Dimensional Synthesis of a Novel 3-URU Translational Manipulator Implemented through a Novel Method

A dimensional synthesis of parallel manipulators (PMs) consists of determining the values of the geometric parameters that affect the platform motion so that a useful workspace with assigned sizes can be suitably located in a free-from-singularity region of its operational space. The main goal of this preliminary dimensioning is to keep the PM far enough from singularities to avoid high internal loads in the links and guarantee a good positioning precision (i.e., for getting good kinematic performances). This paper presents a novel method for the dimensional synthesis of translational PMs (TPMs) and applies it to a TPM previously proposed by the author. The proposed method, which is based on Jacobians’ properties, exploits the fact that TPM parallel Jacobians are block diagonal matrices to overcome typical drawbacks of indices based on Jacobian properties. The proposed method can be also applied to all the lower-mobility PMs with block diagonal Jacobians that separate platform rotations from platform translations (e.g., parallel wrists).

Higher Haantjes Brackets and Integrability

We propose a new, infinite class of brackets generalizing the Frölicher–Nijenhuis bracket. This class can be reduced to a family of generalized Nijenhuis torsions recently introduced. In particular, the Haantjes bracket, the first example of our construction, is relevant in the characterization of Haantjes moduli of operators. We also prove that the vanishing of a higher-level Nijenhuis torsion of an operator field is a sufficient condition for the integrability of its eigen-distributions. This result (which does not require any knowledge of the spectral properties of the operator) generalizes the celebrated Haantjes theorem. The same vanishing condition also guarantees that the operator can be written, in a local chart, in a block-diagonal form.

Virtual samples based robust block-diagonal dictionary learning for face recognition

It is an open question to learn an over-complete dictionary from a limited number of face samples, and the inherent attributes of the samples are underutilized. Besides, the recognition performance may be adversely affected by the noise (and outliers), and the strict binary label based linear classifier is not appropriate for face recognition. To solve above problems, we propose a virtual samples based robust block-diagonal dictionary learning for face recognition. In the proposed model, the original samples and virtual samples are combined to solve the small sample size problem, and both the structure constraint and the low rank constraint are exploited to preserve the intrinsic attributes of the samples. In addition, the fidelity term can effectively reduce negative effects of noise (and outliers), and the ε-dragging is utilized to promote the performance of the linear classifier. Finally, extensive experiments are conducted in comparison with many state-of-the-art methods on benchmark face datasets, and experimental results demonstrate the efficacy of the proposed method.

Multi-Stage Convolutional Broad Learning with Block Diagonal Constraint for Hyperspectral Image Classification

By combining the broad learning and a convolutional neural network (CNN), a block-diagonal constrained multi-stage convolutional broad learning (MSCBL-BD) method is proposed for hyperspectral image (HSI) classification. Firstly, as the linear sparse feature extracted by the conventional broad learning method cannot fully characterize the complex spatial-spectral features of HSIs, we replace the linear sparse features in the mapped feature (MF) with the features extracted by the CNN to achieve more complex nonlinear mapping. Then, in the multi-layer mapping process of the CNN, information loss occurs to a certain degree. To this end, the multi-stage convolutional features (MSCFs) extracted by the CNN are expanded to obtain the multi-stage broad features (MSBFs). MSCFs and MSBFs are further spliced to obtain multi-stage convolutional broad features (MSCBFs). Additionally, in order to enhance the mutual independence between MSCBFs, a block diagonal constraint is introduced, and MSCBFs are mapped by a block diagonal matrix, so that each feature is represented linearly only by features of the same stage. Finally, the output layer weights of MSCBL-BD and the desired block-diagonal matrix are solved by the alternating direction method of multipliers. Experimental results on three popular HSI datasets demonstrate the superiority of MSCBL-BD.