Re: Lmds
Bok Mull
Multi-dimensional scaling (MDS) (Kruskal 1964) is a dimensionality reductionmethod used for visualising and denoising high-dimensional data. However, since MDS requirescalculating the distances between all pairs of data points, it does not scale well to datasetswith a large number of samples.
We released lmds v0.1.0, an implementation ofLandmark MDS (LMDS) (de Silva and Tenenbaum 2004). Landmark MDS only calculates the distances between a set of landmarksand all other data points, thereby sacrificing determinism for scalability.
A single-cell transcriptomics dataset (Treutlein et al. 2016) is used to demonstrate (L)MDS,containing 392 profiles which measure the abundance levels of 2000 different molecules within individual cells.Note that while the dataset is thus only a 3922000 matrix, LMDS is designed to scale to much higher dimensionality, as demonstrated in the last section.
Landmark MDS (LMDS) (de Silva and Tenenbaum 2004) is an extension of MDS which scales muchbetter with respect to the number of data points in the dataset. A short while ago,we published an R package on CRAN implementing this algorithm,lmds v0.1.0.
Landmark MDS only computes the distance matrix between a set of landmarks and all other data points.MDS is then only performed on the landmarks, and all other datapoints are projected intothe landmark space.
LMDS is a heuristic for MDS which scales linearly with respect to the number of pointsin the dataset. Go ahead and check out our implementation for this algorithm,available on CRAN.If you encounter any issues, feel free to let me know by creating anissue post on Github.