11 research outputs found
Subspace Clustering via Optimal Direction Search
This letter presents a new spectral-clustering-based approach to the subspace
clustering problem. Underpinning the proposed method is a convex program for
optimal direction search, which for each data point d finds an optimal
direction in the span of the data that has minimum projection on the other data
points and non-vanishing projection on d. The obtained directions are
subsequently leveraged to identify a neighborhood set for each data point. An
alternating direction method of multipliers framework is provided to
efficiently solve for the optimal directions. The proposed method is shown to
notably outperform the existing subspace clustering methods, particularly for
unwieldy scenarios involving high levels of noise and close subspaces, and
yields the state-of-the-art results for the problem of face clustering using
subspace segmentation
Innovation Pursuit: A New Approach to Subspace Clustering
In subspace clustering, a group of data points belonging to a union of
subspaces are assigned membership to their respective subspaces. This paper
presents a new approach dubbed Innovation Pursuit (iPursuit) to the problem of
subspace clustering using a new geometrical idea whereby subspaces are
identified based on their relative novelties. We present two frameworks in
which the idea of innovation pursuit is used to distinguish the subspaces.
Underlying the first framework is an iterative method that finds the subspaces
consecutively by solving a series of simple linear optimization problems, each
searching for a direction of innovation in the span of the data potentially
orthogonal to all subspaces except for the one to be identified in one step of
the algorithm. A detailed mathematical analysis is provided establishing
sufficient conditions for iPursuit to correctly cluster the data. The proposed
approach can provably yield exact clustering even when the subspaces have
significant intersections. It is shown that the complexity of the iterative
approach scales only linearly in the number of data points and subspaces, and
quadratically in the dimension of the subspaces. The second framework
integrates iPursuit with spectral clustering to yield a new variant of
spectral-clustering-based algorithms. The numerical simulations with both real
and synthetic data demonstrate that iPursuit can often outperform the
state-of-the-art subspace clustering algorithms, more so for subspaces with
significant intersections, and that it significantly improves the
state-of-the-art result for subspace-segmentation-based face clustering
Sparse Subspace Clustering: Algorithm, Theory, and Applications
In many real-world problems, we are dealing with collections of
high-dimensional data, such as images, videos, text and web documents, DNA
microarray data, and more. Often, high-dimensional data lie close to
low-dimensional structures corresponding to several classes or categories the
data belongs to. In this paper, we propose and study an algorithm, called
Sparse Subspace Clustering (SSC), to cluster data points that lie in a union of
low-dimensional subspaces. The key idea is that, among infinitely many possible
representations of a data point in terms of other points, a sparse
representation corresponds to selecting a few points from the same subspace.
This motivates solving a sparse optimization program whose solution is used in
a spectral clustering framework to infer the clustering of data into subspaces.
Since solving the sparse optimization program is in general NP-hard, we
consider a convex relaxation and show that, under appropriate conditions on the
arrangement of subspaces and the distribution of data, the proposed
minimization program succeeds in recovering the desired sparse representations.
The proposed algorithm can be solved efficiently and can handle data points
near the intersections of subspaces. Another key advantage of the proposed
algorithm with respect to the state of the art is that it can deal with data
nuisances, such as noise, sparse outlying entries, and missing entries,
directly by incorporating the model of the data into the sparse optimization
program. We demonstrate the effectiveness of the proposed algorithm through
experiments on synthetic data as well as the two real-world problems of motion
segmentation and face clustering
A geometric analysis of subspace clustering with outliers
This paper considers the problem of clustering a collection of unlabeled data
points assumed to lie near a union of lower-dimensional planes. As is common in
computer vision or unsupervised learning applications, we do not know in
advance how many subspaces there are nor do we have any information about their
dimensions. We develop a novel geometric analysis of an algorithm named sparse
subspace clustering (SSC) [In IEEE Conference on Computer Vision and Pattern
Recognition, 2009. CVPR 2009 (2009) 2790-2797. IEEE], which significantly
broadens the range of problems where it is provably effective. For instance, we
show that SSC can recover multiple subspaces, each of dimension comparable to
the ambient dimension. We also prove that SSC can correctly cluster data points
even when the subspaces of interest intersect. Further, we develop an extension
of SSC that succeeds when the data set is corrupted with possibly
overwhelmingly many outliers. Underlying our analysis are clear geometric
insights, which may bear on other sparse recovery problems. A numerical study
complements our theoretical analysis and demonstrates the effectiveness of
these methods.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1034 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Learning Human Poses from Monocular Images
In this research, we mainly focus on the problem of estimating the 2D human pose from a monocular image and reconstructing the 3D human pose based on the 2D human pose. Here a 3D pose is the locations of the human joints in the 3D space and a 2D pose is the projection of a 3D pose on an image. Unlike many previous works that explicitly use hand-crafted physiological models, both our 2D pose estimation and 3D pose reconstruction approaches implicitly learn the structure of human body from human pose data.
