3,154 research outputs found
Efficient Nearest Neighbor Classification Using a Cascade of Approximate Similarity Measures
Nearest neighbor classification using shape context can yield highly accurate results in a number of recognition problems. Unfortunately, the approach can be too slow for practical applications, and thus approximation strategies are needed to make shape context practical. This paper proposes a method for efficient and accurate nearest neighbor classification in non-Euclidean spaces, such as the space induced by the shape context measure. First, a method is introduced for constructing a Euclidean embedding that is optimized for nearest neighbor classification accuracy. Using that embedding, multiple approximations of the underlying non-Euclidean similarity measure are obtained, at different levels of accuracy and efficiency. The approximations are automatically combined to form a cascade classifier, which applies the slower approximations only to the hardest cases. Unlike typical cascade-of-classifiers approaches, that are applied to binary classification problems, our method constructs a cascade for a multiclass problem. Experiments with a standard shape data set indicate that a two-to-three order of magnitude speed up is gained over the standard shape context classifier, with minimal losses in classification accuracy.National Science Foundation (IIS-0308213, IIS-0329009, EIA-0202067); Office of Naval Research (N00014-03-1-0108
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
Down the Rabbit Hole: Robust Proximity Search and Density Estimation in Sublinear Space
For a set of points in , and parameters and \eps, we present
a data structure that answers (1+\eps,k)-\ANN queries in logarithmic time.
Surprisingly, the space used by the data-structure is \Otilde (n /k); that
is, the space used is sublinear in the input size if is sufficiently large.
Our approach provides a novel way to summarize geometric data, such that
meaningful proximity queries on the data can be carried out using this sketch.
Using this, we provide a sublinear space data-structure that can estimate the
density of a point set under various measures, including:
\begin{inparaenum}[(i)]
\item sum of distances of closest points to the query point, and
\item sum of squared distances of closest points to the query point.
\end{inparaenum}
Our approach generalizes to other distance based estimation of densities of
similar flavor. We also study the problem of approximating some of these
quantities when using sampling. In particular, we show that a sample of size
\Otilde (n /k) is sufficient, in some restricted cases, to estimate the above
quantities. Remarkably, the sample size has only linear dependency on the
dimension
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