Low-Rank Tensorized Neural Networks With Tensor Geometry Optimization

Deep neural networks have demonstrated significant achievements across various fields, yet their memory and time complexities present obstacles for implementing them on resource-constrained devices. Compressing deep neural networks using tensor decomposition can decrease both memory usage and computational costs. The performance of a low-rank tensorized network depends on the choices of hyperparameters including the tensor rank and geometry. Previous studies have concentrated on identifying optimal tensor ranks. This thesis studies the effect of tensor geometry used for folding data for low-rank tensor compression. It is demonstrated that tensor geometry significantly affects compression efficiency of the tensorized data and model parameters. Consequently, a novel mathematical formulation is developed to optimize tensor geometry. The tensor geometry optimization model is adopted for efficient deployment of low-rank neural networks. The presented tensor geometry optimization model is combinatorial and thus challenging to solve. Therefore, surrogate and relaxed versions of the model are developed and various methods including integer linear programming, graph optimization, and random search algorithms are applied to solve the presented optimization model. The proposed tensor geometry optimization achieved a notable reduction in both the memory and time complexities of neural networks while maintaining accuracy. The developed methods can be applied for hardware-software co-design of artificial intelligence (AI) accelerators particularly on resource-constrained devices

A tensor-based selection hyper-heuristic for cross-domain heuristic search

Hyper-heuristics have emerged as automated high level search methodologies that manage a set of low level heuristics for solving computationally hard problems. A generic selection hyper-heuristic combines heuristic selection and move acceptance methods under an iterative single point-based search framework. At each step, the solution in hand is modified after applying a selected heuristic and a decision is made whether the new solution is accepted or not. In this study, we represent the trail of a hyper-heuristic as a third order tensor. Factorization of such a tensor reveals the latent relationships between the low level heuristics and the hyper-heuristic itself. The proposed learning approach partitions the set of low level heuristics into two subsets where heuristics in each subset are associated with a separate move acceptance method. Then a multi-stage hyper-heuristic is formed and while solving a given problem instance, heuristics are allowed to operate only in conjunction with the associated acceptance method at each stage. To the best of our knowledge, this is the first time tensor analysis of the space of heuristics is used as a data science approach to improve the performance of a hyper-heuristic in the prescribed manner. The empirical results across six different problem domains from a benchmark indeed indicate the success of the proposed approach

A Comprehensive Survey of Deep Learning in Remote Sensing: Theories, Tools and Challenges for the Community

In recent years, deep learning (DL), a re-branding of neural networks (NNs), has risen to the top in numerous areas, namely computer vision (CV), speech recognition, natural language processing, etc. Whereas remote sensing (RS) possesses a number of unique challenges, primarily related to sensors and applications, inevitably RS draws from many of the same theories as CV; e.g., statistics, fusion, and machine learning, to name a few. This means that the RS community should be aware of, if not at the leading edge of, of advancements like DL. Herein, we provide the most comprehensive survey of state-of-the-art RS DL research. We also review recent new developments in the DL field that can be used in DL for RS. Namely, we focus on theories, tools and challenges for the RS community. Specifically, we focus on unsolved challenges and opportunities as it relates to (i) inadequate data sets, (ii) human-understandable solutions for modelling physical phenomena, (iii) Big Data, (iv) non-traditional heterogeneous data sources, (v) DL architectures and learning algorithms for spectral, spatial and temporal data, (vi) transfer learning, (vii) an improved theoretical understanding of DL systems, (viii) high barriers to entry, and (ix) training and optimizing the DL.Comment: 64 pages, 411 references. To appear in Journal of Applied Remote Sensin

A new hybridized dimensionality reduction approach using genetic algorithm and folded linear discriminant analysis applied to hyperspectral imaging for effective rice seed classification

Hyperspectral imaging (HSI) has been reported to produce promising results in the classification of rice seeds. However, HSI data often require the use of dimensionality reduction techniques for the removal of redundant data. Folded linear discriminant analysis (F-LDA) is an extension of linear discriminant analysis (LDA, a commonly used technique for dimensionality reduction), and was recently proposed to address the limitations of LDA, particularly its poor performance when dealing with a small number of training samples which is a usual scenario in HSI applications. This article presents an improved version of F-LDA, exploring the feasibility of hybridizing a genetic algorithm (GA) and F-LDA for effective dimensionality reduction in HSI-based rice seeds classification. The proposed approach, inspired by the previous combination of GA with principle component analysis, is evaluated on rice seed datasets containing 256 spectral bands. Experimental results show that, in addition to attaining promising classification accuracies of up to 96.21%, this novel combination of GA and F-LDA (GA + F-LDA) can further reduce the computational complexity and memory requirement in the standalone F-LDA. It is worth noting that these benefits are not without a slight reduction in classification accuracy when evaluated against those reported for the standard F-LDA (up to 96.99%)

