Canonical Correlation Analysis of Datasets with a Common Source Graph

Canonical correlation analysis (CCA) is a powerful technique for discovering whether or not hidden sources are commonly present in two (or more) datasets. Its well-appreciated merits include dimensionality reduction, clustering, classification, feature selection, and data fusion. The standard CCA however, does not exploit the geometry of the common sources, which may be available from the given data or can be deduced from (cross-) correlations. In this paper, this extra information provided by the common sources generating the data is encoded in a graph, and is invoked as a graph regularizer. This leads to a novel graph-regularized CCA approach, that is termed graph (g) CCA. The novel gCCA accounts for the graph-induced knowledge of common sources, while minimizing the distance between the wanted canonical variables. Tailored for diverse practical settings where the number of data is smaller than the data vector dimensions, the dual formulation of gCCA is also developed. One such setting includes kernels that are incorporated to account for nonlinear data dependencies. The resultant graph-kernel (gk) CCA is also obtained in closed form. Finally, corroborating image classification tests over several real datasets are presented to showcase the merits of the novel linear, dual, and kernel approaches relative to competing alternatives.Comment: 10 pages, 7 figure

Graph Multiview Canonical Correlation Analysis

Multiview canonical correlation analysis (MCCA) seeks latent low-dimensional representations encountered with multiview data of shared entities (a.k.a. common sources). However, existing MCCA approaches do not exploit the geometry of the common sources, which may be available \emph{a priori}, or can be constructed using certain domain knowledge. This prior information about the common sources can be encoded by a graph, and be invoked as a regularizer to enrich the maximum variance MCCA framework. In this context, the present paper's novel graph-regularized (G) MCCA approach minimizes the distance between the wanted canonical variables and the common low-dimensional representations, while accounting for graph-induced knowledge of the common sources. Relying on a function capturing the extent low-dimensional representations of the multiple views are similar, a generalization bound of GMCCA is established based on Rademacher's complexity. Tailored for setups where the number of data pairs is smaller than the data vector dimensions, a graph-regularized dual MCCA approach is also developed. To further deal with nonlinearities present in the data, graph-regularized kernel MCCA variants are put forward too. Interestingly, solutions of the graph-regularized linear, dual, and kernel MCCA, are all provided in terms of generalized eigenvalue decomposition. Several corroborating numerical tests using real datasets are provided to showcase the merits of the graph-regularized MCCA variants relative to several competing alternatives including MCCA, Laplacian-regularized MCCA, and (graph-regularized) PCA

An Overview of Cross-media Retrieval: Concepts, Methodologies, Benchmarks and Challenges

Multimedia retrieval plays an indispensable role in big data utilization. Past efforts mainly focused on single-media retrieval. However, the requirements of users are highly flexible, such as retrieving the relevant audio clips with one query of image. So challenges stemming from the "media gap", which means that representations of different media types are inconsistent, have attracted increasing attention. Cross-media retrieval is designed for the scenarios where the queries and retrieval results are of different media types. As a relatively new research topic, its concepts, methodologies and benchmarks are still not clear in the literatures. To address these issues, we review more than 100 references, give an overview including the concepts, methodologies, major challenges and open issues, as well as build up the benchmarks including datasets and experimental results. Researchers can directly adopt the benchmarks to promptly evaluate their proposed methods. This will help them to focus on algorithm design, rather than the time-consuming compared methods and results. It is noted that we have constructed a new dataset XMedia, which is the first publicly available dataset with up to five media types (text, image, video, audio and 3D model). We believe this overview will attract more researchers to focus on cross-media retrieval and be helpful to them.Comment: 14 pages, accepted by IEEE Transactions on Circuits and Systems for Video Technolog

Linked Component Analysis from Matrices to High Order Tensors: Applications to Biomedical Data

