58,903 research outputs found
Sparse Correlation Kernel Analysis and Reconstruction
This paper presents a new paradigm for signal reconstruction and superresolution, Correlation Kernel Analysis (CKA), that is based on the selection of a sparse set of bases from a large dictionary of class- specific basis functions. The basis functions that we use are the correlation functions of the class of signals we are analyzing. To choose the appropriate features from this large dictionary, we use Support Vector Machine (SVM) regression and compare this to traditional Principal Component Analysis (PCA) for the tasks of signal reconstruction, superresolution, and compression. The testbed we use in this paper is a set of images of pedestrians. This paper also presents results of experiments in which we use a dictionary of multiscale basis functions and then use Basis Pursuit De-Noising to obtain a sparse, multiscale approximation of a signal. The results are analyzed and we conclude that 1) when used with a sparse representation technique, the correlation function is an effective kernel for image reconstruction and superresolution, 2) for image compression, PCA and SVM have different tradeoffs, depending on the particular metric that is used to evaluate the results, 3) in sparse representation techniques, L_1 is not a good proxy for the true measure of sparsity, L_0, and 4) the L_epsilon norm may be a better error metric for image reconstruction and compression than the L_2 norm, though the exact psychophysical metric should take into account high order structure in images
Taming Wild High Dimensional Text Data with a Fuzzy Lash
The bag of words (BOW) represents a corpus in a matrix whose elements are the
frequency of words. However, each row in the matrix is a very high-dimensional
sparse vector. Dimension reduction (DR) is a popular method to address sparsity
and high-dimensionality issues. Among different strategies to develop DR
method, Unsupervised Feature Transformation (UFT) is a popular strategy to map
all words on a new basis to represent BOW. The recent increase of text data and
its challenges imply that DR area still needs new perspectives. Although a wide
range of methods based on the UFT strategy has been developed, the fuzzy
approach has not been considered for DR based on this strategy. This research
investigates the application of fuzzy clustering as a DR method based on the
UFT strategy to collapse BOW matrix to provide a lower-dimensional
representation of documents instead of the words in a corpus. The quantitative
evaluation shows that fuzzy clustering produces superior performance and
features to Principal Components Analysis (PCA) and Singular Value
Decomposition (SVD), two popular DR methods based on the UFT strategy
Learning Rank Reduced Interpolation with Principal Component Analysis
In computer vision most iterative optimization algorithms, both sparse and
dense, rely on a coarse and reliable dense initialization to bootstrap their
optimization procedure. For example, dense optical flow algorithms profit
massively in speed and robustness if they are initialized well in the basin of
convergence of the used loss function. The same holds true for methods as
sparse feature tracking when initial flow or depth information for new features
at arbitrary positions is needed. This makes it extremely important to have
techniques at hand that allow to obtain from only very few available
measurements a dense but still approximative sketch of a desired 2D structure
(e.g. depth maps, optical flow, disparity maps, etc.). The 2D map is regarded
as sample from a 2D random process. The method presented here exploits the
complete information given by the principal component analysis (PCA) of that
process, the principal basis and its prior distribution. The method is able to
determine a dense reconstruction from sparse measurement. When facing
situations with only very sparse measurements, typically the number of
principal components is further reduced which results in a loss of
expressiveness of the basis. We overcome this problem and inject prior
knowledge in a maximum a posterior (MAP) approach. We test our approach on the
KITTI and the virtual KITTI datasets and focus on the interpolation of depth
maps for driving scenes. The evaluation of the results show good agreement to
the ground truth and are clearly better than results of interpolation by the
nearest neighbor method which disregards statistical information.Comment: Accepted at Intelligent Vehicles Symposium (IV), Los Angeles, USA,
June 201
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
- …