3,722 research outputs found
CSD: Discriminance with Conic Section for Improving Reverse k Nearest Neighbors Queries
The reverse nearest neighbor (RNN) query finds all points that have
the query point as one of their nearest neighbors (NN), where the NN
query finds the closest points to its query point. Based on the
characteristics of conic section, we propose a discriminance, named CSD (Conic
Section Discriminance), to determine points whether belong to the RNN set
without issuing any queries with non-constant computational complexity. By
using CSD, we also implement an efficient RNN algorithm CSD-RNN with a
computational complexity at . The comparative
experiments are conducted between CSD-RNN and other two state-of-the-art
RkNN algorithms, SLICE and VR-RNN. The experimental results indicate that
the efficiency of CSD-RNN is significantly higher than its competitors
A Graph-Based Semi-Supervised k Nearest-Neighbor Method for Nonlinear Manifold Distributed Data Classification
Nearest Neighbors (NN) is one of the most widely used supervised
learning algorithms to classify Gaussian distributed data, but it does not
achieve good results when it is applied to nonlinear manifold distributed data,
especially when a very limited amount of labeled samples are available. In this
paper, we propose a new graph-based NN algorithm which can effectively
handle both Gaussian distributed data and nonlinear manifold distributed data.
To achieve this goal, we first propose a constrained Tired Random Walk (TRW) by
constructing an -level nearest-neighbor strengthened tree over the graph,
and then compute a TRW matrix for similarity measurement purposes. After this,
the nearest neighbors are identified according to the TRW matrix and the class
label of a query point is determined by the sum of all the TRW weights of its
nearest neighbors. To deal with online situations, we also propose a new
algorithm to handle sequential samples based a local neighborhood
reconstruction. Comparison experiments are conducted on both synthetic data
sets and real-world data sets to demonstrate the validity of the proposed new
NN algorithm and its improvements to other version of NN algorithms.
Given the widespread appearance of manifold structures in real-world problems
and the popularity of the traditional NN algorithm, the proposed manifold
version NN shows promising potential for classifying manifold-distributed
data.Comment: 32 pages, 12 figures, 7 table
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