ltsa: Local Tangent Space Alignment

In jlmelville/flotsam: Finicky LOcal Tangent Space Alignment Method

Local Tangent Space Alignment

Description

Apply the Local Tangent Space Alignment (LTSA) method (Zhang and Zha, 2004) for dimensionality reduction.

Usage

ltsa(
  X,
  n_neighbors = 15,
  ndim = 2,
  nn_method = "nnd",
  eig_method = "rspectra",
  include_self = TRUE,
  normalize = FALSE,
  ret_B = FALSE,
  n_threads = 0,
  verbose = FALSE,
  ...
)

Arguments

X	The input data matrix or dataframe with one observation per row.
n_neighbors	The size of local neighborhood (in terms of number of neighboring sample points) used for manifold approximation.
ndim	The dimension of the space to embed into.
nn_method	Method for finding nearest neighbors. Can be one of: "nnd" Approximate nearest neighbors by Nearest Neighbor Descent. "exact" Exact nearest neighbors by exhaustively comparing all items. Slow for large datasets.
eig_method	How to carry out the eigendecomposition. Possible values are: "rspectra" Use RSpectra::eigs_sym(). "irlba" Use irlba::irlba(). ⁠"svdr⁠ Use irlba::svdr(). "fullsvd" Use the base::svd() function. This is only feasible for small datasets and should be used for diagnostic purposes only. "eigen" Use the base::eigen() function. This is only feasible for small datasets and should be used for diagnostic purposes only.
include_self	Should an item be part of its own neighborhood? This has a minor effect on most results, but work by Zhang and co-workers (2017) suggests that this is in effect the main difference between LTSA and the Hessian Locally Linear Embedding (HLLE) method, so setting this to FALSE may allow emulating the HLLE method.
normalize	If TRUE calculate the eigendecomposition on a normalized version of the Laplacian. This may be slightly easier to converge while giving similar results to the un-normalized case. It may also have suitable better properties if clustering is to be carried out on the eigenvectors.
ret_B	If TRUE, return the matrix instead of the eigenvectors. This is mainly useful for diagnostic purposes if eigendecomposition is failing.
n_threads	Number of threads to use. Applies only to the nearest neighbor calculation.
verbose	If TRUE log information about progress to the console.
...	Extra arguments to be passed to the eigendecomposition method specified by eig_method. For "rspectra", arguments are passed to the opts list. Suitable parameters include: ncv Number of Lanzcos vectors to use. tol Tolerance. maxitr Maximum number of iterations. For "irlba" suitable arguments are: work Working subspace dimension size. tol Tolerance. maxit Maximum number of iterations. For "svdr" suitable arguments are: extra Number of extra vectors to use. tol Tolerance. it Maximum number of iterations. For more details see the documentation for RSpectra::eigs_sym(), irlba::irlba() and irlba::svdr() functions, respectively. Don't pass other arguments unless you know what you are doing, as it may cause the ltsa to fail.

References

Zhang, Z., & Zha, H. (2004). Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. SIAM journal on scientific computing, 26(1), 313-338. https://doi.org/10.1137/S1064827502419154

Zhang, S., Ma, Z., & Tan, H. (2017). On the Equivalence of HLLE and LTSA. IEEE transactions on cybernetics, 48(2), 742-753. https://doi.org/10.1109/TCYB.2017.2655338

Examples

n <- 1000
max_z <- 10

phi <- stats::runif(n, min = 1.5 * pi, max = 4.5 * pi)
x <- phi * cos(phi)
y <- phi * sin(phi)
z <- stats::runif(n, max = max_z)
swiss_roll <- data.frame(x, y, z)

# unroll it
swiss_ltsa <- ltsa(swiss_roll)
plot(swiss_ltsa, col = phi)

# compare with PCA
swiss_pca <- stats::prcomp(swiss_roll, rank. = 2, scale = FALSE, retx = TRUE)$x
plot(swiss_pca, col = phi)

jlmelville/flotsam documentation built on April 17, 2025, 9:30 p.m.