Scholarly Work - Computer Science
Permanent URI for this collectionhttps://scholarworks.montana.edu/handle/1/3034
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Item Univariate Skeleton Prediction in Multivariate Systems Using Transformers(Springer Nature, 2024-08) Morales, Giorgio; Sheppard, John W.Symbolic regression (SR) methods attempt to learn mathematical expressions that approximate the behavior of an observed system. However, when dealing with multivariate systems, they often fail to identify the functional form that explains the relationship between each variable and the system’s response. To begin to address this, we propose an explainable neural SR method that generates univariate symbolic skeletons that aim to explain how each variable influences the system’s response. By analyzing multiple sets of data generated artificially, where one input variable varies while others are fixed, relationships are modeled separately for each input variable. The response of such artificial data sets is estimated using a regression neural network (NN). Finally, the multiple sets of input–response pairs are processed by a pre-trained Multi-Set Transformer that solves a problem we termed Multi-Set Skeleton Prediction and outputs a univariate symbolic skeleton. Thus, such skeletons represent explanations of the function approximated by the regression NN. Experimental results demonstrate that this method learns skeleton expressions matching the underlying functions and outperforms two GP-based and two neural SR methods.Item Hyperspectral Band Selection for Multispectral Image Classification with Convolutional Networks(IEEE, 2021-07) Morales, Giorgio; Sheppard, John; Logan, Riley; Shaw, JosephIn recent years, Hyperspectral Imaging (HSI) has become a powerful source for reliable data in applications such as remote sensing, agriculture, and biomedicine. However, hyperspectral images are highly data-dense and often benefit from methods to reduce the number of spectral bands while retaining the most useful information for a specific application. We propose a novel band selection method to select a reduced set of wavelengths, obtained from an HSI system in the context of image classification. Our approach consists of two main steps: the first utilizes a filter-based approach to find relevant spectral bands based on a collinearity analysis between a band and its neighbors. This analysis helps to remove redundant bands and dramatically reduces the search space. The second step applies a wrapper-based approach to select bands from the reduced set based on their information entropy values, and trains a compact Convolutional Neural Network (CNN) to evaluate the performance of the current selection. We present classification results obtained from our method and compare them to other feature selection methods on two hyperspectral image datasets. Additionally, we use the original hyperspectral data cube to simulate the process of using actual filters in a multispectral imager. We show that our method produces more suitable results for a multispectral sensor design.Item Counterfactual Explanations of Neural Network-Generated Response Curves(IEEE, 2023-06) Morales, Giorgio; Sheppard, JohnResponse curves exhibit the magnitude of the response of a sensitive system to a varying stimulus. However, response of such systems may be sensitive to multiple stimuli (i.e., input features) that are not necessarily independent. As a consequence, the shape of response curves generated for a selected input feature (referred to as “active feature”) might depend on the values of the other input features (referred to as “passive features”). In this work we consider the case of systems whose response is approximated using regression neural networks. We propose to use counterfactual explanations (CFEs) for the identification of the features with the highest relevance on the shape of response curves generated by neural network black boxes. CFEs are generated by a genetic algorithm-based approach that solves a multi-objective optimization problem. In particular, given a response curve generated for an active feature, a CFE finds the minimum combination of passive features that need to be modified to alter the shape of the response curve. We tested our method on a synthetic dataset with 1-D inputs and two crop yield prediction datasets with 2-D inputs. The relevance ranking of features and feature combinations obtained on the synthetic dataset coincided with the analysis of the equation that was used to generate the problem. Results obtained on the yield prediction datasets revealed that the impact on fertilizer responsivity of passive features depends on the terrain characteristics of each field.Item Improved Yield Prediction of Winter Wheat Using a Novel Two-Dimensional Deep Regression Neural Network Trained via Remote Sensing(MDPI AG, 2023-01) Morales, Giorgio; Sheppard, John W.; Hedgedus, Paul B.; Maxwell, Bruce D.In recent years, the use of remotely sensed and on-ground observations of crop fields, in conjunction with machine learning techniques, has led to highly accurate crop yield estimations. In this work, we propose to further improve the yield prediction task by using Convolutional Neural Networks (CNNs) given their unique ability to exploit the spatial information of small regions of the field. We present a novel CNN architecture called Hyper3DNetReg that takes in a multi-channel input raster and, unlike previous approaches, outputs a two-dimensional raster, where each output pixel represents the predicted yield value of the corresponding input pixel. Our proposed method then generates a yield prediction map by aggregating the overlapping yield prediction patches obtained throughout the field. Our data consist of a set of eight rasterized remotely-sensed features: nitrogen rate applied, precipitation, slope, elevation, topographic position index (TPI), aspect, and two radar backscatter coefficients acquired from the Sentinel-1 satellites. We use data collected during the early stage of the winter wheat growing season (March) to predict yield values during the harvest season (August). We present leave-one-out cross-validation