Abstract:
In this paper, we study the co-embedding problem of how to map different types of patterns into one common low-dimensional space, given only the associations (relation va...Show MoreMetadata
Abstract:
In this paper, we study the co-embedding problem of how to map different types of patterns into one common low-dimensional space, given only the associations (relation values) between samples. We conduct a generic analysis to discover the commonalities between existing co-embedding algorithms and indirectly related approaches and investigate possible factors controlling the shapes and distributions of the co-embeddings. The primary contribution of this work is a novel method for computing co--embeddings, termed the automatic co-embedding with adaptive shaping (ACAS) algorithm, based on an efficient transformation of the co-embedding problem. Its advantages include flexible model adaptation to the given data, an economical set of model variables leading to a parametric co-embedding formulation, and a robust model fitting criterion for model optimization based on a quantization procedure. The secondary contribution of this work is the introduction of a set of generic schemes for the qualitative analysis and quantitative assessment of the output of co-embedding algorithms, using existing labeled benchmark datasets. Experiments with synthetic and real-world datasets show that the proposed algorithm is very competitive compared to existing ones.
Published in: IEEE Transactions on Pattern Analysis and Machine Intelligence ( Volume: 35, Issue: 10, October 2013)
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- IEEE Keywords
- Index Terms
- Shape Adaptation ,
- Contributions Of This Work ,
- Real-world Datasets ,
- Low-dimensional Space ,
- Common Space ,
- Output Of Algorithm ,
- Sample Groups ,
- Singular Value ,
- Training Procedure ,
- Original Features ,
- Singular Value Decomposition ,
- Similarity Matrix ,
- Relationship Matrix ,
- Latent Space ,
- Global Structure ,
- Dot Product ,
- Feature Matrix ,
- Class Separation ,
- Correspondence Analysis ,
- Original Space ,
- Eigenvectors Of Matrix ,
- Singular Vectors ,
- Standard Embedding ,
- Non-negative Entries ,
- Unique Class ,
- Individual Error ,
- Gaussian Kernel ,
- Kullback-Leibler ,
- Joint Distribution ,
- Objective Function
- Author Keywords
- MeSH Terms
Keywords assist with retrieval of results and provide a means to discovering other relevant content. Learn more.
- IEEE Keywords
- Index Terms
- Shape Adaptation ,
- Contributions Of This Work ,
- Real-world Datasets ,
- Low-dimensional Space ,
- Common Space ,
- Output Of Algorithm ,
- Sample Groups ,
- Singular Value ,
- Training Procedure ,
- Original Features ,
- Singular Value Decomposition ,
- Similarity Matrix ,
- Relationship Matrix ,
- Latent Space ,
- Global Structure ,
- Dot Product ,
- Feature Matrix ,
- Class Separation ,
- Correspondence Analysis ,
- Original Space ,
- Eigenvectors Of Matrix ,
- Singular Vectors ,
- Standard Embedding ,
- Non-negative Entries ,
- Unique Class ,
- Individual Error ,
- Gaussian Kernel ,
- Kullback-Leibler ,
- Joint Distribution ,
- Objective Function
- Author Keywords
- MeSH Terms