tests/testthat/test_normlaplacian.R

In jlmelville/uwot: The Uniform Manifold Approximation and Projection (UMAP) Method for Dimensionality Reduction

library(uwot)
context("normalized laplacian")

# this exists as a separate file only because it's easier to comment out as
# part of temporarily removing any function calls to rspectra when using rhub
# with sanitizers and valgrind (probably the extended compilation time with
# eigen causes a preperror)

test_that("normalized laplacian", {
  # These numbers come from running UMAP Python code:
  # spectral_layout(pairwise_distances(iris.data[0:10, :]))
  # NB:
  # 1. iris data in scikit-learn is currently from UCI repo, which has errors
  #   (although this doesn't affect the first ten entries)
  # 2. eigenvector calculation is not that converged and specifies a starting
  #   vector that we can't supply with either RSpectra or eigen.
  # 3. The eigenvectors are only identical up to a sign, so we take the absolute
  #   values.
  abs_expected_norm_lap <-
    abs(
    c2y(
      0.7477, -0.1292, -0.03001, 0.02127, -0.563, -0.01149, 0.1402,
      -0.2725, -0.01241, 0.1084, -0.106, -0.5723, 0.2024, -0.3082,
      0.1642, -5.549e-05, -0.04843, -0.1747, 0.1684, 0.6611
    )
    )

  sparse_m <- Matrix::drop0(x2d(iris[1:10, ]))
  res <- normalized_laplacian_init(sparse_m)
  expect_equal(abs(res), abs_expected_norm_lap, tolerance = 0.2)

  # ensure irlba code path gets tested
  res <- irlba_tsvd_normalized_laplacian_init(sparse_m)
  expect_equal(abs(res), abs_expected_norm_lap, tolerance = 0.2)

  res <- irlba_normalized_laplacian_init(sparse_m)
  expect_equal(abs(res), abs_expected_norm_lap, tolerance = 0.2)
})

test_that("laplacian eigenmap", {
  # tested via sklearn
  # things to note:
  # 1. output eigenvectors are not scaled to 1, due to the D^-1/2 transformation
  #    from Lsym's eigenvectors back to Lrw
  # 2. Lsym is formed by calling 
  #    scipy.sparse.csgraph.laplacian(normed=True) on the affinity matrix,
  #    which assumes the diagonal is zero.
  #    
  #    symmetrized normalized graph laplacian 
  # from sklearn.preprocessing import normalize
  # from sklearn.datasets import load_digits
  # from sklearn.manifold import SpectralEmbedding
  # X, _ = load_digits(return_X_y=True)
  # embedding = SpectralEmbedding(n_components=3, n_neighbors=4, affinity="rbf", gamma = 1e-3)
  # X_transformed = embedding.fit_transform(X[:10])
  # normalize(X_transformed, axis = 0)
  expected_lap_eig <- matrix(
      c(0.21050269, -0.07732118,  0.63486516,
        -0.33501476,  0.11755963, -0.40229306,
        -0.36728785,  0.38404235,  0.020391  ,
         0.20458482, -0.04123934, -0.44198941,
        -0.3841261 , -0.47833969,  0.17196966,
         0.3883986 , -0.03743132, -0.22790212,
        -0.36483447, -0.32492041,  0.01860336,
        -0.27419176,  0.68954246,  0.34392682,
         0.04537549,  0.14056785,  0.12175907,
         0.39742651, -0.00077821,  0.15609656),
    ncol = 3, byrow = TRUE)
  

  A <- matrix(
  c(0, 0.0288109, 0.053397, 0.104038, 0.079341, 0.145439, 0.0946093,
    0.0434563, 0.139317, 0.189191, 0.0288109, 0, 0.176753, 0.126438,
    0.100761, 0.108501, 0.197306, 0.0744967, 0.0940433, 0.0614212,
    0.053397, 0.176753, 0, 0.0544213, 0.0662712, 0.0462358, 0.124431,
    0.0876854, 0.162838, 0.0494398, 0.104038, 0.126438, 0.0544213, 0,
    0.0725848, 0.322066, 0.107206, 0.0395971, 0.164969, 0.130029, 0.079341,
    0.100761, 0.0662712, 0.0725848, 0, 0.0532904, 0.255125, 0.0290714,
    0.0634819, 0.0482673, 0.145439, 0.108501, 0.0462358, 0.322066,
    0.0532904, 0, 0.0748701, 0.0202419, 0.187683, 0.380222, 0.0946093,
    0.197306, 0.124431, 0.107206, 0.255125, 0.0748701, 0, 0.0273237,
    0.142702, 0.0647643, 0.0434563, 0.0744967, 0.0876854, 0.0395971,
    0.0290714, 0.0202419, 0.0273237, 0, 0.0584841, 0.0431531, 0.139317,
    0.0940433, 0.162838, 0.164969, 0.0634819, 0.187683, 0.142702,
    0.0584841, 0, 0.158817, 0.189191, 0.0614212, 0.0494398, 0.130029,
    0.0482673, 0.380222, 0.0647643, 0.0431531, 0.158817, 0),
  nrow = 10)
  res <- laplacian_eigenmap(A, ndim = 3)
  expect_equal(abs(res), abs(expected_lap_eig), tolerance = 1e-4)
  
  expect_equal(abs(irlba_laplacian_eigenmap(A, ndim = 3)), abs(expected_lap_eig), tolerance = 1e-4)
})