With the increasing availability of various sensor technologies, we now have access to large amounts of multi-block (also called multi-set, multi-relational, or multi-view) data that need to be jointly analyzed to explore their latent connections. Various component analysis methods have played an increasingly important role for the analysis of such coupled data. In this paper, we first provide a brief review of existing matrix-based (two-way) component analysis methods for the joint analysis of such data with a focus on biomedical applications. Then, we discuss their important extensions and generalization to multi-block multiway (tensor) data. We show how constrained multi-block tensor decomposition methods are able to extract similar or statistically dependent common features that are shared by all blocks, by incorporating the multiway nature of data. Special emphasis is given to the flexible common and individual feature analysis of multi-block data with the aim to simultaneously extract common and individual latent components with desired properties and types of diversity. Illustrative examples are given to demonstrate their effectiveness for biomedical data analysis.Comment: 20 pages, 11 figures, Proceedings of the IEEE, 201

Multi-View Bayesian Correlated Component Analysis

Correlated component analysis as proposed by Dmochowski et al. (2012) is a tool for investigating brain process similarity in the responses to multiple views of a given stimulus. Correlated components are identified under the assumption that the involved spatial networks are identical. Here we propose a hierarchical probabilistic model that can infer the level of universality in such multi-view data, from completely unrelated representations, corresponding to canonical correlation analysis, to identical representations as in correlated component analysis. This new model, which we denote Bayesian correlated component analysis, evaluates favourably against three relevant algorithms in simulated data. A well-established benchmark EEG dataset is used to further validate the new model and infer the variability of spatial representations across multiple subjects

SMILES Enumeration as Data Augmentation for Neural Network Modeling of Molecules

Simplified Molecular Input Line Entry System (SMILES) is a single line text representation of a unique molecule. One molecule can however have multiple SMILES strings, which is a reason that canonical SMILES have been defined, which ensures a one to one correspondence between SMILES string and molecule. Here the fact that multiple SMILES represent the same molecule is explored as a technique for data augmentation of a molecular QSAR dataset modeled by a long short term memory (LSTM) cell based neural network. The augmented dataset was 130 times bigger than the original. The network trained with the augmented dataset shows better performance on a test set when compared to a model built with only one canonical SMILES string per molecule. The correlation coefficient R2 on the test set was improved from 0.56 to 0.66 when using SMILES enumeration, and the root mean square error (RMS) likewise fell from 0.62 to 0.55. The technique also works in the prediction phase. By taking the average per molecule of the predictions for the enumerated SMILES a further improvement to a correlation coefficient of 0.68 and a RMS of 0.52 was found

Alternating Diffusion Map Based Fusion of Multimodal Brain Connectivity Networks for IQ Prediction

To explain individual differences in development, behavior, and cognition, most previous studies focused on projecting resting-state functional MRI (fMRI) based functional connectivity (FC) data into a low-dimensional space via linear dimensionality reduction techniques, followed by executing analysis operations. However, linear dimensionality analysis techniques may fail to capture nonlinearity of brain neuroactivity. Moreover, besides resting-state FC, FC based on task fMRI can be expected to provide complementary information. Motivated by these considerations, we nonlinearly fuse resting-state and task-based FC networks (FCNs) to seek a better representation in this paper. We propose a framework based on alternating diffusion map (ADM), which extracts geometry-preserving low-dimensional embeddings that successfully parameterize the intrinsic variables driving the phenomenon of interest. Specifically, we first separately build resting-state and task-based FCNs by symmetric positive definite matrices using sparse inverse covariance estimation for each subject, and then utilize the ADM to fuse them in order to extract significant low-dimensional embeddings, which are used as fingerprints to identify individuals. The proposed framework is validated on the Philadelphia Neurodevelopmental Cohort data, where we conduct extensive experimental study on resting-state and fractal $n$-back task fMRI for the classification of intelligence quotient (IQ). The fusion of resting-state and $n$-back task fMRI by the proposed framework achieves better classification accuracy than any single fMRI, and the proposed framework is shown to outperform several other data fusion methods. To our knowledge, this paper is the first to demonstrate a successful extension of the ADM to fuse resting-state and task-based fMRI data for accurate prediction of IQ

