MODEC: an unsupervised clustering method integrating omics data for identifying cancer subtypes.

The identification of cancer subtypes can help researchers understand hidden genomic mechanisms, enhance diagnostic accuracy and improve clinical treatments. With the development of high-throughput techniques, researchers can access large amounts of data from multiple sources. Because of the high dimensionality and complexity of multiomics and clinical data, research into the integration of multiomics data is needed, and developing effective tools for such purposes remains a challenge for researchers. In this work, we proposed an entirely unsupervised clustering method without harnessing any prior knowledge (MODEC). We used manifold optimization and deep-learning techniques to integrate multiomics data for the identification of cancer subtypes and the analysis of significant clinical variables. Since there is nonlinearity in the gene-level datasets, we used manifold optimization methodology to extract essential information from the original omics data to obtain a low-dimensional latent subspace. Then, MODEC uses a deep learning-based clustering module to iteratively define cluster centroids and assign cluster labels to each sample by minimizing the Kullback-Leibler divergence loss. MODEC was applied to six public cancer datasets from The Cancer Genome Atlas database and outperformed eight competing methods in terms of the accuracy and reliability of the subtyping results. MODEC was extremely competitive in the identification of survival patterns and significant clinical features, which could help doctors monitor disease progression and provide more suitable treatment strategies.

MOKPE: drug-target interaction prediction via manifold optimization based kernel preserving embedding.

BACKGROUND: In many applications of bioinformatics, data stem from distinct heterogeneous sources. One of the well-known examples is the identification of drug-target interactions (DTIs), which is of significant importance in drug discovery. In this paper, we propose a novel framework, manifold optimization based kernel preserving embedding (MOKPE), to efficiently solve the problem of modeling heterogeneous data. Our model projects heterogeneous drug and target data into a unified embedding space by preserving drug-target interactions and drug-drug, target-target similarities simultaneously. RESULTS: We performed ten replications of ten-fold cross validation on four different drug-target interaction network data sets for predicting DTIs for previously unseen drugs. The classification evaluation metrics showed better or comparable performance compared to previous similarity-based state-of-the-art methods. We also evaluated MOKPE on predicting unknown DTIs of a given network. Our implementation of the proposed algorithm in R together with the scripts that replicate the reported experiments is publicly available at https://github.com/ocbinatli/mokpe .

A Riemannian approach to predicting brain function from the structural connectome.

Ongoing brain function is largely determined by the underlying wiring of the brain, but the specific rules governing this relationship remain unknown. Emerging literature has suggested that functional interactions between brain regions emerge from the structural connections through mono- as well as polysynaptic mechanisms. Here, we propose a novel approach based on diffusion maps and Riemannian optimization to emulate this dynamic mechanism in the form of random walks on the structural connectome and predict functional interactions as a weighted combination of these random walks. Our proposed approach was evaluated in two different cohorts of healthy adults (Human Connectome Project, HCP; Microstructure-Informed Connectomics, MICs). Our approach outperformed existing approaches and showed that performance plateaus approximately around the third random walk. At macroscale, we found that the largest number of walks was required in nodes of the default mode and frontoparietal networks, underscoring an increasing relevance of polysynaptic communication mechanisms in transmodal cortical networks compared to primary and unimodal systems.

Deep Kernel Principal Component Analysis for multi-level feature learning.

Principal Component Analysis (PCA) and its nonlinear extension Kernel PCA (KPCA) are widely used across science and industry for data analysis and dimensionality reduction. Modern deep learning tools have achieved great empirical success, but a framework for deep principal component analysis is still lacking. Here we develop a deep kernel PCA methodology (DKPCA) to extract multiple levels of the most informative components of the data. Our scheme can effectively identify new hierarchical variables, called deep principal components, capturing the main characteristics of high-dimensional data through a simple and interpretable numerical optimization. We couple the principal components of multiple KPCA levels, theoretically showing that DKPCA creates both forward and backward dependency across levels, which has not been explored in kernel methods and yet is crucial to extract more informative features. Various experimental evaluations on multiple data types show that DKPCA finds more efficient and disentangled representations with higher explained variance in fewer principal components, compared to the shallow KPCA. We demonstrate that our method allows for effective hierarchical data exploration, with the ability to separate the key generative factors of the input data both for large datasets and when few training samples are available. Overall, DKPCA can facilitate the extraction of useful patterns from high-dimensional data by learning more informative features organized in different levels, giving diversified aspects to explore the variation factors in the data, while maintaining a simple mathematical formulation.

Characterizing the propagation pathway of neuropathological events of Alzheimer's disease using harmonic wavelet analysis.

