Minimum Density Hyperplanes

Associating distinct groups of objects (clusters) with contiguous regions of high probability density (high-density clusters), is central to many statistical and machine learning approaches to the classification of unlabelled data. We propose a novel hyperplane classifier for clustering and semi-supervised classification which is motivated by this objective. The proposed minimum density hyperplane minimises the integral of the empirical probability density function along it, thereby avoiding intersection with high density clusters. We show that the minimum density and the maximum margin hyperplanes are asymptotically equivalent, thus linking this approach to maximum margin clustering and semi-supervised support vector classifiers. We propose a projection pursuit formulation of the associated optimisation problem which allows us to find minimum density hyperplanes efficiently in practice, and evaluate its performance on a range of benchmark datasets. The proposed approach is found to be very competitive with state of the art methods for clustering and semi-supervised classification

SMART: Unique splitting-while-merging framework for gene clustering

Copyright @ 2014 Fa et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Successful clustering algorithms are highly dependent on parameter settings. The clustering performance degrades significantly unless parameters are properly set, and yet, it is difficult to set these parameters a priori. To address this issue, in this paper, we propose a unique splitting-while-merging clustering framework, named “splitting merging awareness tactics” (SMART), which does not require any a priori knowledge of either the number of clusters or even the possible range of this number. Unlike existing self-splitting algorithms, which over-cluster the dataset to a large number of clusters and then merge some similar clusters, our framework has the ability to split and merge clusters automatically during the process and produces the the most reliable clustering results, by intrinsically integrating many clustering techniques and tasks. The SMART framework is implemented with two distinct clustering paradigms in two algorithms: competitive learning and finite mixture model. Nevertheless, within the proposed SMART framework, many other algorithms can be derived for different clustering paradigms. The minimum message length algorithm is integrated into the framework as the clustering selection criterion. The usefulness of the SMART framework and its algorithms is tested in demonstration datasets and simulated gene expression datasets. Moreover, two real microarray gene expression datasets are studied using this approach. Based on the performance of many metrics, all numerical results show that SMART is superior to compared existing self-splitting algorithms and traditional algorithms. Three main properties of the proposed SMART framework are summarized as: (1) needing no parameters dependent on the respective dataset or a priori knowledge about the datasets, (2) extendible to many different applications, (3) offering superior performance compared with counterpart algorithms.National Institute for Health Researc

Fast Exact Booleans for Iterated CSG using Octree-Embedded BSPs

We present octree-embedded BSPs, a volumetric mesh data structure suited for performing a sequence of Boolean operations (iterated CSG) efficiently. At its core, our data structure leverages a plane-based geometry representation and integer arithmetics to guarantee unconditionally robust operations. These typically present considerable performance challenges which we overcome by using custom-tailored fixed-precision operations and an efficient algorithm for cutting a convex mesh against a plane. Consequently, BSP Booleans and mesh extraction are formulated in terms of mesh cutting. The octree is used as a global acceleration structure to keep modifications local and bound the BSP complexity. With our optimizations, we can perform up to 2.5 million mesh-plane cuts per second on a single core, which creates roughly 40-50 million output BSP nodes for CSG. We demonstrate our system in two iterated CSG settings: sweep volumes and a milling simulation

Optimization and Learning in Energy Efficient Cognitive Radio System

Energy efficiency and spectrum efficiency are two biggest concerns for wireless communication. The constrained power supply is always a bottleneck to the modern mobility communication system. Meanwhile, spectrum resource is extremely limited but seriously underutilized. Cognitive radio (CR) as a promising approach could alleviate the spectrum underutilization and increase the quality of service. In contrast to traditional wireless communication systems, a distinguishing feature of cognitive radio systems is that the cognitive radios, which are typically equipped with powerful computation machinery, are capable of sensing the spectrum environment and making intelligent decisions. Moreover, the cognitive radio systems differ from traditional wireless systems that they can adapt their operating parameters, i.e. transmission power, channel, modulation according to the surrounding radio environment to explore the opportunity. In this dissertation, the study is focused on the optimization and learning of energy efficiency in the cognitive radio system, which can be considered to better utilize both the energy and spectrum resources. Firstly, drowsy transmission, which produces optimized idle period patterns and selects the best sleep mode for each idle period between two packet transmissions through joint power management and transmission power control/rate selection, is introduced to cognitive radio transmitter. Both the optimal solution by dynamic programming and flexible solution by reinforcement learning are provided. Secondly, when cognitive radio system is benefited from the theoretically infinite but unsteady harvested energy, an innovative and flexible control framework mainly based on model predictive control is designed. The solution to combat the problems, such as the inaccurate model and myopic control policy introduced by MPC, is given. Last, after study the optimization problem for point-to-point communication, multi-objective reinforcement learning is applied to the cognitive radio network, an adaptable routing algorithm is proposed and implemented. Epidemic propagation is studied to further understand the learning process in the cognitive radio network

