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.

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 .

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.

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.

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 ℓ_1∕2 norm as a regularizer. The very recent study on ℓ_1∕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.