From 1b7b8bc30ac7326869258483322ce7449205a033 Mon Sep 17 00:00:00 2001 From: tlacombe Date: Fri, 15 Oct 2021 11:59:30 +0200 Subject: [PATCH 01/16] online quantization algorithm for gudhi --- biblio/bibliography.bib | 7 + src/python/CMakeLists.txt | 5 + src/python/doc/img/quantiz.gif | Bin 0 -> 5280066 bytes src/python/doc/wasserstein_distance_user.rst | 66 +++++- src/python/gudhi/wasserstein/quantization.py | 208 +++++++++++++++++++ src/python/test/test_quantization.py | 152 ++++++++++++++ 6 files changed, 436 insertions(+), 2 deletions(-) create mode 100644 src/python/doc/img/quantiz.gif create mode 100644 src/python/gudhi/wasserstein/quantization.py create mode 100644 src/python/test/test_quantization.py diff --git a/biblio/bibliography.bib b/biblio/bibliography.bib index eed871be5d..f0a8f1b1a9 100644 --- a/biblio/bibliography.bib +++ b/biblio/bibliography.bib @@ -78,6 +78,13 @@ @article{boissonnatmariasimplextreealgorithmica language={English} } +@article{divolLacombe2021quantization, + title={Estimation and Quantization of Expected Persistence Diagrams}, + author={Divol, Vincent and Lacombe, Th{\'e}o}, + journal={ICML 2021}, + year={2021} +} + @inproceedings{Garland, author = {Garland, Michael and Heckbert, Paul S.}, title = {Surface simplification using quadric error metrics}, diff --git a/src/python/CMakeLists.txt b/src/python/CMakeLists.txt index 96107cfede..7b943b4440 100644 --- a/src/python/CMakeLists.txt +++ b/src/python/CMakeLists.txt @@ -526,6 +526,11 @@ if(PYTHONINTERP_FOUND) endif() endif() + # Quantization + if(SCIPY_FOUND) + add_gudhi_py_test(test_quantization) + endif() + # Representations if(SKLEARN_FOUND AND MATPLOTLIB_FOUND AND OT_FOUND AND NOT CGAL_VERSION VERSION_LESS 4.11.0) add_gudhi_py_test(test_representations) diff --git a/src/python/doc/img/quantiz.gif b/src/python/doc/img/quantiz.gif new file mode 100644 index 0000000000000000000000000000000000000000..e27655362c366f6a5046460886b0952255f6f958 GIT binary patch literal 5280066 zcmWifXH=6-(}3^vP?Jytgpg1pHS|zTp#&*{qJp&06cG^=6%lyT2%#Df6$=`Qii%1T zv4;QxiV9XlM5=U1rHa3oqj-H;LrY1%{K0bkgf#KodQBhGLA)(31$*HNSSy@>*IXUrhTMhK~ zD$apc&Lia)uwO6WeqOa*ISVXy1ix>K`7@BQD&1mXR-2r3O%MBa4QbSk^2XV5NJ;s# z9`+Li@?Aw`83OsEqPl`W$}#G{)G@!bG?#F=WlgOW9Bvh>`wNBoOf-}e@e6q3FGJ!d zQ_}@&tIumlAM9;EIXW(QdM>z8W=%|%t*w_#OjoU~S4pJb_O`!l?SDHuE_r$`IXbR- zc&xfo{@B`oBH+j9-mmE1A8FnSn)i}7ZO)ta+ne^<-)}TBVk9i|aeVBHSk}uOJ07K^ zyg7JqbWg@}AI3~z;Ea#YLSWzm(|>+L$XvvhIUk?pz`$i6#%h4ys$alrV4#BOzZ4d{ z8Wy}95~c_VTiUpBIXZfI<3>evv|`JaKOtdr@iBApvA<&D=VIf3B_&Sp+&Pn!_<85f zg_P~{dv?tq*gv0?xSY0gDJe;jx=pcdhazpKB4zthX1XFXeJMRtu`6?V@80D@IZJ!@ zDh}>f?9Wl;98zRwFQ;dIqIzED_qkJva(mTHKS*0 zM;gw(ZD}173g=FrnmK)H;n=Z{e7>TzL?IN)E6Np>W#7vy6sJ!uRUJ{BJf=8y^6#lr zilaxD50}r^o>A1+EY;S0I8&=QQ@d1C`|;w%&#hPIueQv!w$8M+e(vm?Ki9C_bY;1r zUUBi z5dW%#_=ay}&_aD3Y{?MNzb@;44fuaE0gwvdrxK3YEbihVH7%q2n`^rZ(I)FoGh6C< zOR$cqWBo1leTNB*Vq8FL!@v>J#!Jxyt>+#cCnr8U9ng0E@hQsQPh$gZ7oMJ_@{|qN zwKopeGmlutJZ!)C{6c8`x|(&@FTK1R(U$t|;q}X}ud%v|4Ffxx-n6AWzZCPRcRPFO)4NAEuD!p{hN$3!I-4iEg_>5egPkqYeIk>buKcFo^bD6 zTy|#u%!dG-TdvbJ4zq29{M>at=GoCY=i+LdVe1msZ9DITw^+OrKnm7ZZVza1`czO? 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zwOXMwGdJ@yJ+tN-KuPCe0X9ZBOw+nWUja5?$&^(EwqOnRU=cQ96?S16wqYIiVIekRC3a#dwqh;zVlg&j zHFje;wqrf^V?j1#MRsIKwq#BAWKlL{Rd!