CUR Decompositions, Similarity Matrices, and Subspace Clustering

A general framework for solving the subspace clustering problem using the CUR decomposition is presented. The CUR decomposition provides a natural way to construct similarity matrices for data that come from a union of unknown subspaces $\mathscr{U}=\underset{i=1}{\overset{M}\bigcup}S_i$. The similarity matrices thus constructed give the exact clustering in the noise-free case. Additionally, this decomposition gives rise to many distinct similarity matrices from a given set of data, which allow enough flexibility to perform accurate clustering of noisy data. We also show that two known methods for subspace clustering can be derived from the CUR decomposition. An algorithm based on the theoretical construction of similarity matrices is presented, and experiments on synthetic and real data are presented to test the method. Additionally, an adaptation of our CUR based similarity matrices is utilized to provide a heuristic algorithm for subspace clustering; this algorithm yields the best overall performance to date for clustering the Hopkins155 motion segmentation dataset.Comment: Approximately 30 pages. Current version contains improved algorithm and numerical experiments from the previous versio

Mathematical and Machine Learning Approaches for Classification of Protein Secondary Structure Elements from Cα Coordinates

Determining Secondary Structure Elements (SSEs) for any protein is crucial as an intermediate step for experimental tertiary structure determination. SSEs are identified using popular tools such as DSSP and STRIDE. These tools use atomic information to locate hydrogen bonds to identify SSEs. When some spatial atomic details are missing, locating SSEs becomes a hinder. To address the problem, when some atomic information is missing, three approaches for classifying SSE types using Ca atoms in protein chains were developed: (1) a mathematical approach, (2) a deep learning approach, and (3) an ensemble of five machine learning models. The proposed methods were compared against each other and with a state-of-the-art approach, PCASSO

Robust feature space separation for deep convolutional neural network training

This paper introduces two deep convolutional neural network training techniques that lead to more robust feature subspace separation in comparison to traditional training. Assume that dataset has M labels. The first method creates M deep convolutional neural networks called {DCNNi}M i=1 . Each of the networks DCNNi is composed of a convolutional neural network ( CNNi ) and a fully connected neural network ( FCNNi ). In training, a set of projection matrices are created and adaptively updated as representations for feature subspaces {S i}M i=1 . A rejection value is computed for each training based on its projections on feature subspaces. Each FCNNi acts as a binary classifier with a cost function whose main parameter is rejection values. A threshold value ti is determined for ith network DCNNi . A testing strategy utilizing {ti}M i=1 is also introduced. The second method creates a single DCNN and it computes a cost function whose parameters depend on subspace separations using the geodesic distance on the Grasmannian manifold of subspaces S i and the sum of all remaining subspaces {S j}M j=1,j≠i . The proposed methods are tested using multiple network topologies. It is shown that while the first method works better for smaller networks, the second method performs better for complex architectures

Adaptive unstructured road detection using close range stereo vision

Detection of road regions is not a trivial problem especially in unstructured and/or off-road domains since traversable regions of these environments do not have common properties unlike urban roads or highways. In this paper a novel unstructured road detection algorithm that can continuously learn the road region is proposed. The algorithm gathers close-range stereovision data and uses this information to estimate the long-range road region. The experiments show that the algorithm gives satisfactory results even under changing light conditions

Self-learning Road Detection with Stereo Vision

It is a hard to solve problem to detect traversable or road regions especially in unstructured roads or paths. In mobile robot applications, robots usually enter these kinds of roads and regions. To successfully complete its mission, it is important to find roads in these environments reliably. In this paper a novel unstructured road detection algorithm with the capability of learning road regions continuously is proposed