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Discovery Projects - Grant ID: DP130100364

Title
Discovery Projects - Grant ID: DP130100364
Funding
ARC | Discovery Projects
Contract (GA) number
DP130100364
Start Date
2013/01/01
End Date
2015/12/31
Open Access mandate
no
Organizations
-
More information
http://purl.org/au-research/grants/arc/DP130100364

 

  • Heterogeneous Tensor Decomposition for Clustering via Manifold Optimization

    Sun, Yanfeng; Gao, Junbin; Hong, Xia; Mishra, Bamdev; Yin, Baocai (2015)
    Projects: ARC | Discovery Projects - Grant ID: DP130100364 (DP130100364)
    Tensors or multiarray data are generalizations of matrices. Tensor clustering has become a very important research topic due to the intrinsically rich structures in real-world multiarray datasets. Subspace clustering based on vectorizing multiarray data has been extensively researched. However, vectorization of tensorial data does not exploit complete structure information. In this paper, we propose a subspace clustering algorithm without adopting any vectorization process. Our approach is ba...

    Estimation of Gaussian process regression model using probability distance measures

    Hong, Xia; Gao, Junbin; Jiang, Xinwei; Harris, Chris J. (2014)
    Projects: ARC | Discovery Projects - Grant ID: DP130100364 (DP130100364)
    A new class of parameter estimation algorithms is introduced for Gaussian process regression (GPR) models. It is shown that the integration of the GPR model with probability distance measures of (i) the integrated square error and (ii) Kullback–Leibler (K–L) divergence are analytically tractable. An efficient coordinate descent algorithm is proposed to iteratively estimate the kernel width using golden section search which includes a fast gradient descent algorithm as an inner loop to estimat...

    Low Rank Representation on Grassmann Manifolds: An Extrinsic Perspective

    Wang, Boyue; Hu, Yongli; Gao, Junbin; Sun, Yanfeng; Yin, Baocai (2015)
    Projects: ARC | Discovery Projects - Grant ID: DP130100364 (DP130100364)
    Many computer vision algorithms employ subspace models to represent data. The Low-rank representation (LRR) has been successfully applied in subspace clustering for which data are clustered according to their subspace structures. The possibility of extending LRR on Grassmann manifold is explored in this paper. Rather than directly embedding Grassmann manifold into a symmetric matrix space, an extrinsic view is taken by building the self-representation of LRR over the tangent space of each Gra...

    l1-norm penalized orthogonal forward regression

    Hong, Xia; Chen, Sheng; Guo, Yi; Gao, Junbin (2017)
    Projects: ARC | Discovery Projects - Grant ID: DP130100364 (DP130100364)
    A l1-norm penalized orthogonal forward regression (l1-POFR) algorithm is proposed based on the concept of leaveone- out mean square error (LOOMSE). Firstly, a new l1-norm penalized cost function is defined in the constructed orthogonal space, and each orthogonal basis is associated with an individually tunable regularization parameter. Secondly, due to orthogonal computation, the LOOMSE can be analytically computed without actually splitting the data set, and moreover a closed form of the opt...

    Relations among Some Low Rank Subspace Recovery Models

    Zhang, Hongyang; Lin, Zhouchen; Zhang, Chao; Gao, Junbin (2014)
    Projects: ARC | Discovery Projects - Grant ID: DP130100364 (DP130100364)
    Recovering intrinsic low dimensional subspaces from data distributed on them is a key preprocessing step to many applications. In recent years, there has been a lot of work that models subspace recovery as low rank minimization problems. We find that some representative models, such as Robust Principal Component Analysis (R-PCA), Robust Low Rank Representation (R-LRR), and Robust Latent Low Rank Representation (R-LatLRR), are actually deeply connected. More specifically, we discover that once...

    Sparse density estimation on the multinomial manifold

    Hong, Xia; Gao, Junbin; Chen, Sheng; Zia, Tanveer (2015)
    Projects: ARC | Discovery Projects - Grant ID: DP130100364 (DP130100364)
    A new sparse kernel density estimator is introduced based\ud on the minimum integrated square error criterion for the finite mixture model. Since the constraint on the mixing coefficients of the finite mixture model is on the multinomial manifold, we use the well-known Riemannian trust-region (RTR) algorithm for solving this problem. The first- and second-order Riemannian geometry of the\ud multinomial manifold are derived and utilized in the RTR algorithm. Numerical examples are employed to ...

    Kernelized Low Rank Representation on Grassmann Manifolds

    Wang, Boyue; Hu, Yongli; Gao, Junbin; Sun, Yanfeng; Yin, Baocai (2015)
    Projects: ARC | Discovery Projects - Grant ID: DP130100364 (DP130100364)
    Low rank representation (LRR) has recently attracted great interest due to its pleasing efficacy in exploring low-dimensional subspace structures embedded in data. One of its successful applications is subspace clustering which means data are clustered according to the subspaces they belong to. In this paper, at a higher level, we intend to cluster subspaces into classes of subspaces. This is naturally described as a clustering problem on Grassmann manifold. The novelty of this paper is to ge...

    Segmentation of Subspaces in Sequential Data

    Tierney, Stephen; Guo, Yi; Gao, Junbin (2015)
    Projects: ARC | Discovery Projects - Grant ID: DP130100364 (DP130100364)
    We propose Ordered Subspace Clustering (OSC) to segment data drawn from a sequentially ordered union of subspaces. Similar to Sparse Subspace Clustering (SSC) we formulate the problem as one of finding a sparse representation but include an additional penalty term to take care of sequential data. We test our method on data drawn from infrared hyper spectral, video and motion capture data. Experiments show that our method, OSC, outperforms the state of the art methods: Spatial Subspace Cluster...

    Kernelized LRR on Grassmann Manifolds for Subspace Clustering

    Wang, Boyue; Hu, Yongli; Gao, Junbin; Sun, Yanfeng; Yin, Baocai (2016)
    Projects: ARC | Discovery Projects - Grant ID: DP130100364 (DP130100364)
    Low rank representation (LRR) has recently attracted great interest due to its pleasing efficacy in exploring low-dimensional sub- space structures embedded in data. One of its successful applications is subspace clustering, by which data are clustered according to the subspaces they belong to. In this paper, at a higher level, we intend to cluster subspaces into classes of subspaces. This is naturally described as a clustering problem on Grassmann manifold. The novelty of this paper is to ge...

    Tensor LRR and sparse coding-based subspace clustering

    Fu, Yifan; Gao, Junbin; Tien, David; Lin, Zhouchen; Hong, Xia (2016)
    Projects: ARC | Discovery Projects - Grant ID: DP130100364 (DP130100364)
    Subspace clustering groups a set of samples from a union of several linear subspaces into clusters, so that the samples in the same cluster are drawn from the same linear subspace. In the majority of the existing work on subspace clustering, clusters are built based on feature information, while sample correlations in their original spatial structure are simply ignored. Besides, original high-dimensional feature vector contains noisy/redundant information, and the time complexity grows expone...
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