`rwq;%RWnngEWp-w1wq|YiW^p!Wb#`Yb IHXr~1I~s|Dpa1{> literal 0 HcmV?d00001 diff --git a/src/python/doc/wasserstein_distance_user.rst b/src/python/doc/wasserstein_distance_user.rst index 76eb146927..def5b50227 100644 --- a/src/python/doc/wasserstein_distance_user.rst +++ b/src/python/doc/wasserstein_distance_user.rst @@ -193,9 +193,71 @@ The output is: [0.7375 0.7625 ] [0.2375 0.2625 ]] -Tutorial -******** +Quantization +------------ + +The quantization problem consists, given a measure :math:`\mu` (e.g. a persistence diagram) and a budget :math:`k`, +in finding a measure :math:`\nu` supported on :math:`k` points that is the best approximation possible of :math:`\mu` ; +the :math:`k`-means problem is a particular example of quantization problem. +The output of a quantization algorithm is often referred to a codebook; it consists of :math:`k` points (centroids) +optimally positioned to summarize the input measure :math:`\mu`. + +If one has access to a sample of measures instead, one may perform online quantization: given a sample +:math:`\mu_1,\dots,\mu_n` and an initial codebook :math:`c`, we progressively update :math:`c` by going through +(possibly batches of) the :math:`(\mu_i)_i`. Theoretical properties (including convergence rates and guarantees) of the +final codebook are provided in :cite:`divolLacombe2021quantization`. + +The Figure below showcases the use of the online-quantization approach provided by the +``gudhi.wasserstein.quantization`` method. +In this experiment, Rips persistence diagrams (in homology dimension 1) are built from random point clouds supported on +different tori with some additional noise. +Starting from an initial codebook ``c0``, centroids are iteratively updated as new diagrams are provided. +As we use the standard metrics between persistence diagrams (denoted here by :math:`\mathrm{OT}_2`), points in the +diagrams that are close to the diagonal do not interfere in the codebook update process. +Doing so, the final codebook is able to properly retrieve the two 1-dimensional features of the underlying points clouds +(the two loops generating the tori). + +.. figure:: + ./img/quantiz.gif + :figclass: align-center + + Online-quantization of a family of persistence diagrams built from random tori. + +.. autofunction:: gudhi.wasserstein.quantization + +Basic example: +************** + +This example outputs a codebook for a set of diagrams with two proeminent modes around :math:`(0,1)` and :math:`(0,3)`. +Diagrams, as often, also contain points near the diagonal. As we compare the codebook and the input diagrams +using the standard :math:`2`-Wasserstein metric between persistence diagram (which maps points to the diagonal rather +than any centroids if it reduces the matching cost), those points do not influence the centroids positions, +an improvment over using vanilla :math:`k`-mean (Lloyd algorithm) to quantize persistence diagrams. + +.. testcode:: + + d1 = np.array([[0, 1.001], [0, 3], [2, 2.001], [3, 3.001], [1, 1.01]]) + d2 = np.array([[0, 1], [0, 3.001], [0, 0.001]]) + d3 = np.array([[0, 0.999], [0, 3.002], [0, 2.998]]) + d4 = np.array([[0, 0.003], [0, 1.001], [0,3.004], [4, 4.01]]) + pdiagset = [d1, d2, d3, d4] + c_final = quantization(pdiagset, k=2) + print("Final codebook obtained:") + print(c_final) + +.. testoutput:: + + Final codebook obtained: + [[0. 1.00025] + [0. 