RESUMEN
Graph signal processing (GSP) is an important methodology for studying data residing on irregular structures. As acquired data is increasingly taking the form of multi-way tensors, new signal processing tools are needed to maximally utilize the multi-way structure within the data. In this paper, we review modern signal processing frameworks generalizing GSP to multi-way data, starting from graph signals coupled to familiar regular axes such as time in sensor networks, and then extending to general graphs across all tensor modes. This widely applicable paradigm motivates reformulating and improving upon classical problems and approaches to creatively address the challenges in tensor-based data. We synthesize common themes arising from current efforts to combine GSP with tensor analysis and highlight future directions in extending GSP to the multi-way paradigm.
RESUMEN
Current methods for comparing single-cell RNA sequencing datasets collected in multiple conditions focus on discrete regions of the transcriptional state space, such as clusters of cells. Here we quantify the effects of perturbations at the single-cell level using a continuous measure of the effect of a perturbation across the transcriptomic space. We describe this space as a manifold and develop a relative likelihood estimate of observing each cell in each of the experimental conditions using graph signal processing. This likelihood estimate can be used to identify cell populations specifically affected by a perturbation. We also develop vertex frequency clustering to extract populations of affected cells at the level of granularity that matches the perturbation response. The accuracy of our algorithm at identifying clusters of cells that are enriched or depleted in each condition is, on average, 57% higher than the next-best-performing algorithm tested. Gene signatures derived from these clusters are more accurate than those of six alternative algorithms in ground truth comparisons.
Asunto(s)
Biología Computacional , Análisis de Secuencia de ARN/tendencias , Análisis de la Célula Individual/tendencias , Transcriptoma/genética , Algoritmos , Análisis por Conglomerados , Simulación por Computador , Humanos , Funciones de VerosimilitudRESUMEN
We propose a novel framework for combining datasets via alignment of their intrinsic geometry. This alignment can be used to fuse data originating from disparate modalities, or to correct batch effects while preserving intrinsic data structure. Importantly, we do not assume any pointwise correspondence between datasets, but instead rely on correspondence between a (possibly unknown) subset of data features. We leverage this assumption to construct an isometric alignment between the data. This alignment is obtained by relating the expansion of data features in harmonics derived from diffusion operators defined over each dataset. These expansions encode each feature as a function of the data geometry. We use this to relate the diffusion coordinates of each dataset through our assumption of partial feature correspondence. Then, a unified diffusion geometry is constructed over the aligned data, which can also be used to correct the original data measurements. We demonstrate our method on several datasets, showing in particular its effectiveness in biological applications including fusion of single-cell RNA sequencing (scRNA-seq) and single-cell ATAC sequencing (scATAC-seq) data measured on the same population of cells, and removal of batch effect between biological samples.
RESUMEN
While neural networks are powerful approximators used to classify or embed data into lower dimensional spaces, they are often regarded as black boxes with uninterpretable features. Here we propose Graph Spectral Regularization for making hidden layers more interpretable without significantly impacting performance on the primary task. Taking inspiration from spatial organization and localization of neuron activations in biological networks, we use a graph Laplacian penalty to structure the activations within a layer. This penalty encourages activations to be smooth either on a predetermined graph or on a feature-space graph learned from the data via co-activations of a hidden layer of the neural network. We show numerous uses for this additional structure including cluster indication and visualization in biological and image data sets.