Stochastic Behavior of the Nonnegative Least Mean Fourth Algorithm for Stationary Gaussian Inputs and Slow Learning

Some system identification problems impose nonnegativity constraints on the parameters to estimate due to inherent physical characteristics of the unknown system. The nonnegative least-mean-square (NNLMS) algorithm and its variants allow to address this problem in an online manner. A nonnegative least mean fourth (NNLMF) algorithm has been recently proposed to improve the performance of these algorithms in cases where the measurement noise is not Gaussian. This paper provides a first theoretical analysis of the stochastic behavior of the NNLMF algorithm for stationary Gaussian inputs and slow learning. Simulation results illustrate the accuracy of the proposed analysis.Comment: 11 pages, 8 figures, submitted for publicatio

Noise-Tolerant Deep Neighborhood Embedding for Remotely Sensed Images With Label Noise

Recently, many deep learning-based methods have been developed for solving remote sensing (RS) scene classification or retrieval tasks. Most of the adopted loss functions for training these models require accurate annotations. However, the presence of noise in such annotations (also known as label noise) cannot be avoided in large-scale RS benchmark archives, resulting from geo-location/registration errors, land-cover changes, and diverse knowledge background of annotators. To overcome the influence of noisy labels on the learning process of deep models, we propose a new loss function called noise-tolerant deep neighborhood embedding which can accurately encode the semantic relationships among RS scenes. Specifically, we target at maximizing the leave-one-out K-NN score for uncovering the inherent neighborhood structure among the images in feature space. Moreover, we down-weight the contribution of potential noisy images by learning their localized structure and pruning the images with low leave-one-out K-NN scores. Based on our newly proposed loss function, classwise features can be more robustly discriminated. Our experiments, conducted on two benchmark RS datasets, validate the effectiveness of the proposed approach on three different RS scene interpretation tasks, including classification, clustering, and retrieval. The codes of this article will be publicly available from https://github.com/jiankang1991

Deep Learning-Based Building Footprint Extraction With Missing Annotations

Most state-of-the-art deep learning-based methods for extraction of building footprints are aimed at designing proper convolutional neural network (CNN) architectures or loss functions able to effectively predict building masks from remote sensing (RS) images. To properly train such CNN models, large-scale and pixel-level building annotations are required. One common approach to obtain scalable benchmark data sets for the segmentation of buildings is to register RS images with auxiliary geospatial information data, such as those available from OpenStreetMaps (OSM). However, due to land-cover changes, urban construction, and delayed geospatial information updating, some building annotations may be missing in the corresponding ground-truth building mask layers. This will likely introduce confusion in the training of CNN models for discriminating between background and building pixels. To solve this important issue, we first formulate the problem as a long-tailed classification one. Then, we introduce a new joint loss function based on three terms: 1) logit adjusted cross entropy (LACE) loss, aimed at discriminating between building and background pixels from a long-tailed label distribution; 2) weighted dice loss, aimed at increasing the F₁ scores of the predicted building masks; and 3) boundary (BD) alignment loss, which is optimized for preserving the fine-grained structure of building boundaries. Our experiments, conducted on two benchmark building segmentation data sets, validate the effectiveness of our newly proposed loss with respect to other state-of-the-art losses commonly used for extracting building footprints. The codes of this letter will be publicly available from https://github.com/jiankang1991/GRSL_BFE_MA

Rotation-Invariant Deep Embedding for Remote Sensing Images

Endowing convolutional neural networks (CNNs) with the rotation-invariant capability is important for characterizing the semantic contents of remote sensing (RS) images since they do not have typical orientations. Most of the existing deep methods for learning rotation-invariant CNN models are based on the design of proper convolutional or pooling layers, which aims at predicting the correct category labels of the rotated RS images equivalently. However, a few works have focused on learning rotation-invariant embeddings in the framework of deep metric learning for modeling the fine-grained semantic relationships among RS images in the embedding space. To fill this gap, we first propose a rule that the deep embeddings of rotated images should be closer to each other than those of any other images (including the images belonging to the same class). Then, we propose to maximize the joint probability of the leave-one-out image classification and rotational image identification. With the assumption of independence, such optimization leads to the minimization of a novel loss function composed of two terms: 1) a class-discrimination term and 2) a rotation-invariant term. Furthermore, we introduce a penalty parameter that balances these two terms and further propose a final loss to Rotation-invariant Deep embedding for RS images, termed RiDe. Extensive experiments conducted on two benchmark RS datasets validate the effectiveness of the proposed approach and demonstrate its superior performance when compared to other state-of-the-art methods. The codes of this article will be publicly available at https://github.com/jiankang1991/TGRS_RiDe