We introduce a new general identifiable framework for principled disentanglement referred to as Structured Nonlinear Independent Component Analysis (SNICA). Our contribution is to extend the identifiability theory of deep generative models for a very broad class of structured models. While previous works have shown identifiability for specific classes of time-series models, our theorems extend this to more general temporal structures as well as to models with more complex structures such as spatial dependencies. In particular, we establish the major result that identifiability for this framework holds even in the presence of noise of unknown distribution. The SNICA setting therefore subsumes all the existing nonlinear ICA models for time-series and also allows for new much richer identifiable models. Finally, as an example of our framework's flexibility, we introduce the first nonlinear ICA model for time-series that combines the following very useful properties: it accounts for both nonstationarity and autocorrelation in a fully unsupervised setting; performs dimensionality reduction; models hidden states; and enables principled estimation and inference by variational maximum-likelihood.

Deep neural network (DNN) generally takes thousands of iterations to optimize via gradient descent and thus has a slow convergence. In addition, softmax, as a decision layer, may ignore the distribution information of the data during classification. Aiming to tackle the referred problems, we propose a novel manifold neural network based on non-gradient optimization, i.e., the closed-form solutions. Considering that the activation function is generally invertible, we reconstruct the network via forward ridge regression and low rank backward approximation, which achieve the rapid convergence. Moreover, by unifying the flexible Stiefel manifold and adaptive support vector machine, we devise the novel decision layer which efficiently fits the manifold structure of the data and label information. Consequently, a jointly non-gradient optimization method is designed to generate the network with closed-form results.

This is a tutorial and survey paper on kernels, kernel methods, and related fields. We start with reviewing the history of kernels in functional analysis and machine learning. Then, Mercer kernel, Hilbert and Banach spaces, Reproducing Kernel Hilbert Space (RKHS), Mercer's theorem and its proof, frequently used kernels, kernel construction from distance metric, important classes of kernels (including bounded, integrally positive definite, universal, stationary, and characteristic kernels), kernel centering and normalization, and eigenfunctions are explained in detail. Then, we introduce types of use of kernels in machine learning including kernel methods (such as kernel support vector machines), kernel learning by semi-definite programming, Hilbert-Schmidt independence criterion, maximum mean discrepancy, kernel mean embedding, and kernel dimensionality reduction. We also cover rank and factorization of kernel matrix as well as the approximation of eigenfunctions and kernels using the Nystr{\"o}m method. This paper can be useful for various fields of science including machine learning, dimensionality reduction, functional analysis in mathematics, and mathematical physics in quantum mechanics.

This work proposes a hybrid Brain Computer Interface system for the automation of a wheelchair for the disabled. Herein a working prototype of a BCI-based wheelchair is detailed that can navigate inside a typical home environment with minimum structural modification and without any visual obstruction and discomfort to the user. The prototype is based on a combined mechanism of steady-state visually evoked potential and eye blinks. To elicit SSVEP, LEDs flickering at 13Hz and 15Hz were used to select the left and right direction, respectively, and EEG data was recorded. In addition, the occurrence of three continuous blinks was used as an indicator for stopping an ongoing action. The wavelet packet denoising method was applied, followed by feature extraction methods such as Wavelet Packet Decomposition and Canonical Correlation Analysis over narrowband reconstructed EEG signals. Bayesian optimization was used to obtain 5 fold cross-validations to optimize the hyperparameters of the Support Vector Machine. The resulting new model was tested and the average cross-validation accuracy 89.65% + 6.6% (SD) and testing accuracy 83.53% + 8.59% (SD) were obtained. The wheelchair was controlled by RaspberryPi through WiFi. The developed prototype demonstrated an average of 86.97% success rate for all trials with 4.015s for each command execution. The prototype can be used efficiently in a home environment without causing any discomfort to the user.

