2 research outputs found
Vectorial Dimension Reduction for Tensors Based on Bayesian Inference
Dimensionality reduction for high-order tensors is a challenging problem. In
conventional approaches, higher order tensors are `vectorized` via Tucker
decomposition to obtain lower order tensors. This will destroy the inherent
high-order structures or resulting in undesired tensors, respectively. This
paper introduces a probabilistic vectorial dimensionality reduction model for
tensorial data. The model represents a tensor by employing a linear combination
of same order basis tensors, thus it offers a mechanism to directly reduce a
tensor to a vector. Under this expression, the projection base of the model is
based on the tensor CandeComp/PARAFAC (CP) decomposition and the number of free
parameters in the model only grows linearly with the number of modes rather
than exponentially. A Bayesian inference has been established via the
variational EM approach. A criterion to set the parameters (factor number of CP
decomposition and the number of extracted features) is empirically given. The
model outperforms several existing PCA-based methods and CP decomposition on
several publicly available databases in terms of classification and clustering
accuracy.Comment: Submiting to TNNL
Localized LRR on Grassmann Manifolds: An Extrinsic View
Subspace data representation has recently become a common practice in many
computer vision tasks. It demands generalizing classical machine learning
algorithms for subspace data. Low-Rank Representation (LRR) is one of the most
successful models for clustering vectorial data according to their subspace
structures. This paper explores the possibility of extending LRR for subspace
data on Grassmann manifolds. Rather than directly embedding the Grassmann
manifolds into the symmetric matrix space, an extrinsic view is taken to build
the LRR self-representation in the local area of the tangent space at each
Grassmannian point, resulting in a localized LRR method on Grassmann manifolds.
A novel algorithm for solving the proposed model is investigated and
implemented. The performance of the new clustering algorithm is assessed
through experiments on several real-world datasets including MNIST handwritten
digits, ballet video clips, SKIG action clips, DynTex++ dataset and highway
traffic video clips. The experimental results show the new method outperforms a
number of state-of-the-art clustering methodsComment: IEEE Transactions on Circuits and Systems for Video Technology with
Minor Revisions. arXiv admin note: text overlap with arXiv:1504.0180