Non-negative matrix factorization of multimodal MRI, fMRI and phenotypic data reveals differential changes in default mode subnetworks in ADHD

Abstract

In the multimodal neuroimaging framework, data on a single subject are collected from inherently different sources such as functional MRI, structural MRI, behavioral and/or phenotypic information. The information each source provides is not independent; a subset of features from each modality maps to one or more common latent dimensions, which can be interpreted using generative models. These latent dimensions, or "topics," provide a sparse summary of the generative process behind the features for each individual. Topic modeling, an unsupervised generative model, has been used to map seemingly disparate features to a common domain. We use Non-Negative Matrix Factorization (NMF) to infer the latent structure of multimodal ADHD data containing fMRI, MRI, phenotypic and behavioral measurements. We compare four different NMF algorithms and find that the sparsest decomposition is also the most differentiating between ADHD and healthy patients. We identify dimensions that map to interpretable, recognizable dimensions such as motion, default mode network activity, and other such features of the input data. For example, structural and functional graph theory features related to default mode subnetworks clustered with the ADHD-Inattentive diagnosis. Structural measurements of the default mode network (DMN) regions such as the posterior cingulate, precuneus, and parahippocampal regions were all related to the ADHD-Inattentive diagnosis. Ventral DMN subnetworks may have more functional connections in ADHD-I, while dorsal DMN may have less. ADHD topics are dependent upon diagnostic site, suggesting diagnostic differences across geographic locations. We assess our findings in light of the ADHD-200 classification competition, and contrast our unsupervised, nominated topics with previously published supervised learning methods. Finally, we demonstrate the validity of these latent variables as biomarkers by using them for classification of ADHD in 730 patients. Cumulatively, this manuscript addresses how multimodal data in ADHD can be interpreted by latent dimensions.

Keywords: ADHD; Attention deficit; Biomarkers; Default mode; Latent variables; MRI; Machine learning; Multimodal data; NMF; Phenotype; Sparsity; Topic modeling; fMRI.

Figure 1

Topic Modeling of Multimodal Features in ADHD: a conceptual illustration. The structural MRI, functional MRI, and phenotypic observations are all generated by latent topics, which in turn generate each subject's multimodal dataset. By learning the topics, we get a mapping across multimodal features and a generative model behind the observed data. The data matrix V has n feature rows and m observation columns. If V contained a collection of multimodal features (total features by patients), then NMF would decompose the data into a set of “basis images” and encodings, such that $V_{i\mu }\approx {\left(WH\right)}_{i\mu }={\sum }_{k=1}^K{W}_{ik}{H}_{k\mu }$ where the W matrix contains the basis set of multimodal features (topics) and is of dimension n × k, and the “encoding matrix” H is of dimensions k × m, for row i and column μ.

Figure 2

Basis Values resulting from NMF factorization of Feature Matrix using four different NMF algorithms: PG (Projected Gradiant), ALS (Alternating Least Squares), Multiplicative Update, and Multinomial Estimation. The number represents the total number of encoding dimensions which were different (statistically significant) between ADHD and TD, based upon a 2-sample t-test. There were 20 total dimensions extracted using NMF.

Figure 3

Sample of features selected within topics 10, 12 and 14 . For each topic, there were 236 features selected. All 20 topics, each containing 236 features, are available at http://ariana82.bol.ucla.edu/downloads-2/files/ALSNMFTopics.xlsx for download.

Figure 4

Phenotypic features selected by topics, across 20 topics. The most common phenotypic variables nominated across topics were IQ-related, describing either the IQ scores on a given test or the IQ test given.

Figure 5

Total feature modality selected within topic. Cortical features were more likely to be present in the topics than others, due to them having a greater representation in the original dataset.

Figure 6

Relative feature modality selected within topic, relative to the total number of features within that modality. After correcting for features which were over-represented in the dataset, we see that phenotypic observations, motion parameters, ICs, and subcortical were selected heavily within topics.

Figure 7

Decision tree for discriminating between ADHD patients and healthy controls. The primary tree split (Topic 15) contained a marker for the Site Pittsburg, which contained only healthy controls. The second split, Topic 1, contained IQ phenotypic variables. The third split, Topic 10, contained many motion parameters.