6,056 research outputs found
Fast Robust PCA on Graphs
Mining useful clusters from high dimensional data has received significant
attention of the computer vision and pattern recognition community in the
recent years. Linear and non-linear dimensionality reduction has played an
important role to overcome the curse of dimensionality. However, often such
methods are accompanied with three different problems: high computational
complexity (usually associated with the nuclear norm minimization),
non-convexity (for matrix factorization methods) and susceptibility to gross
corruptions in the data. In this paper we propose a principal component
analysis (PCA) based solution that overcomes these three issues and
approximates a low-rank recovery method for high dimensional datasets. We
target the low-rank recovery by enforcing two types of graph smoothness
assumptions, one on the data samples and the other on the features by designing
a convex optimization problem. The resulting algorithm is fast, efficient and
scalable for huge datasets with O(nlog(n)) computational complexity in the
number of data samples. It is also robust to gross corruptions in the dataset
as well as to the model parameters. Clustering experiments on 7 benchmark
datasets with different types of corruptions and background separation
experiments on 3 video datasets show that our proposed model outperforms 10
state-of-the-art dimensionality reduction models. Our theoretical analysis
proves that the proposed model is able to recover approximate low-rank
representations with a bounded error for clusterable data
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
KCRC-LCD: Discriminative Kernel Collaborative Representation with Locality Constrained Dictionary for Visual Categorization
We consider the image classification problem via kernel collaborative
representation classification with locality constrained dictionary (KCRC-LCD).
Specifically, we propose a kernel collaborative representation classification
(KCRC) approach in which kernel method is used to improve the discrimination
ability of collaborative representation classification (CRC). We then measure
the similarities between the query and atoms in the global dictionary in order
to construct a locality constrained dictionary (LCD) for KCRC. In addition, we
discuss several similarity measure approaches in LCD and further present a
simple yet effective unified similarity measure whose superiority is validated
in experiments. There are several appealing aspects associated with LCD. First,
LCD can be nicely incorporated under the framework of KCRC. The LCD similarity
measure can be kernelized under KCRC, which theoretically links CRC and LCD
under the kernel method. Second, KCRC-LCD becomes more scalable to both the
training set size and the feature dimension. Example shows that KCRC is able to
perfectly classify data with certain distribution, while conventional CRC fails
completely. Comprehensive experiments on many public datasets also show that
KCRC-LCD is a robust discriminative classifier with both excellent performance
and good scalability, being comparable or outperforming many other
state-of-the-art approaches
Graph-Based Decoding Model for Functional Alignment of Unaligned fMRI Data
Aggregating multi-subject functional magnetic resonance imaging (fMRI) data
is indispensable for generating valid and general inferences from patterns
distributed across human brains. The disparities in anatomical structures and
functional topographies of human brains warrant aligning fMRI data across
subjects. However, the existing functional alignment methods cannot handle well
various kinds of fMRI datasets today, especially when they are not
temporally-aligned, i.e., some of the subjects probably lack the responses to
some stimuli, or different subjects might follow different sequences of
stimuli. In this paper, a cross-subject graph that depicts the
(dis)similarities between samples across subjects is used as a priori for
developing a more flexible framework that suits an assortment of fMRI datasets.
However, the high dimension of fMRI data and the use of multiple subjects makes
the crude framework time-consuming or unpractical. To address this issue, we
further regularize the framework, so that a novel feasible kernel-based
optimization, which permits nonlinear feature extraction, could be
theoretically developed. Specifically, a low-dimension assumption is imposed on
each new feature space to avoid overfitting caused by the
highspatial-low-temporal resolution of fMRI data. Experimental results on five
datasets suggest that the proposed method is not only superior to several
state-of-the-art methods on temporally-aligned fMRI data, but also suitable for
dealing `with temporally-unaligned fMRI data.Comment: 17 pages, 10 figures, Proceedings of the Association for the
Advancement of Artificial Intelligence (AAAI-20
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