Graph is an usual representation of relational data, which are ubiquitous in manydomains such as molecules, biological and social networks. A popular approach to learningwith graph structured data is to make use of graph kernels, which measure the similaritybetween graphs and are plugged into a kernel machine such as a support vector machine.Weisfeiler-Lehman (WL) based graph kernels, which employ WL labeling scheme to extract subtree patterns and perform node embedding, are demonstrated to achieve great performance while being efficiently computable. However, one of the main drawbacks of ageneral kernel is the decoupling of kernel construction and learning process. For moleculargraphs, usual kernels such as WL subtree, based on substructures of the molecules, consider all available substructures having the same importance, which might not be suitable inpractice. In this paper, we propose a method to learn the weights of subtree patterns in the framework of WWL kernels, the state of the art method for graph classification task [14]. To overcome the computational issue on large scale data sets, we present an efficient learning algorithm and also derive a generalization gap bound to show its convergence. Finally, through experiments on synthetic and real-world data sets, we demonstrate the effectiveness of our proposed method for learning the weights of subtree patterns.

Cross-lingual document representations enable language understanding in multilingual contexts and allow transfer learning from high-resource to low-resource languages at the document level. Recently large pre-trained language models such as BERT, XLM and XLM-RoBERTa have achieved great success when fine-tuned on sentence-level downstream tasks. It is tempting to apply these cross-lingual models to document representation learning. However, there are two challenges: (1) these models impose high costs on long document processing and thus many of them have strict length limit; (2) model fine-tuning requires extra data and computational resources, which is not practical in resource-limited settings. In this work, we address these challenges by proposing unsupervised Language-Agnostic Weighted Document Representations (LAWDR). We study the geometry of pre-trained sentence embeddings and leverage it to derive document representations without fine-tuning. Evaluated on cross-lingual document alignment, LAWDR demonstrates comparable performance to state-of-the-art models on benchmark datasets.

Radar-based recognition and localization of people and things in the home environment has certain advantages over computer vision, including increased user privacy, low power consumption, zero-light operation and more sensor flexible placement. Shallow machine learning techniques such as Support Vector Machines and Logistic Regression can be used to classify images from radar, and in my previous work, Teaching Radar to Understand the Home and Using Stochastic Gradient Descent to Train Linear Classifiers I shared how to apply some of these methods. In this article, you will learn how to develop Deep Neural Networks (DNN)and train them to classify objects in radar images. In addition, you will learn how to use a Semi-Supervised Generative Adversarial Network (SGAN) [1] that only needs a small number of labeled data to train a DNN classifier. This is important in dealing with radar data sets because of the dearth of large training sets, in contrast to those available for camera-based images (e.g., ImageNet) which has helped to make computer vision ubiquitous.

Here just for classification, You may use SVC() class. If you want to perform the Regression task, You may use SVR() class. Here if you do not set the default kernel automatically, it will be "rbf" by default. Here we are using pipeline method to make the implementation to stream align. The First step here is to import all the requirement libraries for our example.

An analysis of high dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few important features, but they are limited due to the lack of interpretability and connectivity to actual decision making associated with each physical variable. Important variable selection techniques, as an alternative, can maintain the interpretability, but they often involve a greedy search that is susceptible to failure in capturing important interactions. This research proposes a new method that produces subspaces, reduced-dimensional physical spaces, based on a randomized search and forms an ensemble of models for critical subspaces. When applied to high-dimensional data collected from a composite metal development process, the proposed method shows its superiority in prediction and important variable selection.

Active learning methods have recently surged in the literature due to their ability to solve complex structural reliability problems within an affordable computational cost. These methods are designed by adaptively building an inexpensive surrogate of the original limit-state function. Examples of such surrogates include Gaussian process models which have been adopted in many contributions, the most popular ones being the efficient global reliability analysis (EGRA) and the active Kriging Monte Carlo simulation (AK-MCS), two milestone contributions in the field. In this paper, we first conduct a survey of the recent literature, showing that most of the proposed methods actually span from modifying one or more aspects of the two aforementioned methods. We then propose a generalized modular framework to build on-the-fly efficient active learning strategies by combining the following four ingredients or modules: surrogate model, reliability estimation algorithm, learning function and stopping criterion. Using this framework, we devise 39 strategies for the solution of 20 reliability benchmark problems. The results of this extensive benchmark are analyzed under various criteria leading to a synthesized set of recommendations for practitioners. These may be refined with a priori knowledge about the feature of the problem to solve, i.e., dimensionality and magnitude of the failure probability. This benchmark has eventually highlighted the importance of using surrogates in conjunction with sophisticated reliability estimation algorithms as a way to enhance the efficiency of the latter.