3.00125]] + + +Tutorials +--------- This `notebook `_ presents the concept of barycenter, or Fréchet mean, of a family of persistence diagrams. + +This `notebook `_ +presents the concept of quantization, or codebooks, of a family of persistence diagrams. \ No newline at end of file diff --git a/src/python/gudhi/wasserstein/quantization.py b/src/python/gudhi/wasserstein/quantization.py new file mode 100644 index 0000000000..2b1bb6b2ac --- /dev/null +++ b/src/python/gudhi/wasserstein/quantization.py @@ -0,0 +1,208 @@ +import numpy as np +import scipy.spatial.distance as sc +import warnings + + +############################## +### Quantization algorithm ### +############################## + +def _dist_to_diag(X, internal_p): + return ((X[:, 1] - X[:, 0]) * 2 ** (1. / internal_p - 1)) + + +def _build_dist_matrix(X, Y, order=2., internal_p=2): + ''' + :param X: (n x 2) numpy.array encoding the (points of the) first diagram. + :param Y: (m x 2) numpy.array encoding the second diagram. + :param order: exponent for the Wasserstein metric. + :param internal_p: Ground metric (i.e. norm L^p). + :returns: (n+1) x (m+1) np.array encoding the cost matrix C. + For 0 <= i < n, 0 <= j < m, C[i,j] encodes the distance between X[i] and Y[j], + while C[i, m] (resp. C[n, j]) encodes the distance (to the p) between X[i] (resp Y[j]) + and its orthogonal projection onto the diagonal. + note also that C[n, m] = 0 (it costs nothing to move from the diagonal to the diagonal). + ''' + Cxd = _dist_to_diag(X, internal_p=internal_p)**order #((X[:, 1] - X[:,0]) * 2 ** (1./internal_p - 1))**order + Cdy = _dist_to_diag(Y, internal_p=internal_p)**order #((Y[:, 1] - Y[:,0]) * 2 ** (1./internal_p - 1))**order + if np.isinf(internal_p): + C = sc.cdist(X, Y, metric='chebyshev') ** order + else: + C = sc.cdist(X, Y, metric='minkowski', p=internal_p) ** order + + Cf = np.hstack((C, Cxd[:, None])) + Cdy = np.append(Cdy, 0) + + Cf = np.vstack((Cf, Cdy[None, :])) + + return Cf + + +def _get_cells(X, c, withdiag, internal_p): + """ + Given a point cloud `X` and a codebook (set of centroids) `c`, + assign to each point in X its nearest centroid in c. + If withdiag is True, points which are nearest to the diagonal than any centroid are assigned to an + additional cell. + + Parameters + ---------- + :param X: Current set of points, of size (n x d) (n : number of points, and d=2 for persistence diagrams). + :type X: `numpy.array` + :param c: Current set of centroids (codebook), of size (k x d). (k centroids in dimension d, d=2 for PDs). + It is assumed that k >= 1. + :param withdiag: Indicate if we consider the diagonal into account (True when working with PDs). + :type withdiag: bool + :param internal_p: The ground metric used to compute distances between points (norm_p). + + :returns: list `cells` of affectation, such that cells[j] = points in `X` matched to `c[j]`, + with convention that `cells[k]` represents the diagonal whenever `withdiags=True`. + + .. note: if the input X is empty, returns the empty list. Should not happen as _get_batches remove + batches of empty points. + + """ + k = c.shape[0] + + if X.shape[0] == 0: + warnings.warn("Input point cloud is empty, Cells affectation is a list of empty lists.") + return [[]] * (k+withdiag) # k or (k+1) depending on additional centroid for the diagonal. + + if X.shape[1] != 2: + raise ValueError("Input batch must be of shape (n x 2), not (%s,%s)" %(X.shape)) + + M = _build_dist_matrix(X, c, internal_p=internal_p) # Note: Order is useless here + + if withdiag: + a = np.argmin(M[:-1, :], axis=1) + else: + a = np.argmin(M[:-1, :-1], axis=1) + + cells = [X[a == j] for j in range(k)] + + if withdiag: + cells.append(X[a == k]) # this is the (k+1)-th centroid corresponding to the diagonal + + return cells + + +def _from_batch(pdiagset, batches_indices): + """ + Given a pdiagset and a list of indices, compute the "empirical expected persistence diagram" + (in practice, concatenates) on the corresponding batch of diagrams. + Note that we may encounter empty diagrams, hence the specific check .ndim==2. + If the resulting list is empty (all diagrams are empty), returns empty array. + """ + list_of_non_empty_diags = [pdiagset[i] for i in batches_indices if pdiagset[i].ndim==2] + if list_of_non_empty_diags: # There are some non-empty diagrams + X_batch = np.concatenate(list_of_non_empty_diags) + return X_batch + else: + return np.array([]) + +def _init_c(pdiagset, k, internal_p=2): + """ + A naive heuristic to initialize a codebook: we take the k points with largest distances to the diagonal + in the first diagram of the list. + + Parameters + ---------- + :param list_diags: The list of diagrams we want to quantize. Assume it is not empty (checked by quantization). + :param k: number of centroids in the codebook. + :param internal_p: Internal ground metric. Should not play a role specific role. + + :returns: an initial codebook c0 with `k` entries. + ------- + + """ + dgm = pdiagset[0] + w = _dist_to_diag(dgm, internal_p) + s = np.argsort(w) + c0 = dgm[s[-k:]] # Elements in dgm with larger persistence are last + return c0 + + +def quantization(pdiagset, k=2, c0=None, batch_size=1, order=2., internal_p=2.): + """ + This quantization algorithm takes a list of diagrams ``pdiagset``, an integer ``k`` + (or an initial codebook guess ``c0``) + and returns a codebook of ``k`` centroids that aims at minimizing the distance between the codebook and the + expected persistence diagram underneath the diagrams in ``pdiagset``. + The codebook is iteratively updated by going through (batches of) persistence diagrams. + + :param pdiagset: A list of ``numpy.array`` of shape (n x 2) (``n`` can variate) representing a + set of persistence diagrams that we want to quantize. + :param k: number of centroids. Default is ``2``. A naive heuristic is used to initialize the codebook. + Not used if an initial codebook ``c0`` has been provided. + :type k: ``int`` + :param c0: If provided, overwrite the provided ``k`` (which is now ``c0.shape[0]``), and is used as an + initialization for the algorithm. Default is ``None``. + :type c0: (n x 2) ``numpy.array``, or ``None``. + :param batch_size: Size of batches used during the online exploration of the ``pdiagset``. + Default is ``1``. + :type batch_size: ``int`` + :param order: Order of the Wasserstein distance we want to minimize. + Only 2 is implemented for now. Default is ``2.``. + :type order: ``float`` + :param internal_p: Ground metric to assess centroid affectation. Default is ``2.