Inferring a Transcriptional Regulatory Network from Gene Expression Data Using Nonlinear Manifold Embedding

Transcriptional networks consist of multiple regulatory layers corresponding to the activity of global regulators, specialized repressors and activators of transcription as well as proteins and enzymes shaping the DNA template. Such intrinsic multi-dimensionality makes uncovering connectivity patterns difficult and unreliable and it calls for adoption of methodologies commensurate with the underlying organization of the data source. Here we present a new computational method that predicts interactions between transcription factors and target genes using a compendium of microarray gene expression data and the knowledge of known interactions between genes and transcription factors. The proposed method called Kernel Embedding of REgulatory Networks (KEREN) is based on the concept of gene-regulon association and it captures hidden geometric patterns of the network via manifold embedding. We applied KEREN to reconstruct gene regulatory interactions in the model bacteria E.coli on a genome-wide scale. Our method not only yields accurate prediction of verifiable interactions, which outperforms on certain metrics comparable methodologies, but also demonstrates the utility of a geometric approach to the analysis of high-dimensional biological data. We also describe the general application of kernel embedding techniques to some other function and network discovery algorithms

Rotationally Invariant Image Representation for Viewing Direction Classification in Cryo-EM

We introduce a new rotationally invariant viewing angle classification method for identifying, among a large number of Cryo-EM projection images, similar views without prior knowledge of the molecule. Our rotationally invariant features are based on the bispectrum. Each image is denoised and compressed using steerable principal component analysis (PCA) such that rotating an image is equivalent to phase shifting the expansion coefficients. Thus we are able to extend the theory of bispectrum of 1D periodic signals to 2D images. The randomized PCA algorithm is then used to efficiently reduce the dimensionality of the bispectrum coefficients, enabling fast computation of the similarity between any pair of images. The nearest neighbors provide an initial classification of similar viewing angles. In this way, rotational alignment is only performed for images with their nearest neighbors. The initial nearest neighbor classification and alignment are further improved by a new classification method called vector diffusion maps. Our pipeline for viewing angle classification and alignment is experimentally shown to be faster and more accurate than reference-free alignment with rotationally invariant K-means clustering, MSA/MRA 2D classification, and their modern approximations

Intrinsic Dimension Estimation: Relevant Techniques and a Benchmark Framework

When dealing with datasets comprising high-dimensional points, it is usually advantageous to discover some data structure. A fundamental information needed to this aim is the minimum number of parameters required to describe the data while minimizing the information loss. This number, usually called intrinsic dimension, can be interpreted as the dimension of the manifold from which the input data are supposed to be drawn. Due to its usefulness in many theoretical and practical problems, in the last decades the concept of intrinsic dimension has gained considerable attention in the scientific community, motivating the large number of intrinsic dimensionality estimators proposed in the literature. However, the problem is still open since most techniques cannot efficiently deal with datasets drawn from manifolds of high intrinsic dimension and nonlinearly embedded in higher dimensional spaces. This paper surveys some of the most interesting, widespread used, and advanced state-of-the-art methodologies. Unfortunately, since no benchmark database exists in this research field, an objective comparison among different techniques is not possible. Consequently, we suggest a benchmark framework and apply it to comparatively evaluate relevant state-of-the-art estimators

The intrinsic dimension of biological data landscapes

Analyzing large volumes of high-dimensional data is an issue of fundamental importance in science and beyond. Several approaches work on the assumption that the important content of a dataset belongs to a manifold whose Intrinsic Dimension (ID) is much lower than the crude large number of coordinates. That manifold however is generally twisted and curved; in addition points on it will be non-uniformly distributed: two factors that make the identification of the ID and its exploitation really hard. Here we propose a new ID estimator using only the distance of the first and the second nearest neighbor of each point in the sample. This extreme minimality enables us to reduce the effects of curvature, of density variation, and the resulting computational cost. The ID estimator is theoretically exact in uniformly distributed data sets, and provides consistent measures in general. When used in combination with block analysis, it allows discriminating the relevant dimensions as a function of the block size. This allows estimating the ID even when the data lie on a manifold perturbed by a high-dimensional noise, a situation often encountered in real world data sets. Upon defining a notion of distance between protein sequences, This tools is used to estimate the ID of protein families, and to assess the consistency of generative models. Moreover, If coupled with a density estimator, our ID allows to measure the density of points by taking into account the space in which they actually lie, thus allowing for a cleaner estimation. Here we move a step further towards an automatic classification of protein sequences by using three new tools: our ID estimator, a density estimator and a clustering algorithm. We present the analysis performed on a Pfam PUA clan, showing that these combined tools allow to successfully separate protein domains into architectures. Finally, we present a generalized model for the estimation of the ID that is able to work in data sets with multiple dimensionalities: taking advantage of Bayesian inference techniques, the method allows discriminating manifolds with different dimensions as well as assigning all the points to the respective manifolds. We test the method on a molecular dynamics trajectory, showing that the folded state has a higher dimension with respect to the unfolded one

Construction of embedded fMRI resting state functional connectivity networks using manifold learning

We construct embedded functional connectivity networks (FCN) from benchmark resting-state functional magnetic resonance imaging (rsfMRI) data acquired from patients with schizophrenia and healthy controls based on linear and nonlinear manifold learning algorithms, namely, Multidimensional Scaling (MDS), Isometric Feature Mapping (ISOMAP) and Diffusion Maps. Furthermore, based on key global graph-theoretical properties of the embedded FCN, we compare their classification potential using machine learning techniques. We also assess the performance of two metrics that are widely used for the construction of FCN from fMRI, namely the Euclidean distance and the lagged cross-correlation metric. We show that the FCN constructed with Diffusion Maps and the lagged cross-correlation metric outperform the other combinations

An overview of clustering methods with guidelines for application in mental health research

Cluster analyzes have been widely used in mental health research to decompose inter-individual heterogeneity by identifying more homogeneous subgroups of individuals. However, despite advances in new algorithms and increasing popularity, there is little guidance on model choice, analytical framework and reporting requirements. In this paper, we aimed to address this gap by introducing the philosophy, design, advantages/disadvantages and implementation of major algorithms that are particularly relevant in mental health research. Extensions of basic models, such as kernel methods, deep learning, semi-supervised clustering, and clustering ensembles are subsequently introduced. How to choose algorithms to address common issues as well as methods for pre-clustering data processing, clustering evaluation and validation are then discussed. Importantly, we also provide general guidance on clustering workflow and reporting requirements. To facilitate the implementation of different algorithms, we provide information on R functions and librarie