12,452 research outputs found
Analysis of Alignment Algorithms with Mixed Dimensions for Dimensionality Reduction
SUMMARY We consider an alignment algorithm for reconstructing global coordinates of a given data set from coordinates constructed for data points in small local neighborhoods through computing a spectral subspace of an alignment matrix. We show that, under certain conditions, the null space of the alignment matrix recovers global coordinates even when local point sets have different dimensions. This result generalizes a previous analysis to allow alignment of local coordinates of mixed dimensions. We also extend this result to the setting of a semi-supervised learning problem and we present several examples to illustrate our results
Simultaneous Spectral-Spatial Feature Selection and Extraction for Hyperspectral Images
In hyperspectral remote sensing data mining, it is important to take into
account of both spectral and spatial information, such as the spectral
signature, texture feature and morphological property, to improve the
performances, e.g., the image classification accuracy. In a feature
representation point of view, a nature approach to handle this situation is to
concatenate the spectral and spatial features into a single but high
dimensional vector and then apply a certain dimension reduction technique
directly on that concatenated vector before feed it into the subsequent
classifier. However, multiple features from various domains definitely have
different physical meanings and statistical properties, and thus such
concatenation hasn't efficiently explore the complementary properties among
different features, which should benefit for boost the feature
discriminability. Furthermore, it is also difficult to interpret the
transformed results of the concatenated vector. Consequently, finding a
physically meaningful consensus low dimensional feature representation of
original multiple features is still a challenging task. In order to address the
these issues, we propose a novel feature learning framework, i.e., the
simultaneous spectral-spatial feature selection and extraction algorithm, for
hyperspectral images spectral-spatial feature representation and
classification. Specifically, the proposed method learns a latent low
dimensional subspace by projecting the spectral-spatial feature into a common
feature space, where the complementary information has been effectively
exploited, and simultaneously, only the most significant original features have
been transformed. Encouraging experimental results on three public available
hyperspectral remote sensing datasets confirm that our proposed method is
effective and efficient
Diffusion Component Analysis: Unraveling Functional Topology in Biological Networks
Complex biological systems have been successfully modeled by biochemical and
genetic interaction networks, typically gathered from high-throughput (HTP)
data. These networks can be used to infer functional relationships between
genes or proteins. Using the intuition that the topological role of a gene in a
network relates to its biological function, local or diffusion based
"guilt-by-association" and graph-theoretic methods have had success in
inferring gene functions. Here we seek to improve function prediction by
integrating diffusion-based methods with a novel dimensionality reduction
technique to overcome the incomplete and noisy nature of network data. In this
paper, we introduce diffusion component analysis (DCA), a framework that plugs
in a diffusion model and learns a low-dimensional vector representation of each
node to encode the topological properties of a network. As a proof of concept,
we demonstrate DCA's substantial improvement over state-of-the-art
diffusion-based approaches in predicting protein function from molecular
interaction networks. Moreover, our DCA framework can integrate multiple
networks from heterogeneous sources, consisting of genomic information,
biochemical experiments and other resources, to even further improve function
prediction. Yet another layer of performance gain is achieved by integrating
the DCA framework with support vector machines that take our node vector
representations as features. Overall, our DCA framework provides a novel
representation of nodes in a network that can be used as a plug-in architecture
to other machine learning algorithms to decipher topological properties of and
obtain novel insights into interactomes.Comment: RECOMB 201
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