4,084 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
Manifold Elastic Net: A Unified Framework for Sparse Dimension Reduction
It is difficult to find the optimal sparse solution of a manifold learning
based dimensionality reduction algorithm. The lasso or the elastic net
penalized manifold learning based dimensionality reduction is not directly a
lasso penalized least square problem and thus the least angle regression (LARS)
(Efron et al. \cite{LARS}), one of the most popular algorithms in sparse
learning, cannot be applied. Therefore, most current approaches take indirect
ways or have strict settings, which can be inconvenient for applications. In
this paper, we proposed the manifold elastic net or MEN for short. MEN
incorporates the merits of both the manifold learning based dimensionality
reduction and the sparse learning based dimensionality reduction. By using a
series of equivalent transformations, we show MEN is equivalent to the lasso
penalized least square problem and thus LARS is adopted to obtain the optimal
sparse solution of MEN. In particular, MEN has the following advantages for
subsequent classification: 1) the local geometry of samples is well preserved
for low dimensional data representation, 2) both the margin maximization and
the classification error minimization are considered for sparse projection
calculation, 3) the projection matrix of MEN improves the parsimony in
computation, 4) the elastic net penalty reduces the over-fitting problem, and
5) the projection matrix of MEN can be interpreted psychologically and
physiologically. Experimental evidence on face recognition over various popular
datasets suggests that MEN is superior to top level dimensionality reduction
algorithms.Comment: 33 pages, 12 figure
Unsupervised spectral sub-feature learning for hyperspectral image classification
Spectral pixel classification is one of the principal techniques used in hyperspectral image (HSI) analysis. In this article, we propose an unsupervised feature learning method for classification of hyperspectral images. The proposed method learns a dictionary of sub-feature basis representations from the spectral domain, which allows effective use of the correlated spectral data. The learned dictionary is then used in encoding convolutional samples from the hyperspectral input pixels to an expanded but sparse feature space. Expanded hyperspectral feature representations enable linear separation between object classes present in an image. To evaluate the proposed method, we performed experiments on several commonly used HSI data sets acquired at different locations and by different sensors. Our experimental results show that the proposed method outperforms other pixel-wise classification methods that make use of unsupervised feature extraction approaches. Additionally, even though our approach does not use any prior knowledge, or labelled training data to learn features, it yields either advantageous, or comparable, results in terms of classification accuracy with respect to recent semi-supervised methods
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