Complex rotated CCA: a method to correlate lagged geophysical variables

<p>The nature of the climate system is very complex: a network of mutual interactions between ocean and atmosphere lead to a multitude of overlapping geophysical processes. As a consequence, the same process has often a signature on different climate variables but with spatial and temporal shifts. Orthogonal decompositions, such as Canonical Correlation Analysis (CCA), of geophysical data fields allow to filter out common dominant patterns between two different variables by maximizing cross-correlation. In general, however, CCA suffers from (i) the orthogonality constraint, which tends to produce unphysical patterns, and (ii) the use of direct correlations, which leads to signals that are merely shifted in time being considered as distinct patterns.</p><p>In this work, we propose an extension of CCA, complex rotated CCA (crCCA), to address both limitations. First, we generate complex signals by using the Hilbert transforms. To reduce the spatial leakage inherent in Hilbert transforms, we extend the time series using the Theta model, thus creating an anti-leakage buffer space. We then perform the orthogonal decomposition in complex space, allowing us to detect out-of-phase signals. Subsequent Varimax rotation removes the orthogonal constraints to allow more geophysically meaningful modes.</p><p>We applied crCCA to a pair of variables expected to be coupled: Pacific sea surface temperature and continental precipitation. We show that crCCA successfully captures the temporally and spatially complex modes of (i) seasonal cycle, (ii) canonical ENSO, and (iii) ENSO Modoki, in a compact manner that allows an easy geophysical interpretation. The proposed method has the potential to be useful especially, but not limited to, studies on the prediction of continental precipitation by other climate variables. An implementation of the method is readily available as a Python package.</p>

Trace minimization method via penalty for linear response eigenvalue problems

<p style='text-indent:20px;'>In various applications, such as the computation of energy excitation states of electrons and molecules, and the analysis of interstellar clouds, the linear response eigenvalue problem, which is a special type of the Hamiltonian eigenvalue problem, is frequently encountered. However, traditional eigensolvers may not be applicable to this problem owing to its inherently large scale. In fact, we are usually more interested in computing some of the smallest positive eigenvalues. To this end, a trace minimum principle optimization model with orthogonality constraint has been proposed. On this basis, we propose an unconstrained surrogate model called trace minimization via penalty, and we establish its equivalence with the original constrained model, provided that the penalty parameter is larger than a certain threshold. By avoiding the orthogonality constraint, we can use a gradient-type method to solve this model. Specifically, we use the gradient descent method with Barzilai–Borwein step size. Moreover, we develop a restarting strategy for the proposed algorithm whereby higher accuracy and faster convergence can be achieved. This is verified by preliminary experimental results.</p>

Partial Multi-Label Learning via Multi-Subspace Representation

Partial Multi-Label Learning (PML) aims to learn from the training data where each instance is associated with a set of candidate labels, among which only a part of them are relevant. Existing PML methods mainly focus on label disambiguation, while they lack the consideration of noise in the feature space. To tackle the problem, we propose a novel framework named partial multi-label learning via MUlti-SubspacE Representation (MUSER), where the redundant labels together with noisy features are jointly taken into consideration during the training process. Specifically, we first decompose the original label space into a latent label subspace and a label correlation matrix to reduce the negative effects of redundant labels, then we utilize the correlations among features to project the original noisy feature space to a feature subspace to resist the noisy feature information. Afterwards, we introduce a graph Laplacian regularization to constrain the label subspace to keep intrinsic structure among features and impose an orthogonality constraint on the correlations among features to guarantee discriminability of the feature subspace. Extensive experiments conducted on various datasets demonstrate the superiority of our proposed method.

Hyperspectral Feature Extraction Using Sparse and Smooth Low-Rank Analysis

In this paper, we develop a hyperspectral feature extraction method called sparse and smooth low-rank analysis (SSLRA). First, we propose a new low-rank model for hyperspectral images (HSIs) where we decompose the HSI into smooth and sparse components. Then, these components are simultaneously estimated using a nonconvex constrained penalized cost function (CPCF). The proposed CPCF exploits total variation penalty, ℓ 1 penalty, and an orthogonality constraint. The total variation penalty is used to promote piecewise smoothness, and, therefore, it extracts spatial (local neighborhood) information. The ℓ 1 penalty encourages sparse and spatial structures. Additionally, we show that this new type of decomposition improves the classification of the HSIs. In the experiments, SSLRA was applied on the Houston (urban) and the Trento (rural) datasets. The extracted features were used as an input into a classifier (either support vector machines (SVM) or random forest (RF)) to produce the final classification map. The results confirm improvement in classification accuracy compared to the state-of-the-art feature extraction approaches.

Extrinsic Calibration of 2D Laser Rangefinders Using an Existing Cuboid-Shaped Corridor as the Reference

Laser rangefinders (LRFs) are widely used in autonomous systems for indoor positioning and mobile mapping through the simultaneous localization and mapping (SLAM) approach. The extrinsic parameters of multiple LRFs need to be determined, and they are one of the key factors impacting system performance. This study presents an extrinsic calibration method of multiple LRFs that requires neither extra calibration sensors nor special artificial reference landmarks. Instead, it uses a naturally existing cuboid-shaped corridor as the calibration reference, and it hence needs no additional cost. The present method takes advantage of two types of geometric constraints for the calibration, which can be found in a common cuboid-shaped corridor. First, the corresponding point cloud is scanned by the set of LRFs. Second, the lines that are scanned on the corridor surfaces are extracted from the point cloud. Then, the lines within the same surface and the lines within two adjacent surfaces satisfy the coplanarity constraint and the orthogonality constraint, respectively. As such, the calibration problem is converted into a nonlinear optimization problem with the constraints. Simulation experiments and experiments based on real data verified the feasibility and stability of the proposed method.

Decoupled Independent Vector Analysis Algorithm for Convolutive Blind Source Separation without Orthogonality Constraint on the Demixing Matrices

In this paper, we consider the problem of convolutive blind source separation in frequency domain and introduce a solution to the problem in an independent vector analysis (IVA) framework. IVA utilizes both the statistical independence of different sources in each frequency bin and the statistical dependence of the same source in different frequency bins. However, most of previous works impose orthogonality constraint on the rows of each separation matrix which may undermine the separation performance. In this work, we propose a nonorthogonal IVA algorithm based on decoupled relative Newton method. This proposed algorithm updates the separation matrices row by row, and unlike deflation separation algorithm, there is no separation error accumulation arising. Simulation results are provided to show the superior convergence behavior and separation performance of the proposed algorithm.