Graph Embeddings and Laplacian Eigenvalues
SIAM Journal on Matrix Analysis and Applications
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Synthesizing bidirectional texture functions for real-world surfaces
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Document clustering based on non-negative matrix factorization
Proceedings of the 26th annual international ACM SIGIR conference on Research and development in informaion retrieval
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Content-based image retrieval by clustering
MIR '03 Proceedings of the 5th ACM SIGMM international workshop on Multimedia information retrieval
Locality preserving clustering for image database
Proceedings of the 12th annual ACM international conference on Multimedia
Spectral structuring of home videos
CIVR'03 Proceedings of the 2nd international conference on Image and video retrieval
Deriving semantics for image clustering from accumulated user feedbacks
Proceedings of the 15th international conference on Multimedia
Hierarchical Tensor Approximation of Multi-Dimensional Visual Data
IEEE Transactions on Visualization and Computer Graphics
Classification of multivariate time series using locality preserving projections
Knowledge-Based Systems
Active post-refined multimodality video semantic concept detection with tensor representation
MM '08 Proceedings of the 16th ACM international conference on Multimedia
Multi-modality video shot clustering with tensor representation
Multimedia Tools and Applications
Tensor linear Laplacian discrimination (TLLD) for feature extraction
Pattern Recognition
Image co-clustering with multi-modality features and user feedbacks
MM '09 Proceedings of the 17th ACM international conference on Multimedia
Supervised manifold learning for image and video classification
Proceedings of the international conference on Multimedia
A polynomial characterization of hypergraphs using the Ihara zeta function
Pattern Recognition
Edge-preserving color image denoising through tensor voting
Computer Vision and Image Understanding
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We consider the problem of image representation and clustering. Traditionally, an n1 x n2 image is represented by a vector in the Euclidean space ℝ n1 x n2. Some learning algorithms are then applied to these vectors in such a high dimensional space for dimensionality reduction, classification, and clustering. However, an image is intrinsically a matrix, or the second order tensor. The vector representation of the images ignores the spatial relationships between the pixels in an image. In this paper, we introduce a tensor framework for image analysis. We represent the images as points in the tensor space Rn1 mathcal Rn2 which is a tensor product of two vector spaces. Based on the tensor representation, we propose a novel image representation and clustering algorithm which explicitly considers the manifold structure of the tensor space. By preserving the local structure of the data manifold, we can obtain a tensor subspace which is optimal for data representation in the sense of local isometry. We call it TensorImage approach. Traditional clustering algorithm such as k-means is then applied in the tensor subspace. Our algorithm shares many of the data representation and clustering properties of other techniques such as Locality Preserving Projections, Laplacian Eigenmaps, and spectral clustering, yet our algorithm is much more computationally efficient. Experimental results show the efficiency and effectiveness of our algorithm.