Thick Boundaries in Binary Space and Their Influence on Nearest-Neighbor Search

Binary descriptors allow faster similarity computation than real-valued ones while requiring much less storage. As a result, many algorithms have recently been proposed to binarize floating-point descriptors so that they can be searched for quickly. Unfortunately, even if the similarity between vectors can be computed fast, exhaustive linear search remains impractical for truly large databases and Approximate Nearest Neighbor (ANN) search is still required. It is therefore surprising that relatively little attention has been paid to the efficiency of ANN algorithms on binary vectors and this is the focus of this paper. We first show that binary-space Voronoi diagrams have thick boundaries, meaning that there are many points that lie at the same distance from two random points. This violates the implicit assumption made by most ANN algorithms that points can be neatly assigned to clusters centered around a set of cluster centers. As a result, state-of-the-art algorithms that can operate on binary vectors exhibit much lower performance than those that work with floating point ones. The above analysis is the first contribution of the paper. The second one is two effective ways to overcome this limitation, by appropriately randomizing either a tree-based algorithm or hashing-based one. In both cases, we show that we obtain precision/recall curves that are similar to those than can be obtained using floating point number calculation, but at much reduced computational cost

Evaluation of Hashing Methods Performance on Binary Feature Descriptors

In this paper we evaluate performance of data-dependent hashing methods on binary data. The goal is to find a hashing method that can effectively produce lower dimensional binary representation of 512-bit FREAK descriptors. A representative sample of recent unsupervised, semi-supervised and supervised hashing methods was experimentally evaluated on large datasets of labelled binary FREAK feature descriptors

Tuning magnetocrystalline anisotropy of Fe3_{3}Sn by alloying

The electronic structure, magnetic properties and phase formation of hexagonal ferromagnetic Fe$_{3}$Sn-based alloys have been studied from first principles and by experiment. The pristine Fe$_{3}$Sn compound is known to fulfill all the requirements for a good permanent magnet, except for the magnetocrystalline anisotropy energy (MAE). The latter is large, but planar, i.e. the easy magnetization axis is not along the hexagonal c direction, whereas a good permanent magnet requires the MAE to be uniaxial. Here we consider Fe$_{3}$Sn$_{0.75}$M$_{0.25}$, where M= Si, P, Ga, Ge, As, Se, In, Sb, Te and Bi, and show how different dopants on the Sn sublattice affect the MAE and can alter it from planar to uniaxial. The stability of the doped Fe$_{3}$Sn phases is elucidated theoretically via the calculations of their formation enthalpies. A micromagnetic model is developed in order to estimate the energy density product (BH)max and coercive field $\mu_{0}$H$_{c}$ of a potential magnet made of Fe$_{3}$Sn$_{0.75}$Sb$_{0.25}$, the most promising candidate from theoretical studies. The phase stability and magnetic properties of the Fe$_{3}$Sn compound doped with Sb and Mn has been checked experimentally on the samples synthesised using the reactive crucible melting technique as well as by solid state reaction. The Fe$_{3}$Sn-Sb compound is found to be stable when alloyed with Mn. It is shown that even small structural changes, such as a change of the c/a ratio or volume, that can be induced by, e.g., alloying with Mn, can influence anisotropy and reverse it from planar to uniaxial and back

The APOGEE-2 Survey of the Orion Star Forming Complex: I. Target Selection and Validation with early observations

The Orion Star Forming Complex (OSFC) is a central target for the APOGEE-2 Young Cluster Survey. Existing membership catalogs span limited portions of the OSFC, reflecting the difficulty of selecting targets homogeneously across this extended, highly structured region. We have used data from wide field photometric surveys to produce a less biased parent sample of young stellar objects (YSOs) with infrared (IR) excesses indicative of warm circumstellar material or photometric variability at optical wavelengths across the full 420 square degrees extent of the OSFC. When restricted to YSO candidates with H < 12.4, to ensure S/N ~100 for a six visit source, this uniformly selected sample includes 1307 IR excess sources selected using criteria vetted by Koenig & Liesawitz and 990 optical variables identified in the Pan-STARRS1 3$\pi$ survey: 319 sources exhibit both optical variability and evidence of circumstellar disks through IR excess. Objects from this uniformly selected sample received the highest priority for targeting, but required fewer than half of the fibers on each APOGEE-2 plate. We fill the remaining fibers with previously confirmed and new color-magnitude selected candidate OSFC members. Radial velocity measurements from APOGEE-1 and new APOGEE-2 observations taken in the survey's first year indicate that ~90% of the uniformly selected targets have radial velocities consistent with Orion membership.The APOGEE-2 Orion survey will include >1100 bona fide YSOs whose uniform selection function will provide a robust sample for comparative analyses of the stellar populations and properties across all sub-regions of Orion.Comment: Accepted for publication in ApJ

Efficient Yao Graph Construction

Yao graphs are geometric spanners that connect each point of a given point set to its nearest neighbor in each of k cones drawn around it. Yao graphs were introduced to construct minimum spanning trees in d dimensional spaces. Moreover, they are used for instance in topology control in wireless networks. An optimal ?(n log n)-time algorithm to construct Yao graphs for a given point set has been proposed in the literature but - to the best of our knowledge - never been implemented. Instead, algorithms with a quadratic complexity are used in popular packages to construct these graphs. In this paper we present the first implementation of the optimal Yao graph algorithm. We engineer the data structures required to achieve the ?(n log n) time bound and detail algorithmic adaptations necessary to take the original algorithm from theory to practice. We propose a priority queue data structure that separates static and dynamic events and might be of independent interest for other sweepline algorithms. Additionally, we propose a new Yao graph algorithm based on a uniform grid data structure that performs well for medium-sized inputs. We evaluate our implementations on a wide variety of synthetic and real-world datasets and show that our implementation outperforms current publicly available implementations by at least an order of magnitude