3,415 research outputs found
A study of the classification of low-dimensional data with supervised manifold learning
Supervised manifold learning methods learn data representations by preserving
the geometric structure of data while enhancing the separation between data
samples from different classes. In this work, we propose a theoretical study of
supervised manifold learning for classification. We consider nonlinear
dimensionality reduction algorithms that yield linearly separable embeddings of
training data and present generalization bounds for this type of algorithms. A
necessary condition for satisfactory generalization performance is that the
embedding allow the construction of a sufficiently regular interpolation
function in relation with the separation margin of the embedding. We show that
for supervised embeddings satisfying this condition, the classification error
decays at an exponential rate with the number of training samples. Finally, we
examine the separability of supervised nonlinear embeddings that aim to
preserve the low-dimensional geometric structure of data based on graph
representations. The proposed analysis is supported by experiments on several
real data sets
Segmentation-Aware Convolutional Networks Using Local Attention Masks
We introduce an approach to integrate segmentation information within a
convolutional neural network (CNN). This counter-acts the tendency of CNNs to
smooth information across regions and increases their spatial precision. To
obtain segmentation information, we set up a CNN to provide an embedding space
where region co-membership can be estimated based on Euclidean distance. We use
these embeddings to compute a local attention mask relative to every neuron
position. We incorporate such masks in CNNs and replace the convolution
operation with a "segmentation-aware" variant that allows a neuron to
selectively attend to inputs coming from its own region. We call the resulting
network a segmentation-aware CNN because it adapts its filters at each image
point according to local segmentation cues. We demonstrate the merit of our
method on two widely different dense prediction tasks, that involve
classification (semantic segmentation) and regression (optical flow). Our
results show that in semantic segmentation we can match the performance of
DenseCRFs while being faster and simpler, and in optical flow we obtain clearly
sharper responses than networks that do not use local attention masks. In both
cases, segmentation-aware convolution yields systematic improvements over
strong baselines. Source code for this work is available online at
http://cs.cmu.edu/~aharley/segaware
The Structure Transfer Machine Theory and Applications
Representation learning is a fundamental but challenging problem, especially
when the distribution of data is unknown. We propose a new representation
learning method, termed Structure Transfer Machine (STM), which enables feature
learning process to converge at the representation expectation in a
probabilistic way. We theoretically show that such an expected value of the
representation (mean) is achievable if the manifold structure can be
transferred from the data space to the feature space. The resulting structure
regularization term, named manifold loss, is incorporated into the loss
function of the typical deep learning pipeline. The STM architecture is
constructed to enforce the learned deep representation to satisfy the intrinsic
manifold structure from the data, which results in robust features that suit
various application scenarios, such as digit recognition, image classification
and object tracking. Compared to state-of-the-art CNN architectures, we achieve
the better results on several commonly used benchmarks\footnote{The source code
is available. https://github.com/stmstmstm/stm }
Masking Strategies for Image Manifolds
We consider the problem of selecting an optimal mask for an image manifold,
i.e., choosing a subset of the pixels of the image that preserves the
manifold's geometric structure present in the original data. Such masking
implements a form of compressive sensing through emerging imaging sensor
platforms for which the power expense grows with the number of pixels acquired.
Our goal is for the manifold learned from masked images to resemble its full
image counterpart as closely as possible. More precisely, we show that one can
indeed accurately learn an image manifold without having to consider a large
majority of the image pixels. In doing so, we consider two masking methods that
preserve the local and global geometric structure of the manifold,
respectively. In each case, the process of finding the optimal masking pattern
can be cast as a binary integer program, which is computationally expensive but
can be approximated by a fast greedy algorithm. Numerical experiments show that
the relevant manifold structure is preserved through the data-dependent masking
process, even for modest mask sizes
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