13,713 research outputs found
Graph Construction from Data using Non Negative Kernel regression (NNK Graphs)
Data driven graph constructions are often used in various applications,
including several machine learning tasks, where the goal is to make predictions
and discover patterns. However, learning an optimal graph from data is still a
challenging task. Weighted -nearest neighbor and -neighborhood
methods are among the most common graph construction methods, due to their
computational simplicity but the choice of parameters such as and
associated with these methods is often ad hoc and lacks a clear
interpretation. We formulate graph construction as the problem of finding a
sparse signal approximation in kernel space, identifying key similarities
between methods in signal approximation and existing graph learning methods. We
propose non-negative kernel regression~(NNK), an improved approach for graph
construction with interesting geometric and theoretical properties. We show
experimentally the efficiency of NNK graphs, its robustness to choice of
sparsity and better performance over state of the art graph methods in semi
supervised learning tasks on real world data
Self-weighted Multiple Kernel Learning for Graph-based Clustering and Semi-supervised Classification
Multiple kernel learning (MKL) method is generally believed to perform better
than single kernel method. However, some empirical studies show that this is
not always true: the combination of multiple kernels may even yield an even
worse performance than using a single kernel. There are two possible reasons
for the failure: (i) most existing MKL methods assume that the optimal kernel
is a linear combination of base kernels, which may not hold true; and (ii) some
kernel weights are inappropriately assigned due to noises and carelessly
designed algorithms. In this paper, we propose a novel MKL framework by
following two intuitive assumptions: (i) each kernel is a perturbation of the
consensus kernel; and (ii) the kernel that is close to the consensus kernel
should be assigned a large weight. Impressively, the proposed method can
automatically assign an appropriate weight to each kernel without introducing
additional parameters, as existing methods do. The proposed framework is
integrated into a unified framework for graph-based clustering and
semi-supervised classification. We have conducted experiments on multiple
benchmark datasets and our empirical results verify the superiority of the
proposed framework.Comment: Accepted by IJCAI 2018, Code is availabl
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