Multiview pattern recognition methods for data visualization, embedding and clustering

Multiview data is defined as data for whose samples there exist several different data views, i.e. different data matrices obtained through different experiments, methods or situations. Multiview dimensionality reduction methods transform a high­dimensional, multiview dataset into a single, low-dimensional space or projection. Their goal is to provide a more manageable representation of the original data, either for data visualization or to simplify the following analysis stages. Multiview clustering methods receive a multiview dataset and propose a single clustering assignment of the data samples in the dataset, considering the information from all the input data views. The main hypothesis defended in this work is that using multiview data along with methods able to exploit their information richness produces better dimensionality reduction and clustering results than simply using single views or concatenating all views into a single matrix. Consequently, the objectives of this thesis are to develop and test multiview pattern recognition methods based on well known single-view dimensionality reduction and clustering methods. Three multiview pattern recognition methods are presented: multiview t-distributed stochastic neighbourhood embedding (MV-tSNE), multiview multimodal scaling (MV-MDS) and a novel formulation of multiview spectral clustering (MVSC-CEV). These methods can be applied both to dimensionality reduction tasks and to clustering tasks. The MV-tSNE method computes a matrix of probabilities based on distances between sam ples for each input view. Then it merges the different probability matrices using results from expert opinion pooling theory to get a common matrix of probabilities, which is then used as reference to build a low-dimensional projection of the data whose probabilities are similar. The MV-MDS method computes the common eigenvectors of all the normalized distance matrices in order to obtain a single low-dimensional space that embeds the essential information from all the input spaces, avoiding redundant information to be included. The MVSC-CEV method computes the symmetric Laplacian matrices of the similaritymatrices of all data views. Then it generates a single, low-dimensional representation of the input data by computing the common eigenvectors of the Laplacian matrices, obtaining a projection of the data that embeds the most relevan! information of the input data views, also avoiding the addition of redundant information. A thorough set of experiments has been designed and run in order to compare the proposed methods with their single view counterpart. Also, the proposed methods have been compared with all the available results of equivalent methods in the state of the art. Finally, a comparison between the three proposed methods is presented in order to provide guidelines on which method to use for a given task. MVSC-CEV consistently produces better clustering results than other multiview methods in the state of the art. MV-MDS produces overall better results than the reference methods in dimensionality reduction experiments. MV-tSNE does not excel on any of these tasks. As a consequence, for multiview clustering tasks it is recommended to use MVSC-CEV, and MV-MDS for multiview dimensionality reduction tasks. Although several multiview dimensionality reduction or clustering methods have been proposed in the state of the art, there is no software implementation available. In order to compensate for this fact and to provide the communitywith a potentially useful set of multiview pattern recognition methods, an R software package containg the proposed methods has been developed and released to the public.