A New Hybridized Dimensionality Reduction Approach Using Genetic Algorithm and Folded Linear Discriminant Analysis Applied to Hyperspectral Imaging for Effective Rice Seed Classification

Hyperspectral imaging (HSI) has been reported to produce promising results in the classification of rice seeds. However, HSI data often require the use of dimensionality reduction techniques for the removal of redundant data. Folded linear discriminant analysis (F-LDA) is an extension of linear discriminant analysis (LDA, a commonly used technique for dimensionality reduction), and was recently proposed to address the limitations of LDA, particularly its poor performance when dealing with a small number of training samples which is a usual scenario in HSI applications. This article presents an improved version of F-LDA, exploring the feasibility of hybridizing a genetic algorithm (GA) and F-LDA for effective dimensionality reduction in HSI-based rice seeds classification. The proposed approach, inspired by the previous combination of GA with principle component analysis, is evaluated on rice seed datasets containing 256 spectral bands. Experimental results show that, in addition to attaining promising classification accuracies of up to 96.21%, this novel combination of GA and F-LDA (GA + F-LDA) can further reduce the computational complexity and memory requirement in the standalone F-LDA. It is worth noting that these benefits are not without a slight reduction in classification accuracy when evaluated against those reported for the standard F-LDA (up to 96.99%)

Multimodal Data Fusion: An Overview of Methods, Challenges and Prospects

International audienceIn various disciplines, information about the same phenomenon can be acquired from different types of detectors, at different conditions, in multiple experiments or subjects, among others. We use the term "modality" for each such acquisition framework. Due to the rich characteristics of natural phenomena, it is rare that a single modality provides complete knowledge of the phenomenon of interest. The increasing availability of several modalities reporting on the same system introduces new degrees of freedom, which raise questions beyond those related to exploiting each modality separately. As we argue, many of these questions, or "challenges" , are common to multiple domains. This paper deals with two key questions: "why we need data fusion" and "how we perform it". The first question is motivated by numerous examples in science and technology, followed by a mathematical framework that showcases some of the benefits that data fusion provides. In order to address the second question, "diversity" is introduced as a key concept, and a number of data-driven solutions based on matrix and tensor decompositions are discussed, emphasizing how they account for diversity across the datasets. The aim of this paper is to provide the reader, regardless of his or her community of origin, with a taste of the vastness of the field, the prospects and opportunities that it holds

Tensor-based Hyperspectral Image Processing Methodology and its Applications in Impervious Surface and Land Cover Mapping

The emergence of hyperspectral imaging provides a new perspective for Earth observation, in addition to previously available orthophoto and multispectral imagery. This thesis focused on both the new data and new methodology in the field of hyperspectral imaging. First, the application of the future hyperspectral satellite EnMAP in impervious surface area (ISA) mapping was studied. During the search for the appropriate ISA mapping procedure for the new data, the subpixel classification based on nonnegative matrix factorization (NMF) achieved the best success. The simulated EnMAP image shows great potential in urban ISA mapping with over 85% accuracy. Unfortunately, the NMF based on the linear algebra only considers the spectral information and neglects the spatial information in the original image. The recent wide interest of applying the multilinear algebra in computer vision sheds light on this problem and raised the idea of nonnegative tensor factorization (NTF). This thesis found that the NTF has more advantages over the NMF when work with medium- rather than the high-spatial-resolution hyperspectral image. Furthermore, this thesis proposed to equip the NTF-based subpixel classification methods with the variations adopted from the NMF. By adopting the variations from the NMF, the urban ISA mapping results from the NTF were improved by ~2%. Lastly, the problem known as the curse of dimensionality is an obstacle in hyperspectral image applications. The majority of current dimension reduction (DR) methods are restricted to using only the spectral information, when the spatial information is neglected. To overcome this defect, two spectral-spatial methods: patch-based and tensor-patch-based, were thoroughly studied and compared in this thesis. To date, the popularity of the two solutions remains in computer vision studies and their applications in hyperspectral DR are limited. The patch-based and tensor-patch-based variations greatly improved the quality of dimension-reduced hyperspectral images, which then improved the land cover mapping results from them. In addition, this thesis proposed to use an improved method to produce an important intermediate result in the patch-based and tensor-patch-based DR process, which further improved the land cover mapping results

