9,170 research outputs found
Fast Construction of Nets in Low Dimensional Metrics, and Their Applications
We present a near linear time algorithm for constructing hierarchical nets in
finite metric spaces with constant doubling dimension. This data-structure is
then applied to obtain improved algorithms for the following problems:
Approximate nearest neighbor search, well-separated pair decomposition, compact
representation scheme, doubling measure, and computation of the (approximate)
Lipschitz constant of a function. In all cases, the running (preprocessing)
time is near-linear and the space being used is linear.Comment: 41 pages. Extensive clean-up of minor English error
Finding a needle in an exponential haystack: Discrete RRT for exploration of implicit roadmaps in multi-robot motion planning
We present a sampling-based framework for multi-robot motion planning which
combines an implicit representation of a roadmap with a novel approach for
pathfinding in geometrically embedded graphs tailored for our setting. Our
pathfinding algorithm, discrete-RRT (dRRT), is an adaptation of the celebrated
RRT algorithm for the discrete case of a graph, and it enables a rapid
exploration of the high-dimensional configuration space by carefully walking
through an implicit representation of a tensor product of roadmaps for the
individual robots. We demonstrate our approach experimentally on scenarios of
up to 60 degrees of freedom where our algorithm is faster by a factor of at
least ten when compared to existing algorithms that we are aware of.Comment: Kiril Solovey and Oren Salzman contributed equally to this pape
Angle Tree: Nearest Neighbor Search in High Dimensions with Low Intrinsic Dimensionality
We propose an extension of tree-based space-partitioning indexing structures
for data with low intrinsic dimensionality embedded in a high dimensional
space. We call this extension an Angle Tree. Our extension can be applied to
both classical kd-trees as well as the more recent rp-trees. The key idea of
our approach is to store the angle (the "dihedral angle") between the data
region (which is a low dimensional manifold) and the random hyperplane that
splits the region (the "splitter"). We show that the dihedral angle can be used
to obtain a tight lower bound on the distance between the query point and any
point on the opposite side of the splitter. This in turn can be used to
efficiently prune the search space. We introduce a novel randomized strategy to
efficiently calculate the dihedral angle with a high degree of accuracy.
Experiments and analysis on real and synthetic data sets shows that the Angle
Tree is the most efficient known indexing structure for nearest neighbor
queries in terms of preprocessing and space usage while achieving high accuracy
and fast search time.Comment: To be submitted to IEEE Transactions on Pattern Analysis and Machine
Intelligenc
Approximate Nearest Neighbor Search for Low Dimensional Queries
We study the Approximate Nearest Neighbor problem for metric spaces where the
query points are constrained to lie on a subspace of low doubling dimension,
while the data is high-dimensional. We show that this problem can be solved
efficiently despite the high dimensionality of the data.Comment: 25 page
Spin Glasses on the Hypercube
We present a mean field model for spin glasses with a natural notion of
distance built in, namely, the Edwards-Anderson model on the diluted
D-dimensional unit hypercube in the limit of large D. We show that finite D
effects are strongly dependent on the connectivity, being much smaller for a
fixed coordination number. We solve the non trivial problem of generating these
lattices. Afterwards, we numerically study the nonequilibrium dynamics of the
mean field spin glass. Our three main findings are: (i) the dynamics is ruled
by an infinite number of time-sectors, (ii) the aging dynamics consists on the
growth of coherent domains with a non vanishing surface-volume ratio, and (iii)
the propagator in Fourier space follows the p^4 law. We study as well finite D
effects in the nonequilibrium dynamics, finding that a naive finite size
scaling ansatz works surprisingly well.Comment: 14 pages, 22 figure
Identifying Real Estate Opportunities using Machine Learning
The real estate market is exposed to many fluctuations in prices because of
existing correlations with many variables, some of which cannot be controlled
or might even be unknown. Housing prices can increase rapidly (or in some
cases, also drop very fast), yet the numerous listings available online where
houses are sold or rented are not likely to be updated that often. In some
cases, individuals interested in selling a house (or apartment) might include
it in some online listing, and forget about updating the price. In other cases,
some individuals might be interested in deliberately setting a price below the
market price in order to sell the home faster, for various reasons. In this
paper, we aim at developing a machine learning application that identifies
opportunities in the real estate market in real time, i.e., houses that are
listed with a price substantially below the market price. This program can be
useful for investors interested in the housing market. We have focused in a use
case considering real estate assets located in the Salamanca district in Madrid
(Spain) and listed in the most relevant Spanish online site for home sales and
rentals. The application is formally implemented as a regression problem that
tries to estimate the market price of a house given features retrieved from
public online listings. For building this application, we have performed a
feature engineering stage in order to discover relevant features that allows
for attaining a high predictive performance. Several machine learning
algorithms have been tested, including regression trees, k-nearest neighbors,
support vector machines and neural networks, identifying advantages and
handicaps of each of them.Comment: 24 pages, 13 figures, 5 table
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