs and demonstrate significant performance improvements over both non-learning and learning algorithms in the existing literature. Furthermore, our experiments confirm that the knowledge learned by SeedGNN from training graphs can be generalized to test graphs of different sizes and categories.</p>