On the Use of Imaging Spectroscopy from Unmanned Aerial Systems (UAS) to Model Yield and Assess Growth Stages of a Broadacre Crop

Snap bean production was valued at $363 million in 2018. Moreover, the increasing need in food production, caused by the exponential increase in population, makes this crop vitally important to study. Traditionally, harvest time determination and yield prediction are performed by collecting limited number of samples. While this approach could work, it is inaccurate, labor-intensive, and based on a small sample size. The ambiguous nature of this approach furthermore leaves the grower with under-ripe and over-mature plants, decreasing the final net profit and the overall quality of the product. A more cost-effective method would be a site-specific approach that would save time and labor for farmers and growers, while providing them with exact detail to when and where to harvest and how much is to be harvested (while forecasting yield). In this study we used hyperspectral (i.e., point-based and image-based), as well as biophysical data, to identify spectral signatures and biophysical attributes that could schedule harvest and forecast yield prior to harvest. Over the past two decades, there have been immense advances in the field of yield and harvest modeling using remote sensing data. Nevertheless, there still exists a wide gap in the literature covering yield and harvest assessment as a function of time using both ground-based and unmanned aerial systems. There is a need for a study focusing on crop-specific yield and harvest assessment using a rapid, affordable system. We hypothesize that a down-sampled multispectral system, tuned with spectral features identified from hyperspectral data, could address the mentioned gaps. Moreover, we hypothesize that the airborne data will contain noise that could negatively impact the performance and the reliability of the utilized models. Thus, We address these knowledge gaps with three objectives as below: 1. Assess yield prediction of snap bean crop using spectral and biophysical data and identify discriminating spectral features via statistical and machine learning approaches. 2. Evaluate snap bean harvest maturity at both the plant growth stage and pod maturity level, by means of spectral and biophysical indicators, and identify the corresponding discriminating spectral features. 3. Assess the feasibility of using a deep learning architecture for reducing noise in the hyperspectral data. In the light of the mentioned objectives, we carried out a greenhouse study in the winter and spring of 2019, where we studied temporal change in spectra and physical attributes of snap-bean crop, from Huntington cultivar, using a handheld spectrometer in the visible- to shortwave-infrared domain (400-2500 nm). Chapter 3 of this dissertation focuses on yield assessment of the greenhouse study. Findings from this best-case scenario yield study showed that the best time to study yield is approximately 20-25 days prior to harvest that would give out the most accurate yield predictions. The proposed approach was able to explain variability as high as R2 = 0.72, with spectral features residing in absorption regions for chlorophyll, protein, lignin, and nitrogen, among others. The captured data from this study contained minimal noise, even in the detector fall-off regions. Moving the focus to harvest maturity assessment, Chapter 4 presents findings from this objective in the greenhouse environment. Our findings showed that four stages of maturity, namely vegetative growth, budding, flowering, and pod formation, are distinguishable with 79% and 78% accuracy, respectively, via the two introduced vegetation indices, as snap-bean growth index (SGI) and normalized difference snap-bean growth index (NDSI), respectively. Moreover, pod-level maturity classification showed that ready-to-harvest and not-ready-to-harvest pods can be separated with 78% accuracy with identified wavelengths residing in green, red edge, and shortwave-infrared regions. Moreover, Chapters 5 and 6 focus on transitioning the learned concepts from the mentioned greenhouse scenario to UAS domain. We transitioned from a handheld spectrometer in the visible to short-wave infrared domain (400-2500 nm) to a UAS-mounted hyperspectral imager in the visible-to-near-infrared region (400-1000 nm). Two years worth of data, at two different geographical locations, were collected in upstate New York and examined for yield modeling and harvest scheduling objectives. For analysis of the collected data, we introduced a feature selection library in Python, named “Jostar”, to identify the most discriminating wavelengths. The findings from the yield modeling UAS study show that pod weight and seed length, as two different yield indicators, can be explained with R2 as high as 0.93 and 0.98, respectively. Identified wavelengths resided in blue, green, red, and red edge regions, and 44-55 days after planting (DAP) showed to be the optimal time for yield assessment. Chapter 6, on the other hand, evaluates maturity assessment, in terms of pod classification, from the UAS perspective. Results from this study showed that the identified features resided in blue, green, red, and red-edge regions, contributing to F1 score as high as 0.91 for differentiating between ready-to-harvest vs. not ready-to-harvest. The identified features from this study is in line with those detected from the UAS yield assessment study. In order to have a parallel comparison of the greenhouse study against the UAS study, we adopted the methodology employed for UAS studies and applied it to the greenhouse studies, in Chapter 7. Since the greenhouse data were captured in the visible-to-shortwave-infrared (400-2500 nm) domain, and the UAS study data were captured in the VNIR (400-1000 nm) domain, we truncated the spectral range of the collected data from the greenhouse study to the VNIR domain. The comparison experiment between the greenhouse study and the UAS studies for yield assessment, at two harvest stages early and late, showed that spectral features in 450-470, 500-520, 650, 700-730 nm regions were repeated on days with highest coefficient of determination. Moreover, 46-48 DAP with high coefficient of determination for yield prediction were repeated in five out of six data sets (two early stages, each three data sets). On the other hand, the harvest maturity comparison between the greenhouse study and the UAS data sets showed that similar identified wavelengths reside in ∼450, ∼530, ∼715, and ∼760 nm regions, with performance metric (F1 score) of 0.78, 0.84, and 0.9 for greenhouse, 2019 UAS, and 2020 UAS data, respectively. However, the incorporated noise in the captured data from the UAS study, along with the high computational cost of the classical mathematical approach employed for denoising hyperspectral data, have inspired us to leverage the computational performance of hyperspectral denoising by assessing the feasibility of transferring the learned concepts to deep learning models. In Chapter 8, we approached hyperspectral denoising in spectral domain (1D fashion) for two types of noise, integrated noise and non-independent and non-identically distributed (non-i.i.d.) noise. We utilized Memory Networks due to their power in image denoising for hyperspectral denoising, introduced a new loss and benchmarked it against several data sets and models. The proposed model, HypeMemNet, ranked first - up to 40% in terms of signal-to-noise ratio (SNR) for resolving integrated noise, and first or second, by a small margin for resolving non-i.i.d. noise. Our findings showed that a proper receptive field and a suitable number of filters are crucial for denoising integrated noise, while parameter size was shown to be of the highest importance for non-i.i.d. noise. Results from the conducted studies provide a comprehensive understanding encompassing yield modeling, harvest scheduling, and hyperspectral denoising. Our findings bode well for transitioning from an expensive hyperspectral imager to a multispectral imager, tuned with the identified bands, as well as employing a rapid deep learning model for hyperspectral denoising