Unsupervised Multi-modal Hashing for Cross-modal retrieval

With the advantage of low storage cost and high efficiency, hashing learning has received much attention in the domain of Big Data. In this paper, we propose a novel unsupervised hashing learning method to cope with this open problem to directly preserve the manifold structure by hashing. To address this problem, both the semantic correlation in textual space and the locally geometric structure in the visual space are explored simultaneously in our framework. Besides, the `2;1-norm constraint is imposed on the projection matrices to learn the discriminative hash function for each modality. Extensive experiments are performed to evaluate the proposed method on the three publicly available datasets and the experimental results show that our method can achieve superior performance over the state-of-the-art methods.Comment: 4 pages, 4 figure

Modality-specific Cross-modal Similarity Measurement with Recurrent Attention Network

Nowadays, cross-modal retrieval plays an indispensable role to flexibly find information across different modalities of data. Effectively measuring the similarity between different modalities of data is the key of cross-modal retrieval. Different modalities such as image and text have imbalanced and complementary relationships, which contain unequal amount of information when describing the same semantics. For example, images often contain more details that cannot be demonstrated by textual descriptions and vice versa. Existing works based on Deep Neural Network (DNN) mostly construct one common space for different modalities to find the latent alignments between them, which lose their exclusive modality-specific characteristics. Different from the existing works, we propose modality-specific cross-modal similarity measurement (MCSM) approach by constructing independent semantic space for each modality, which adopts end-to-end framework to directly generate modality-specific cross-modal similarity without explicit common representation. For each semantic space, modality-specific characteristics within one modality are fully exploited by recurrent attention network, while the data of another modality is projected into this space with attention based joint embedding to utilize the learned attention weights for guiding the fine-grained cross-modal correlation learning, which can capture the imbalanced and complementary relationships between different modalities. Finally, the complementarity between the semantic spaces for different modalities is explored by adaptive fusion of the modality-specific cross-modal similarities to perform cross-modal retrieval. Experiments on the widely-used Wikipedia and Pascal Sentence datasets as well as our constructed large-scale XMediaNet dataset verify the effectiveness of our proposed approach, outperforming 9 state-of-the-art methods.Comment: 13 pages, submitted to IEEE Transactions on Image Processin

CM-GANs: Cross-modal Generative Adversarial Networks for Common Representation Learning

It is known that the inconsistent distribution and representation of different modalities, such as image and text, cause the heterogeneity gap that makes it challenging to correlate such heterogeneous data. Generative adversarial networks (GANs) have shown its strong ability of modeling data distribution and learning discriminative representation, existing GANs-based works mainly focus on generative problem to generate new data. We have different goal, aim to correlate heterogeneous data, by utilizing the power of GANs to model cross-modal joint distribution. Thus, we propose Cross-modal GANs to learn discriminative common representation for bridging heterogeneity gap. The main contributions are: (1) Cross-modal GANs architecture is proposed to model joint distribution over data of different modalities. The inter-modality and intra-modality correlation can be explored simultaneously in generative and discriminative models. Both of them beat each other to promote cross-modal correlation learning. (2) Cross-modal convolutional autoencoders with weight-sharing constraint are proposed to form generative model. They can not only exploit cross-modal correlation for learning common representation, but also preserve reconstruction information for capturing semantic consistency within each modality. (3) Cross-modal adversarial mechanism is proposed, which utilizes two kinds of discriminative models to simultaneously conduct intra-modality and inter-modality discrimination. They can mutually boost to make common representation more discriminative by adversarial training process. To the best of our knowledge, our proposed CM-GANs approach is the first to utilize GANs to perform cross-modal common representation learning. Experiments are conducted to verify the performance of our proposed approach on cross-modal retrieval paradigm, compared with 10 methods on 3 cross-modal datasets