Nonlinear subspace clustering using curvature constrained distances

Abstract

1 Research Highlights (Required)To create your highlights, please type the highlights against each \item command. It should be short collection of bullet points that convey the core findings of the article. It should include 3 to 5 bullet points (maximum 85 characters, including spaces, per bullet point.)• We proposed a new method to cluster multiple manifolds with the intersection.• We define a new notion of distance between points based on shortest constrained path.• We apply our method to simulated and some real datasets and get good results. ABSTRACTThe massive amount of high-dimensional data in science and engineering demands new trends in data analysis. Subspace techniques have shown remarkable success in numerous problems in computer vision and data mining, where the goal is to recover the low-dimensional structure of data in an ambient space. Traditional subspace methods like PCA and ICA assume that the data is coming from a single manifold. However, the data might come from several (possibly intersected) manifolds (surfaces). This has caused the development of new nonlinear techniques to cluster subspaces of high-dimensional data. In this paper, we propose a new algorithm for subspace clustering of data, where the data consists of several possibly intersected manifolds. To this end, we first propose a curvature constraint to find the shortest path between data points and then use it in Isomap for subspace learning. The algorithm chooses several landmark nodes at random and then checks whether there is a curvature constrained path between each landmark node and all other nodes in the neighborhood graph. It builds a binary feature vector for each point where each entry represents the the connectivity of that point to a particular landmark. Then the binary feature vectors could be used as a input of conventional clustering algorithms such as hierarchical clustering. The performed experiments on both synthetic and real data sets confirm the performance of our algorithm.

Biologically-Inspired Computational Neural Mechanism for Human Action/activity Recognition: A Review

“…Figure 2 represents the similarity between MLD and active basis model (ABM) [15,16]. An unsupervised approach performs synthetic biological movement recognition [23] and shows great potential for use in the mechanism of biological movements and the importance on geometric model implying synthetic data. Schema of the model shown and symbols are shown following the brain areas and their functionality: MT: middle temporal area; V1: primary visual cortex; FFA: fusiform face area; STS: superior temporal sulcus; KO: kinetic occipital area.…”

Speeding up Memory-based Collaborative Filtering with Landmarks

“…Another pitfall of landmark approach is to choose the most representative observation as landmarks, once the data representation depends on the similarity to these points. Several selection strategies are proposed in literature (Chen et al 2006;Crawford 2013, 2014;Orsenigo 2014;Shi et al 2016Shi et al , 2015Silva et al 2005), most of them related to select landmarks for Land-mark Isomap, which is a nonlinear reduction method variation to improve scalability (Babaeian et al 2015;Shang et al 2011;Silva and Tenenbaum 2002;Sun et al 2014).…”

Large sample spectral analysis of graph-based multi-manifold clustering

“…Some strategies include the use of local tangent planes from data [3,23,29,51] (whose angles are compared), and the construction of paths between different points (e.g. geodesics) that are considered admissible if they do not exhibit sudden turns (effectively imposing a curvature constraint) [5]. All these methods are inspired by heuristics that are meaningful at the continuum level (i.e.…”

“…In [17] the authors present some theoretical analysis of SCC in the setting where the data are sampled from multiple flats with the same dimension. Curvature can also be captured by measuring how quickly paths turn as proposed in [5]. Our graph construction from section 3 is inspired by the one proposed in [5], but with some important differences that we will motivate and explain throughout the paper.…”

“…Curvature can also be captured by measuring how quickly paths turn as proposed in [5]. Our graph construction from section 3 is inspired by the one proposed in [5], but with some important differences that we will motivate and explain throughout the paper.…”