Multimodal Diffusion Maps for Single-Cell Data Visualization
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Solution Overview
Problem
Current methods for visualizing developmental landscapes from single-cell multimodal data face challenges such as noise in single-cell data, limited execution speed for high-throughput data, the need for extensive data for deep learning models, lack of interpretability, unequal treatment of single-cell modalities, and incompatibility with various data formats.
Innovation Solution
The Multimodal Diffusion Maps (MDM) method preprocesses data using Latent Dirichlet Allocation, models each modality as a diffusion process with an adaptive Gaussian kernel, calculates cell-specific multimodal weights, and eigendecomposes the multimodal Markov chain matrix to produce a low-dimensional representation, allowing for interpretable and efficient visualization of developmental processes across multiple modalities.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If deep learning models (autoencoders) are used for multimodal embedding, then high-quality low-dimensional representations are generated, but the models lack explainability and require extensive data
Solution Approach 1:
The patent replaces deep learning models (autoencoders) with a diffusion-based mathematical framework. Instead of using neural networks with black-box parameters, the invention uses diffusion maps that model data generation as a stochastic process, enabling explicit computation of cell probabilities and interpretability while maintaining high-dimensional to low-dimensional transformation capabilities
Solution Approach 2:
The invention changes the fundamental parameters of the modeling approach by using diffusion coefficients and transition probabilities instead of neural network weights. This allows for explicit calculation of cell probabilities and interpretability while maintaining the ability to generate high-quality low-dimensional representations through the diffusion process
2Loss of information
If diffusion-based methods are used to model data as Markov chains, then interpretability is improved, but execution speed is reduced for high-throughput data
Solution Approach 1:
The patent performs preliminary computations by pre-calculating diffusion maps for each modality separately before integrating them. This preliminary processing of individual modalities enables more efficient subsequent integration and reduces the computational burden for high-throughput data analysis while maintaining interpretability
Solution Approach 2:
The invention segments the complex multimodal diffusion process into separate unimodal diffusion maps for each modality. By computing and storing these individual diffusion maps beforehand, the system can efficiently integrate multiple modalities without reprocessing all data from scratch, thereby improving execution speed for high-throughput scenarios
3Adaptability or versatility
If existing multimodal algorithms are used, then integration of multiple modalities is achieved, but the significance of each modality is not identified
Solution Approach 1:
The patent applies local quality by computing cell-specific weights that determine the importance of each modality for each individual cell. Instead of treating all modalities equally or using global weights, the method calculates localized weights for each cell-modality pair, enabling the system to identify which modalities are most significant for each specific cell's developmental state
Data Source
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Figure 3~3b
AI summary
The invention is related to a method of visualization of developmental landscapes from single-cell multimodal data, comprising the following steps: a) Providing input data for two or more modalities, relating to cells being subject to investigations, each modality characterized by a set of investigated features, the data for each modality being in a form of a matrix presenting quantitative intensity of each of the investigated features in each of the cells being subject to investigations; b) Pre-processing said input data acquired in step a) for each of said two or more modalities so as to reduce the noise level of said input data; c1) Processing the pre-processed input data obtained in step b) by modelling separately each of said two or more modalities as a diffusion process with an adaptive Gaussian kernel, so as to obtain an unimodal Markov chain matrix for each of said two or more modalities; c2) Calculating multimodal weights for each of the cells being subject to investigations and for each of said two or more modalities; d) Calculating a multimodal Markov chain matrix, wherein consecutive values in each particular row of values in the multimodal Markov chain matrix, corresponding to a particular cell being subject to investigations, are calculated by adding corresponding values from the corresponding row of each of the unimodal Markov chain matrix obtained for each of said two or more modalities in step c1) weighted with the corresponding multimodal weights obtained for said cell and the modality in question in step c2); e) Eigendecomposing the multimodal Markov chain matrix obtained in step d) so as to obtain a diffusion-based dimensionally reduced Multimodal Diffusion Maps (MDM) representation of the two or more modalities; f) Visualizing a developmental landscape based on the joint Multimodal Diffusion Maps (MDM) representation obtained in step e), reduced to two dimensions or three dimensions with inclusion of cell fate probabilities.