The mining and utilization of features directly affect the classification performance of models used in the classification and recognition of hyperspectral remote sensing images. Traditional models usually conduct feature mining from a single perspective, with the features mined being limited and the internal relationships between them being ignored. Consequently, useful features are lost and classification results are unsatisfactory. To fully mine and utilize image features, a new multi-scale feature-mining learning algorithm (MGRNet) is proposed. The model uses principal component analysis to reduce the dimensionality of the original hyperspectral image (HSI) to retain 99.99% of its semantic information and extract dimensionality reduction features. Using a multi-scale convolution algorithm, the input dimensionality reduction features were mined to obtain shallow features, which then served as inputs into a multi-scale graph convolution algorithm to construct the internal relationships between eigenvalues at different scales. We then carried out cross fusion of multi-scale information obtained by graph convolution, before inputting the new information obtained into the residual network algorithm for deep feature mining. Finally, a flexible maximum transfer function classifier was used to predict the final features and complete the classification. Experiments on three common hyperspectral datasets showed the MGRNet algorithm proposed in this paper to be superior to traditional methods in recognition accuracy.

For an image query, unsupervised contrastive learning labels crops of the same image as positives, and other image crops as negatives. Although intuitive, such a native label assignment strategy cannot reveal the underlying semantic similarity between a query and its positives and negatives, and impairs performance, since some negatives are semantically similar to the query or even share the same semantic class as the query. In this work, we first prove that for contrastive learning, inaccurate label assignment heavily impairs its generalization for semantic instance discrimination, while accurate labels benefit its generalization. Inspired by this theory, we propose a novel self-labeling refinement approach for contrastive learning. It improves the label quality via two complementary modules: (i) self-labeling refinery (SLR) to generate accurate labels and (ii) momentum mixup (MM) to enhance similarity between query and its positive. SLR uses a positive of a query to estimate semantic similarity between a query and its positive and negatives, and combines estimated similarity with vanilla label assignment in contrastive learning to iteratively generate more accurate and informative soft labels. We theoretically show that our SLR can exactly recover the true semantic labels of label-corrupted data, and supervises networks to achieve zero prediction error on classification tasks. MM randomly combines queries and positives to increase semantic similarity between the generated virtual queries and their positives so as to improves label accuracy. Experimental results on CIFAR10, ImageNet, VOC and COCO show the effectiveness of our method. PyTorch code and model will be released online.

Unsupervised continual learning remains a relatively uncharted territory in the existing literature because the vast majority of existing works call for unlimited access of ground truth incurring expensive labelling cost. Another issue lies in the problem of task boundaries and task IDs which must be known for model's updates or model's predictions hindering feasibility for real-time deployment. Knowledge Retention in Self-Adaptive Deep Continual Learner, (KIERA), is proposed in this paper. KIERA is developed from the notion of flexible deep clustering approach possessing an elastic network structure to cope with changing environments in the timely manner. The centroid-based experience replay is put forward to overcome the catastrophic forgetting problem. KIERA does not exploit any labelled samples for model updates while featuring a task-agnostic merit. The advantage of KIERA has been numerically validated in popular continual learning problems where it shows highly competitive performance compared to state-of-the art approaches. Our implementation is available in \textit{\url{https://github.com/ContinualAL/KIERA}}.

This tutorial presents two essential concepts in data science and automated learning. One is the machine learning pipeline, and the second is its optimization. These two principles are the key to implementing any successful intelligent system based on machine learning. A machine learning pipeline can be created by putting together a sequence of steps involved in training a machine learning model. It can be used to automate a machine learning workflow.

Therefore, feature elimination in statistics and machine learning is referred to as choosing a subset of relevant features from the dataset to use in further …

We consider non-convex stochastic optimization using first-order algorithms for which the gradient estimates may have heavy tails. We show that a combination of gradient clipping, momentum, and normalized gradient descent yields convergence to critical points in high-probability with best-known rates for smooth losses when the gradients only have bounded $\mathfrak{p}$th moments for some $\mathfrak{p}\in(1,2]$. We then consider the case of second-order smooth losses, which to our knowledge have not been studied in this setting, and again obtain high-probability bounds for any $\mathfrak{p}$. Moreover, our results hold for arbitrary smooth norms, in contrast to the typical SGD analysis which requires a Hilbert space norm. Further, we show that after a suitable "burn-in" period, the objective value will monotonically decrease for every iteration until a critical point is identified, which provides intuition behind the popular practice of learning rate "warm-up" and also yields a last-iterate guarantee.

