Show Reference: "Semisupervised Multimodal Dimensionality Reduction"

Semisupervised Multimodal Dimensionality Reduction Computational Intelligence, Vol. 29, No. 1. (1 February 2013), pp. 70-110, doi:10.1111/j.1467-8640.2012.00429.x by Zhao Zhang, Tommy W. S. Chow, Ning Ye
    abstract = {The problem of learning from both labeled and unlabeled data is considered. In this paper, we present a novel semisupervised multimodal dimensionality reduction ({SSMDR}) algorithm for feature reduction and extraction. {SSMDR} can preserve the local and multimodal structures of labeled and unlabeled samples. As a result, data pairs in the close vicinity of the original space are projected in the nearby of the embedding space. Due to overfitting, supervised dimensionality reduction methods tend to perform inefficiently when only few labeled samples are available. In such cases, unlabeled samples play a significant role in boosting the learning performance. The proposed discriminant technique has an analytical form of the embedding transformations that can be effectively obtained by applying the eigen decomposition, or finding two close optimal sets of transforming basis vectors. By employing the standard kernel trick, {SSMDR} can be extended to the nonlinear dimensionality reduction scenarios. We verify the feasibility and effectiveness of {SSMDR} through conducting extensive simulations including data visualization and classification on the synthetic and real-world datasets. Our obtained results reveal that {SSMDR} offers significant advantages over some widely used techniques. Compared with other methods, the proposed {SSMDR} exhibits superior performance on multimodal cases.},
    author = {Zhang, Zhao and Chow, Tommy W. S. and Ye, Ning},
    day = {1},
    doi = {10.1111/j.1467-8640.2012.00429.x},
    journal = {Computational Intelligence},
    keywords = {dimensionality-reduction, multisensory-integration, supervised-learning, unsupervised-learning},
    month = feb,
    number = {1},
    pages = {70--110},
    posted-at = {2013-08-13 02:06:58},
    priority = {2},
    publisher = {Blackwell Publishing Inc},
    title = {Semisupervised Multimodal Dimensionality Reduction},
    url = {},
    volume = {29},
    year = {2013}

See the CiteULike entry for more info, PDF links, BibTex etc.

Zhang et al. propose an unsupervised dimensionality reduction algorithm, which they call 'multi-modal'.

Their notion of multi-modality is a different notion from the one used in my work: it means that a latent, low-dimensional variable is expressed according to a multi-modal PDF.

This is can be difficult depending the transformation function mapping the high-dimensional data into low-dimensional space. Especially linear methods, like PCA will suffer from this.

The authors focus on (mostly binary) classification. In that context, multi-modality requires complex decision boundaries.

According to Zhang et al., ViSOM (and other unsupervised methods) do not take data labels and their intrinsic structure into account if they are present.