A self-learning algorithm for biased molecular dynamics

A new self-learning algorithm for accelerated dynamics, reconnaissance metadynamics, is proposed that is able to work with a very large number of collective coordinates. Acceleration of the dynamics is achieved by constructing a bias potential in terms of a patchwork of one-dimensional, locally valid collective coordinates. These collective coordinates are obtained from trajectory analyses so that they adapt to any new features encountered during the simulation. We show how this methodology can be used to enhance sampling in real chemical systems citing examples both from the physics of clusters and from the biological sciences.Comment: 6 pages, 5 figures + 9 pages of supplementary informatio

A Mixture of Manhattan Frames: Beyond the Manhattan World

Objects and structures within man-made environments typically exhibit a high degree of organization in the form of orthogonal and parallel planes. Traditional approaches to scene representation exploit this phenomenon via the somewhat restrictive assumption that every plane is perpendicular to one of the axes of a single coordinate system. Known as the Manhattan-World model, this assumption is widely used in computer vision and robotics. The complexity of many real-world scenes, however, necessitates a more flexible model. We propose a novel probabilistic model that describes the world as a mixture of Manhattan frames: each frame defines a different orthogonal coordinate system. This results in a more expressive model that still exploits the orthogonality constraints. We propose an adaptive Markov-Chain Monte-Carlo sampling algorithm with Metropolis-Hastings split/merge moves that utilizes the geometry of the unit sphere. We demonstrate the versatility of our Mixture-of-Manhattan-Frames model by describing complex scenes using depth images of indoor scenes as well as aerial-LiDAR measurements of an urban center. Additionally, we show that the model lends itself to focal-length calibration of depth cameras and to plane segmentation.United States. Office of Naval Research. Multidisciplinary University Research Initiative (Award N00014-11-1-0688)United States. Defense Advanced Research Projects Agency (Award FA8650-11-1-7154)Technion, Israel Institute of Technology (MIT Postdoctoral Fellowship Program

Online Mutual Foreground Segmentation for Multispectral Stereo Videos

The segmentation of video sequences into foreground and background regions is a low-level process commonly used in video content analysis and smart surveillance applications. Using a multispectral camera setup can improve this process by providing more diverse data to help identify objects despite adverse imaging conditions. The registration of several data sources is however not trivial if the appearance of objects produced by each sensor differs substantially. This problem is further complicated when parallax effects cannot be ignored when using close-range stereo pairs. In this work, we present a new method to simultaneously tackle multispectral segmentation and stereo registration. Using an iterative procedure, we estimate the labeling result for one problem using the provisional result of the other. Our approach is based on the alternating minimization of two energy functions that are linked through the use of dynamic priors. We rely on the integration of shape and appearance cues to find proper multispectral correspondences, and to properly segment objects in low contrast regions. We also formulate our model as a frame processing pipeline using higher order terms to improve the temporal coherence of our results. Our method is evaluated under different configurations on multiple multispectral datasets, and our implementation is available online.Comment: Preprint accepted for publication in IJCV (December 2018

Chiral CP^2 skyrmions in three-band superconductors

It is shown that under certain conditions, three-component superconductors (and in particular three-band systems) allow stable topological defects different from vortices. We demonstrate the existence of these excitations, characterized by a $CP^2$ topological invariant, in models for three-component superconductors with broken time reversal symmetry. We term these topological defects "chiral $GL^{(3)}$ skyrmions", where "chiral" refers to the fact that due to broken time reversal symmetry, these defects come in inequivalent left- and right-handed versions. In certain cases these objects are energetically cheaper than vortices and should be induced by an applied magnetic field. In other situations these skyrmions are metastable states, which can be produced by a quench. Observation of these defects can signal broken time reversal symmetry in three-band superconductors or in Josephson-coupled bilayers of $s_\pm$ and s-wave superconductors.Comment: minor presentation changes; replaced journal version; 30 pages, 21 figure