Empirical imaging biomarkers such as the level of the regional pathological burden are widely used to measure the risk of developing neurodegenerative diseases such as Alzheimer's disease (AD). However, ample evidence shows that the brain network (wirings of white matter fibers) plays a vital role in the progression of AD, where neuropathological burdens often propagate across the brain network in a prion-like manner. In this context, characterizing the spreading pathway of AD-related neuropathological events sheds new light on understanding the heterogeneity of pathophysiological mechanisms in AD. In this work, we propose a manifold-based harmonic network analysis approach to explore a novel imaging biomarker in the form of the AD propagation pattern, which eventually allows us to identify the AD-related spreading pathways of neuropathological events throughout the brain. The backbone of this new imaging biomarker is a set of region-adaptive harmonic wavelets that represent the common network topology across individuals. We conceptualize that the individual's brain network and its associated pathology pattern form a unique system, which vibrates as do all natural objects in the universe. Thus, we can computationally excite such a brain system using selected harmonic wavelets that match the system's resonance frequency, where the resulting oscillatory wave manifests the system-level propagation pattern of neuropathological events across the brain network. We evaluate the statistical power of our harmonic network analysis approach on large-scale neuroimaging data from ADNI. Compared with the other empirical biomarkers, our harmonic wavelets not only yield a new imaging biomarker to potentially predict the cognitive decline in the early stage but also offer a new window to capture the in-vivo spreading pathways of neuropathological burden with a rigorous mathematics insight.

Multiway p-spectral graph cuts on Grassmann manifolds.

Nonlinear reformulations of the spectral clustering method have gained a lot of recent attention due to their increased numerical benefits and their solid mathematical background. We present a novel direct multiway spectral clustering algorithm in the p-norm, for p ∈ ( 1 , 2 ] . The problem of computing multiple eigenvectors of the graph p-Laplacian, a nonlinear generalization of the standard graph Laplacian, is recasted as an unconstrained minimization problem on a Grassmann manifold. The value of p is reduced in a pseudocontinuous manner, promoting sparser solution vectors that correspond to optimal graph cuts as p approaches one. Monitoring the monotonic decrease of the balanced graph cuts guarantees that we obtain the best available solution from the p-levels considered. We demonstrate the effectiveness and accuracy of our algorithm in various artificial test-cases. Our numerical examples and comparative results with various state-of-the-art clustering methods indicate that the proposed method obtains high quality clusters both in terms of balanced graph cut metrics and in terms of the accuracy of the labelling assignment. Furthermore, we conduct studies for the classification of facial images and handwritten characters to demonstrate the applicability in real-world datasets.

Structure in Neural Activity during Observed and Executed Movements Is Shared at the Neural Population Level, Not in Single Neurons.

In multiple cortical areas, including the motor cortex, neurons have similar firing rate statistics whether we observe or execute movements. These "congruent" neurons are hypothesized to support action understanding by participating in a neural circuit consistently activated in both observed and executed movements. We examined this hypothesis by analyzing neural population structure and dynamics between observed and executed movements. We find that observed and executed movements exhibit similar neural population covariation in a shared subspace capturing significant neural variance. Further, neural dynamics are more similar between observed and executed movements within the shared subspace than outside it. Finally, we find that this shared subspace has a heterogeneous composition of congruent and incongruent neurons. Together, these results argue that similar neural covariation and dynamics between observed and executed movements do not occur via activation of a subpopulation of congruent single neurons, but through consistent temporal activation of a heterogeneous neural population.

Manifold optimization-based analysis dictionary learning with an ℓ1∕2-norm regularizer.

Recently there has been increasing attention towards analysis dictionary learning. In analysis dictionary learning, it is an open problem to obtain the strong sparsity-promoting solutions efficiently while simultaneously avoiding the trivial solutions of the dictionary. In this paper, to obtain the strong sparsity-promoting solutions, we employ the ℓ1∕2 norm as a regularizer. The very recent study on ℓ1∕2 norm regularization theory in compressive sensing shows that its solutions can give sparser results than using the ℓ1 norm. We transform a complex nonconvex optimization into a number of one-dimensional minimization problems. Then the closed-form solutions can be obtained efficiently. To avoid trivial solutions, we apply manifold optimization to update the dictionary directly on the manifold satisfying the orthonormality constraint, so that the dictionary can avoid the trivial solutions well while simultaneously capturing the intrinsic properties of the dictionary. The experiments with synthetic and real-world data verify that the proposed algorithm for analysis dictionary learning can not only obtain strong sparsity-promoting solutions efficiently, but also learn more accurate dictionary in terms of dictionary recovery and image processing than the state-of-the-art algorithms.