Tensor Regression

Regression analysis is a key area of interest in the field of data analysis and machine learning which is devoted to exploring the dependencies between variables, often using vectors. The emergence of high dimensional data in technologies such as neuroimaging, computer vision, climatology and social networks, has brought challenges to traditional data representation methods. Tensors, as high dimensional extensions of vectors, are considered as natural representations of high dimensional data. In this book, the authors provide a systematic study and analysis of tensor-based regression models and their applications in recent years. It groups and illustrates the existing tensor-based regression methods and covers the basics, core ideas, and theoretical characteristics of most tensor-based regression methods. In addition, readers can learn how to use existing tensor-based regression methods to solve specific regression tasks with multiway data, what datasets can be selected, and what software packages are available to start related work as soon as possible. Tensor Regression is the first thorough overview of the fundamentals, motivations, popular algorithms, strategies for efficient implementation, related applications, available datasets, and software resources for tensor-based regression analysis. It is essential reading for all students, researchers and practitioners of working on high dimensional data.Comment: 187 pages, 32 figures, 10 table

Computational Optimizations for Machine Learning

The present book contains the 10 articles finally accepted for publication in the Special Issue “Computational Optimizations for Machine Learning” of the MDPI journal Mathematics, which cover a wide range of topics connected to the theory and applications of machine learning, neural networks and artificial intelligence. These topics include, among others, various types of machine learning classes, such as supervised, unsupervised and reinforcement learning, deep neural networks, convolutional neural networks, GANs, decision trees, linear regression, SVM, K-means clustering, Q-learning, temporal difference, deep adversarial networks and more. It is hoped that the book will be interesting and useful to those developing mathematical algorithms and applications in the domain of artificial intelligence and machine learning as well as for those having the appropriate mathematical background and willing to become familiar with recent advances of machine learning computational optimization mathematics, which has nowadays permeated into almost all sectors of human life and activity