3,351 research outputs found
Nonlinear Supervised Dimensionality Reduction via Smooth Regular Embeddings
The recovery of the intrinsic geometric structures of data collections is an
important problem in data analysis. Supervised extensions of several manifold
learning approaches have been proposed in the recent years. Meanwhile, existing
methods primarily focus on the embedding of the training data, and the
generalization of the embedding to initially unseen test data is rather
ignored. In this work, we build on recent theoretical results on the
generalization performance of supervised manifold learning algorithms.
Motivated by these performance bounds, we propose a supervised manifold
learning method that computes a nonlinear embedding while constructing a smooth
and regular interpolation function that extends the embedding to the whole data
space in order to achieve satisfactory generalization. The embedding and the
interpolator are jointly learnt such that the Lipschitz regularity of the
interpolator is imposed while ensuring the separation between different
classes. Experimental results on several image data sets show that the proposed
method outperforms traditional classifiers and the supervised dimensionality
reduction algorithms in comparison in terms of classification accuracy in most
settings
Adaptive Locality Preserving Regression
This paper proposes a novel discriminative regression method, called adaptive
locality preserving regression (ALPR) for classification. In particular, ALPR
aims to learn a more flexible and discriminative projection that not only
preserves the intrinsic structure of data, but also possesses the properties of
feature selection and interpretability. To this end, we introduce a target
learning technique to adaptively learn a more discriminative and flexible
target matrix rather than the pre-defined strict zero-one label matrix for
regression. Then a locality preserving constraint regularized by the adaptive
learned weights is further introduced to guide the projection learning, which
is beneficial to learn a more discriminative projection and avoid overfitting.
Moreover, we replace the conventional `Frobenius norm' with the special l21
norm to constrain the projection, which enables the method to adaptively select
the most important features from the original high-dimensional data for feature
extraction. In this way, the negative influence of the redundant features and
noises residing in the original data can be greatly eliminated. Besides, the
proposed method has good interpretability for features owing to the
row-sparsity property of the l21 norm. Extensive experiments conducted on the
synthetic database with manifold structure and many real-world databases prove
the effectiveness of the proposed method.Comment: The paper has been accepted by IEEE Transactions on Circuits and
Systems for Video Technology (TCSVT), and the code can be available at
https://drive.google.com/file/d/1iNzONkRByIaUhXwdEhOkkh_0d2AAXNE8/vie
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