experiments for rain-fed winter wheat over four fields and show that our proposed methodology produces better predictions than five compared methods, including Bayesian multiple linear regression, standard multiple linear regression, random forest, an ensemble of feedforward networks using AdaBoost, a stacked autoencoder, and two other CNN architectures.Item Reduced-cost hyperspectral convolutional neural networks(2020-09) Morales, Giorgio; Sheppard, John W.; Scherrer, Bryan; Shaw, Joseph A.Hyperspectral imaging provides a useful tool for extracting complex information when visual spectral bands are not enough to solve certain tasks. However, processing hyperspectral images (HSIs) is usually computationally expensive due to the great amount of both spatial and spectral data they incorporate. We present a low-cost convolutional neural network designed for HSI classification. Its architecture consists of two parts: a series of densely connected three-dimensional (3-D) convolutions used as a feature extractor, and a series of two-dimensional (2-D) separable convolutions used as a spatial encoder. We show that this design involves fewer trainable parameters compared to other approaches, yet without detriment to its performance. What is more, we achieve comparable state-of-the-art results testing our architecture on four public remote sensing datasets: Indian Pines, Pavia University, Salinas, and EuroSAT; and a dataset of Kochia leaves [Bassia scoparia] with three different levels of herbicide resistance. The source code and datasets are available online.Item Hyperspectral Band Selection for Multispectral Image Classification with Convolutional Networks(2021) Morales, Giorgio; Sheppard, John W.; Logan, Riley D.; Shaw, Joseph A.In recent years, Hyperspectral Imaging (HSI) has become a powerful source for reliable data in applications such as remote sensing, agriculture, and biomedicine. However, hyperspectral images are highly data-dense and often benefit from methods to reduce the number of spectral bands while retaining the most useful information for a specific application. We propose a novel band selection method to select a reduced set of wavelengths, obtained from an HSI system in the context of image classification. Our approach consists of two main steps: the first utilizes a filter-based approach to find relevant spectral bands based on a collinearity analysis between a band and its neighbors. This analysis helps to remove redundant bands and dramatically reduces the search space. The second step applies a wrapper-based approach to select bands from the reduced set based on their information entropy values, and trains a compact Convolutional Neural Network (CNN) to evaluate the performance of the current selection. We present classification results obtained from our method and compare them to other feature selection methods on two hyperspectral image datasets. Additionally, we use the original hyperspectral data cube to simulate the process of using actual filters in a multispectral imager. We show that our method produces more suitable results for a multispectral sensor design.Item Two-dimensional deep regression for early yield prediction of winter wheat(2021-11) Morales, Giorgio; Sheppard, John W.Crop yield prediction is one of the tasks of Precision Agriculture that can be automated based on multi-source periodic observations of the fields. We tackle the yield prediction problem using a Convolutional Neural Network (CNN) trained on data that combines radar satellite imagery and on-ground information. We present a CNN architecture called Hyper3DNetReg that takes in a multi-channel input image and outputs a two-dimensional raster, where each pixel represents the predicted yield value of the corresponding input pixel. We utilize radar data acquired from the Sentinel-1 satellites, while the on-ground data correspond to a set of six raster features: nitrogen rate applied, precipitation, slope, elevation, topographic position index (TPI), and aspect. We use data collected during the early stage of the winter wheat growing season (March) to predict yield values during the harvest season (August). We present experiments over four fields of winter wheat and show that our proposed methodology yields better results than five compared methods, including multiple linear regression, an ensemble of feedforward networks using AdaBoost, a stacked autoencoder, and two other CNN architectures.Item Hyperspectral Dimensionality Reduction Based on Inter-Band Redundancy Analysis and Greedy Spectral Selection(2021-09) Morales, Giorgio; Sheppard, John W.; Logan, Riley D.; Shaw, Joseph A.Hyperspectral imaging systems are becoming widely used due to their increasing accessibility and their ability to provide detailed spectral responses based on hundreds of spectral bands. However, the resulting hyperspectral images (HSIs) come at the cost of increased storage requirements, increased computational time to process, and highly redundant data. Thus, dimensionality reduction techniques are necessary to decrease the number of spectral bands while retaining the most useful information. Our contribution is two-fold: First, we propose a filter-based method called interband redundancy analysis (IBRA) based on a collinearity analysis between a band and its neighbors. This analysis helps to remove redundant bands and dramatically reduces the search space. Second, we apply a wrapper-based approach called greedy spectral selection (GSS) to the results of IBRA to select bands based on their information entropy values and train a compact convolutional neural network to evaluate the performance of the current selection. We also propose a feature extraction framework that consists of two main steps: first, it reduces the total number of bands using IBRA; then, it can use any feature extraction method to obtain the desired number of feature channels. We present classification results obtained from our methods and compare them to other dimensionality reduction methods on three hyperspectral image datasets. Additionally, we used the original hyperspectral data cube to simulate the process of using actual filters in a multispectral imager.