Convexity Of Data Research Articles

Superpixel-guided preprocessing algorithm for accelerating hyperspectral endmember extraction based on spatial–spectral analysis

Preprocessing is a major area of interest in the field of hyperspectral endmember extraction, for it can provide a few high-quality candidates for fast endmember extraction without sacrificing endmember accuracy. We propose a superpixel-guided preprocessing (SGPP) algorithm to accelerate endmember extraction based on spatial compactness and spectral purity analysis. The proposed SGPP first transforms a hyperspectral image into low-dimension data using principal component analysis. SGPP then utilizes the superpixel method, which normally has linear complexity, to segment the first three components into a set of superpixels. Next, SGPP transforms low-dimension superpixels into noise-reduced superpixels and calculates their spatial compactness and spectral purity based on Tukey’s test and data convexity. SGPP finally retains a few high-quality pixels from each superpixel with high spatial compactness and spectral purity indices for subsequent endmember identification. Based on the spectral angle distance, root-mean-square error, and speedup, experiments are conducted on synthetic and real hyperspectral datasets, and they indicate that SGPP is superior to current state-of-the-art preprocessing techniques.

Data Convexity and Parameter Independent Clustering for Biomedical Datasets.

In machine learning, the nature of the dataset itself such as convexity of the data point sets affects the right choice of clustering algorithm to give good performance. This brief paper first focuses on how data convexity influences the clustering performance on biomedical datasets. Then it addresses the main challenges of two well-known clustering groups which are centroid-based and density-based clustering. These techniques typically require a set of parameters to be provided by the user before the algorithms can perform well in terms of good clustering and give the optimal number of clusters. Two parameter independent clustering techniques utilizing unique neighborhood sets (UNSs) called Parameter Independent Convex Centroid-based Clustering (ConvexClust) for convex-dominated datasets and Parameter Independent Non-Convex Density-based Clustering (NonConvexClust) for nonconvex-dominated datasets are introduced. The ConvexClust and NonConvex Clust algorithms are extensively evaluated on real-world biomedical datasets. Their performances are also compared with other clustering algorithms using evaluation criteria such as SSE, entropy and purity. The results have revealed the good performance of the proposed parameter-independent clustering techniques and also shown that most of the biomedical datasets in the experiments demonstrated their tendency towards convex-dominated data point sets.

On Efficiency Conditions for Nonsmooth Vector Equilibrium Problems with Equilibrium Constraints

In this article, necessary conditions of Fritz John type for weak efficient solutions of a nonsmooth vector equilibrium problem involving equilibrium constraints (VEPEC) in terms of the Clarke subdifferentials are established. Under constraint qualifications which are suitable for (VEPEC), necessary conditions of Kuhn-Tucker type for efficiency are derived. Under assumptions on generalized convexity of data, sufficient conditions for efficiency are developed. Some applications to vector variational inequalities and vector optimization problems with equilibrium constraints are also given.

Discrete weighted cubic splines

This paper presents methods for shape preserving spline interpolation. These methods are based on discrete weighted cubic splines. The analysis results in two algorithms with automatic selection of the shape control parameters: one to preserve the data monotonicity and other to retain the data convexity. Discrete weighted cubic B-splines and control point approximation are also considered.