Correntropy-Based Multiview Subspace Clustering.

Multiview subspace clustering, which aims to cluster the given data points with information from multiple sources or features into their underlying subspaces, has a wide range of applications in the communities of data mining and pattern recognition. Compared with the single-view subspace clustering, it is challenging to efficiently learn the structure of the representation matrix from each view and make use of the extra information embedded in multiple views. To address the two problems, a novel correntropy-based multiview subspace clustering (CMVSC) method is proposed in this article. The objective function of our model mainly includes two parts. The first part utilizes the Frobenius norm to efficiently estimate the dense connections between the points lying in the same subspace instead of following the standard compressive sensing approach. In the second part, the correntropy-induced metric (CIM) is introduced to characterize the noise in each view and utilize the information embedded in different views from an information-theoretic perspective. Furthermore, an efficient iterative algorithm based on the half-quadratic technique (HQ) and the alternating direction method of multipliers (ADMM) is developed to optimize the proposed joint learning problem, and extensive experimental results on six real-world multiview benchmarks demonstrate that the proposed methods can outperform several state-of-the-art multiview subspace clustering methods.

Probability Density Rank-Based Quantization for Convex Universal Learning Machines.

The distributions of input data are very important for learning machines, such as the convex universal learning machines (CULMs). The CULMs are a family of universal learning machines with convex optimization. However, the computational complexity is a crucial problem in CULMs, because the dimension of the nonlinear mapping layer (the hidden layer) of the CULMs is usually rather large in complex system modeling. In this article, we propose an efficient quantization method called Probability density Rank-based Quantization (PRQ) to decrease the computational complexity of CULMs. The PRQ ranks the data according to the estimated probability densities and then selects a subset whose elements are equally spaced in the ranked data sequence. We apply the PRQ to kernel ridge regression (KRR) and random Fourier feature recursive least squares (RFF-RLS), which are two typical algorithms of CULMs. The proposed method not only keeps the similarity of data distribution between the code book and data set but also reduces the computational cost by using the kd-tree. Meanwhile, for a given data set, the method yields deterministic quantization results, and it can also exclude the outliers and avoid too many borders in the code book. This brings great convenience to practical applications of the CULMs. The proposed PRQ is evaluated on several real-world benchmark data sets. Experimental results show satisfactory performance of PRQ compared with some state-of-the-art methods.

Unraveling the Mystery of Stöber Silica's Microporosity.

Puzzling aspects of the microporous structure of Stöber silica, including inconsistencies in the BET specific surface area and the long measurement time required for N2 adsorption, hinder further research on and potential applications of this material. In this work, Stöber silica samples prepared using systematic and detailed post-treatment methods were characterized by N2 adsorption, scanning electron microscopy, transmission electron microscopy, inductively coupled plasma optical emission spectrometry, elemental analysis, and Fourier transform infrared spectroscopy. We have found that the often overlooked sample preparation conditions may be the main causes that perplex the gas adsorption characterization results of Stöber silica samples. The pore-blocking processes associated with a variety of sample treatment methods are discussed in detail. Strong evidence for the particle growth model and pore-blocking mechanism involving ethoxyl groups, Si species, and condensation of silanols is provided. A remarkable result is that the measurement time is shortened from 1 month in our previous work to 2-3 days for samples with large specific surface areas. A suitable post-treatment condition is recommended to obtain microporous Stöber silica with a short measurement time, including water washing, low temperature drying without a vacuum, and a short storage time.

Understanding Stöber silica's pore characteristics measured by gas adsorption.

Controversial reports regarding Stöber silica's microporosity and specific surface area remain in the literature despite decades of widespread applications. In this work, Stöber silica samples prepared under controlled reaction time and postsynthesis washing/drying conditions were characterized by nitrogen adsorption at 77 K, transmission electron microscopy, elemental analysis, Fourier transform infrared spectroscopy, thermal analysis, and evolved gas analysis. Our experimental results demonstrated the important but often overlooked effects of reaction time and postsynthesis treatments on Stöber silica's pore characteristics, as evidenced by the strikingly large range of BET specific surface area (11.3-309.7 m(2)/g). A simple micropore filling and blocking mechanism compatible with an existing Stöber silica growth model incorporating both aggregation and monomer addition steps was proposed to explain all our experimental findings. The carbon and nitrogen contents appear to serve well as the indicative link between our experimental variables and the resulting pore blocking by TEOS and its derivatives. A suitable combination of experimental conditions is recommended in order to make microporous Stöber silica samples with large specific surface area, including a short reaction time, water washing, and drying at moderate temperature preferably under vacuum.