降维是将数据从高维空间转换为低维空间,以便低维表示保留原始数据的某些有意义的属性,理想情况下接近其固有维。降维在处理大量观察和/或大量变量的领域很常见,例如信号处理,语音识别,神经信息学和生物信息学。

最新论文

Non-linear dimensionality reduction can be performed by \textit{manifold learning} approaches, such as Stochastic Neighbour Embedding (SNE), Locally Linear Embedding (LLE) and Isometric Feature Mapping (ISOMAP). These methods aim to produce two or three latent embeddings, primarily to visualise the data in intelligible representations. This manuscript proposes extensions of Student's t-distributed SNE (t-SNE), LLE and ISOMAP, for dimensionality reduction and visualisation of multi-view data. Multi-view data refers to multiple types of data generated from the same samples. The proposed multi-view approaches provide more comprehensible projections of the samples compared to the ones obtained by visualising each data-view separately. Commonly visualisation is used for identifying underlying patterns within the samples. By incorporating the obtained low-dimensional embeddings from the multi-view manifold approaches into the K-means clustering algorithm, it is shown that clusters of the samples are accurately identified. Through the analysis of real and synthetic data the proposed multi-SNE approach is found to have the best performance. We further illustrate the applicability of the multi-SNE approach for the analysis of multi-omics single-cell data, where the aim is to visualise and identify cell heterogeneity and cell types in biological tissues relevant to health and disease.

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