This 3D pose reconstruction is an ill-posed problem without considering any prior knowledge. In this research, we propose a new approach, namely Pose Locality Constrained Representation (PLCR), to constrain the search space for the underlying 3D human pose and use it to improve 3D human pose reconstruction. In this approach, an over-complete pose dictionary is constructed by hierarchically clustering the 3D pose space into many subspaces. Then PLCR utilizes the structure of the over-complete dictionary to constrain the 3D pose solution to a set of highly-related subspaces. Finally, PLCR is combined into the matching-pursuit based algorithm for 3D human-pose reconstruction.
The 2D human pose used in 3D pose reconstruction can be manually annotated or automatically estimated from a single image. In this research, we develop a new learning-based 2D human pose estimation approach based on a Dual-Source Deep Convolutional Neural Networks (DS-CNN). The proposed DS-CNN model learns the appearance of each local body part and the relations between parts simultaneously, while most of existing approaches consider them as two separate steps. In our experiments, the proposed DS-CNN model produces superior or comparable performance against the state-of-the-art 2D human-pose estimation approaches based on pose priors learned from hand-crafted models or holistic perspectives.
Finally, we use our 2D human pose estimation approach to recognize human attributes by utilizing the strong correspondence between human attributes and human body parts. Then we probe if and when the CNN can find such correspondence by itself on human attribute recognition and bird species recognition. We find that there is direct correlation between the recognition accuracy and the correctness of the correspondence that the CNN finds
Improved image analysis by maximised statistical use of geometry-shape constraints
Identifying the underlying models in a set of data points contaminated by noise and outliers, leads to a highly complex multi-model fitting problem. This problem can be posed as a clustering problem by the construction of higher order affinities between data points into a hypergraph, which can then be partitioned using spectral clustering. Calculating the weights of all hyperedges is computationally expensive. Hence an approximation is required. In this thesis, the aim is to find an efficient and effective approximation that produces an excellent segmentation outcome. Firstly, the effect of hyperedge sizes on the speed and accuracy of the clustering is investigated. Almost all previous work on hypergraph clustering in computer vision, has considered the smallest possible hyperedge size, due to the lack of research into the potential benefits of large hyperedges and effective algorithms to generate them. In this thesis, it is shown that large hyperedges are better from both theoretical and empirical standpoints. The efficiency of this technique on various higher-order grouping problems is investigated. In particular, we show that our approach improves the accuracy and efficiency of motion segmentation from dense, long-term, trajectories. A shortcoming of the above approach is that the probability of a generated sample being impure increases as the size of the sample increases. To address this issue, a novel guided sampling strategy for large hyperedges, based on the concept of minimizing the largest residual, is also included. It is proposed to guide each sample by optimizing over a \textsuperscript{th} order statistics based cost function. Samples are generated using a greedy algorithm coupled with a data sub-sampling strategy. The experimental analysis shows that this proposed step is both accurate and computationally efficient compared to state-of-the-art robust multi-model fitting techniques. However, the optimization method for guiding samples involves hard-to-tune parameters. Thus a sampling method is eventually developed that significantly facilitates solving the segmentation problem using a new form of the Markov-Chain-Monte-Carlo (MCMC) method to efficiently sample from hyperedge distribution. To sample from the above distribution effectively, the proposed Markov Chain includes new types of long and short jumps to perform exploration and exploitation of all structures. Unlike common sampling methods, this method does not require any specific prior knowledge about the distribution of models. The output set of samples leads to a clustering solution by which the final model parameters for each segment are obtained. The overall method competes favorably with the state-of-the-art both in terms of computation power and segmentation accuracy