We study the asymmetric low-rank factorization problem: \[\min_{\mathbf{U} \in \mathbb{R}^{m \times d}, \mathbf{V} \in \mathbb{R}^{n \times d}} \frac{1}{2}\|\mathbf{U}\mathbf{V}^\top -\mathbf{\Sigma}\|_F^2\] where $\mathbf{\Sigma}$ is a given matrix of size $m \times n$ and rank $d$. This is a canonical problem that admits two difficulties in optimization: 1) non-convexity and 2) non-smoothness (due to unbalancedness of $\mathbf{U}$ and $\mathbf{V}$). This is also a prototype for more complex problems such as asymmetric matrix sensing and matrix completion. Despite being non-convex and non-smooth, it has been observed empirically that the randomly initialized gradient descent algorithm can solve this problem in polynomial time. Existing theories to explain this phenomenon all require artificial modifications of the algorithm, such as adding noise in each iteration and adding a balancing regularizer to balance the $\mathbf{U}$ and $\mathbf{V}$. This paper presents the first proof that shows randomly initialized gradient descent converges to a global minimum of the asymmetric low-rank factorization problem with a polynomial rate. For the proof, we develop 1) a new symmetrization technique to capture the magnitudes of the symmetry and asymmetry, and 2) a quantitative perturbation analysis to approximate matrix derivatives. We believe both are useful for other related non-convex problems.

We present a new way of study of Mercer kernels, by corresponding to a special kernel $K$ a pseudo-differential operator $p({\mathbf x}, D)$ such that $\mathcal{F} p({\mathbf x}, D)^\dag p({\mathbf x}, D) \mathcal{F}^{-1}$ acts on smooth functions in the same way as an integral operator associated with $K$ (where $\mathcal{F}$ is the Fourier transform). We show that kernels defined by pseudo-differential operators are able to approximate uniformly any continuous Mercer kernel on a compact set. The symbol $p({\mathbf x}, {\mathbf y})$ encapsulates a lot of useful information about the structure of the Maximum Mean Discrepancy distance defined by the kernel $K$. We approximate $p({\mathbf x}, {\mathbf y})$ with the sum of the first $r$ terms of the Singular Value Decomposition of $p$, denoted by $p_r({\mathbf x}, {\mathbf y})$. If ordered singular values of the integral operator associated with $p({\mathbf x}, {\mathbf y})$ die down rapidly, the MMD distance defined by the new symbol $p_r$ differs from the initial one only slightly. Moreover, the new MMD distance can be interpreted as an aggregated result of comparing $r$ local moments of two probability distributions. The latter results holds under the condition that right singular vectors of the integral operator associated with $p$ are uniformly bounded. But even if this is not satisfied we can still hold that the Hilbert-Schmidt distance between $p$ and $p_r$ vanishes. Thus, we report an interesting phenomenon: the MMD distance measures the difference of two probability distributions with respect to a certain number of local moments, $r^\ast$, and this number $r^\ast$ depends on the speed with which singular values of $p$ die down.

We consider the problem of interpretable network representation learning for samples of network-valued data. We propose the Principal Component Analysis for Networks (PCAN) algorithm to identify statistically meaningful low-dimensional representations of a network sample via subgraph count statistics. The PCAN procedure provides an interpretable framework for which one can readily visualize, explore, and formulate predictive models for network samples. We furthermore introduce a fast sampling-based algorithm, sPCAN, which is significantly more computationally efficient than its counterpart, but still enjoys advantages of interpretability. We investigate the relationship between these two methods and analyze their large-sample properties under the common regime where the sample of networks is a collection of kernel-based random graphs. We show that under this regime, the embeddings of the sPCAN method enjoy a central limit theorem and moreover that the population level embeddings of PCAN and sPCAN are equivalent. We assess PCAN's ability to visualize, cluster, and classify observations in network samples arising in nature, including functional connectivity network samples and dynamic networks describing the political co-voting habits of the U.S. Senate. Our analyses reveal that our proposed algorithm provides informative and discriminatory features describing the networks in each sample. The PCAN and sPCAN methods build on the current literature of network representation learning and set the stage for a new line of research in interpretable learning on network-valued data. Publicly available software for the PCAN and sPCAN methods are available at https://www.github.com/jihuilee/.

Determinantal Point Process (DPPs) are statistical models for repulsive point patterns. Both sampling and inference are tractable for DPPs, a rare feature among models with negative dependence that explains their popularity in machine learning and spatial statistics. Parametric and nonparametric inference methods have been proposed in the finite case, i.e. when the point patterns live in a finite ground set. In the continuous case, only parametric methods have been investigated, while nonparametric maximum likelihood for DPPs -- an optimization problem over trace-class operators -- has remained an open question. In this paper, we show that a restricted version of this maximum likelihood (MLE) problem falls within the scope of a recent representer theorem for nonnegative functions in an RKHS. This leads to a finite-dimensional problem, with strong statistical ties to the original MLE. Moreover, we propose, analyze, and demonstrate a fixed point algorithm to solve this finite-dimensional problem. Finally, we also provide a controlled estimate of the correlation kernel of the DPP, thus providing more interpretability.