Machine learning in spectral domain

Deep neural networks are usually trained in the space of the nodes, by adjusting the weights of existing links via suitable optimization protocols. We here propose a radically new approach which anchors the learning process to reciprocal space. Specifically, the training acts on the spectral domain and seeks to modify the eigenvectors and eigenvalues of transfer operators in direct space. The proposed method is ductile and can be tailored to return either linear or non linear classifiers. The performance are competitive with standard schemes, while allowing for a significant reduction of the learning parameter space. Spectral learning restricted to eigenvalues could be also employed for pre-training of the deep neural network, in conjunction with conventional machine-learning schemes. Further, it is surmised that the nested indentation of eigenvectors that defines the core idea of spectral learning could help understanding why deep networks work as well as they do

Acoustic spectral imaging and transfer learning for reliable bearing fault diagnosis under variable speed conditions.

Incipient fault diagnosis of a bearing requires robust feature representation for an accurate condition-based monitoring system. Existing fault diagnosis schemes are mostly confined to manual features and traditional machine learning approaches such as artificial neural networks (ANN) and support vector machines (SVM). These handcrafted features require substantial human expertise and domain knowledge. In addition, these feature characteristics vary with the bearing's rotational speed. Thus, such methods do not yield the best results under variable speed conditions. To address this issue, this paper presents a reliable fault diagnosis scheme based on acoustic spectral imaging (ASI) of acoustic emission (AE) signals as a precise health state. These health states are further utilized with transfer learning, which is a machine learning technique, which shares knowledge with convolutional neural networks (CNN) for accurate diagnosis under variable operating conditions. In ASI, the amplitudes of the spectral components of the windowed time-domain acoustic emission signal are transformed into spectrum imaging. ASI provides a visual representation of acoustic emission spectral features in images. This ensures enhanced spectral images for transfer learning (TL) testing and training, and thus provides a robust classifier technique with high diagnostic accuracy

Multi-Spectral Image Classification with Ultra-Lean Complex-Valued Models

Multi-spectral imagery is invaluable for remote sensing due to different spectral signatures exhibited by materials that often appear identical in greyscale and RGB imagery. Paired with modern deep learning methods, this modality has great potential utility in a variety of remote sensing applications, such as humanitarian assistance and disaster recovery efforts. State-of-the-art deep learning methods have greatly benefited from large-scale annotations like in ImageNet, but existing MSI image datasets lack annotations at a similar scale. As an alternative to transfer learning on such data with few annotations, we apply complex-valued co-domain symmetric models to classify real-valued MSI images. Our experiments on 8-band xView data show that our ultra-lean model trained on xView from scratch without data augmentations can outperform ResNet with data augmentation and modified transfer learning on xView. Our work is the first to demonstrate the value of complex-valued deep learning on real-valued MSI data.Comment: NeuRIPS 2022 HADR workshop submissio

Spectral-DP: Differentially Private Deep Learning through Spectral Perturbation and Filtering

Differential privacy is a widely accepted measure of privacy in the context of deep learning algorithms, and achieving it relies on a noisy training approach known as differentially private stochastic gradient descent (DP-SGD). DP-SGD requires direct noise addition to every gradient in a dense neural network, the privacy is achieved at a significant utility cost. In this work, we present Spectral-DP, a new differentially private learning approach which combines gradient perturbation in the spectral domain with spectral filtering to achieve a desired privacy guarantee with a lower noise scale and thus better utility. We develop differentially private deep learning methods based on Spectral-DP for architectures that contain both convolution and fully connected layers. In particular, for fully connected layers, we combine a block-circulant based spatial restructuring with Spectral-DP to achieve better utility. Through comprehensive experiments, we study and provide guidelines to implement Spectral-DP deep learning on benchmark datasets. In comparison with state-of-the-art DP-SGD based approaches, Spectral-DP is shown to have uniformly better utility performance in both training from scratch and transfer learning settings.Comment: Accepted in 2023 IEEE Symposium on Security and Privacy (SP

Graph enabled cross-domain knowledge transfer

The world has never been more connected, led by the information technology revolution in the past decades that has fundamentally changed the way people interact with each other using social networks. Consequently, enormous human activity data are collected from the business world and machine learning techniques are widely adopted to aid our decision processes. Despite of the success of machine learning in various application scenarios, there are still many questions that need to be well answered, such as optimizing machine learning outcomes when desired knowledge cannot be extracted from the available data. This naturally drives us to ponder if one can leverage some side information to populate the knowledge domain of their interest, such that the problems within that knowledge domain can be better tackled. In this work, such problems are investigated and practical solutions are proposed. To leverage machine learning in any decision-making process, one must convert the given knowledge (for example, natural language, unstructured text) into representation vectors that can be understood and processed by machine learning model in their compatible language and data format. The frequently encountered difficulty is, however, the given knowledge is not rich or reliable enough in the first place. In such cases, one seeks to fuse side information from a separate domain to mitigate the gap between good representation learning and the scarce knowledge in the domain of interest. This approach is named Cross-Domain Knowledge Transfer. It is crucial to study the problem because of the commonality of scarce knowledge in many scenarios, from online healthcare platform analyses to financial market risk quantification, leaving an obstacle in front of us benefiting from automated decision making. From the machine learning perspective, the paradigm of semi-supervised learning takes advantage of large amount of data without ground truth and achieves impressive learning performance improvement. It is adopted in this dissertation for cross-domain knowledge transfer. Furthermore, graph learning techniques are indispensable given that networks commonly exist in real word, such as taxonomy networks and scholarly article citation networks. These networks contain additional useful knowledge and are ought to be incorporated in the learning process, which serve as an important lever in solving the problem of cross-domain knowledge transfer. This dissertation proposes graph-based learning solutions and demonstrates their practical usage via empirical studies on real-world applications. Another line of effort in this work lies in leveraging the rich capacity of neural networks to improve the learning outcomes, as we are in the era of big data. In contrast to many Graph Neural Networks that directly iterate on the graph adjacency to approximate graph convolution filters, this work also proposes an efficient Eigenvalue learning method that directly optimizes the graph convolution in the spectral space. This work articulates the importance of network spectrum and provides detailed analyses on the spectral properties in the proposed EigenLearn method, which well aligns with a series of CNN models that attempt to have meaningful spectral interpretation in designing graph neural networks. The disser-tation also addresses the efficiency, which can be categorized in two folds. First, by adopting approximate solutions it mitigates the complexity concerns for graph related algorithms, which are naturally quadratic in most cases and do not scale to large datasets. Second, it mitigates the storage and computation overhead in deep neural network, such that they can be deployed on many light-weight devices and significantly broaden the applicability. Finally, the dissertation is concluded by future endeavors

State-of-the-art and gaps for deep learning on limited training data in remote sensing

Deep learning usually requires big data, with respect to both volume and variety. However, most remote sensing applications only have limited training data, of which a small subset is labeled. Herein, we review three state-of-the-art approaches in deep learning to combat this challenge. The first topic is transfer learning, in which some aspects of one domain, e.g., features, are transferred to another domain. The next is unsupervised learning, e.g., autoencoders, which operate on unlabeled data. The last is generative adversarial networks, which can generate realistic looking data that can fool the likes of both a deep learning network and human. The aim of this article is to raise awareness of this dilemma, to direct the reader to existing work and to highlight current gaps that need solving.Comment: arXiv admin note: text overlap with arXiv:1709.0030