``. + :type internal_p: ``float`` + + :returns: The final codebook obtained after going through the all pdiagset. + + .. note:: The exact algorithm presented in the reference paper + requires more technical considerations in order to prove theoretical convergence rates. + A theoretically motivated value (asymptotically optimal) for the ``batch_size`` is + ``int(log(len(pdiagset)))``. + However, numerical experiments suggest that this simplified version yields substantially similar results. + """ + + # We take the diagonal into account in the following. + # This could be turned into a parameter of the algorithm (so that it would encompass the standard + # "online-Lloyd algorithm"), but I thought this may be confusing. + withdiag = True + + if not pdiagset: + raise ValueError("Input pdiagset is empty.") + # If no codebook has been provided, we propose an initialization. + if c0 is None: + c0 = _init_c(pdiagset, k) + # Number of centroids in the codebook (updated in the case c0 was provided by the user). + k = c0.shape[0] + + # Variable that will store the centroid evolution. + c_current = c0.copy() + + # number of diagrams + n = len(pdiagset) + + # Building the batches (size batch_size, except possibly for the last one): a list of the form + # [[0,1,..., batch_size-1],[batch_size,..., 2batch_size-1],...,[remaining diags]] + # Note : we have to add (n % batch_size != 0) to increase the number of batches by 1 if needed. + nb_step = n // batch_size + (n % batch_size != 0) + batches = np.array_split(np.arange(0, n, dtype=int), nb_step) + + # We now iterate through the diagrams + for t in range(nb_step): + # Get the empirical expected persistence diagram on the current batch + X_bar_t = _from_batch(pdiagset, batches[t]) + # We compute the corresponding cells + cells = _get_cells(X_bar_t, c_current, withdiag=withdiag, internal_p=internal_p) + + if order == 2.: + # We update the position of each centroid. + for j in range(k): + lc1 = len(cells[j]) + # The batch may be empty (if c_current[j] does not catch any point) + # In which case we do not update it. + if lc1 > 0: + # We compute the "gradient", i.e. the optimal descent direction for c_current[j] + # When order == 2, it just consists of pushing c_current[j] towards the barycenter + # of the cells[j] it defines. + grad = np.mean(c_current[j] - cells[j], axis=0) + # We then apply the gradient, with a 1/(1+t) factor to guarantee the convergence of this + # stochastic-gradient-descent like approach (decreasing learning rate). + c_current[j] = c_current[j] - grad / (t + 1) + else: + raise NotImplemented('Order = %s is not available yet. Only order=2. is valid' %order) + + return c_current diff --git a/src/python/test/test_quantization.py b/src/python/test/test_quantization.py new file mode 100644 index 0000000000..a1c111eec2 --- /dev/null +++ b/src/python/test/test_quantization.py @@ -0,0 +1,152 @@ +from gudhi.wasserstein.quantization import _get_cells, _from_batch, _init_c, quantization +import numpy as np + +__author__ = "Theo Lacombe" +__license__ = "MIT" + + +def test_get_cells(): + # Basic test + X = np.array([[0, 0.01], [0, 1.], [0, 1.2], [0, 5.]]) + c = np.array([[0, 1.], [0, 5.]]) + res = _get_cells(X, c, withdiag=True, internal_p=2.) + answer = [np.array([[0., 1.], [0, 1.2]]), + np.array([[0.,5.]]), + np.array([[0,0.01]])] + assert all([np.array_equal(x,y) for x,y in zip(res,answer)]) + + # Test withdiag=False + X = np.array([[0, 0.01], [0, 1.], [0, 1.2], [0, 5.]]) + c = np.array([[0, 1.], [0, 5.]]) + res = _get_cells(X, c, withdiag=False, internal_p=2.) + answer = [np.array([[0, 0.01], [0., 1.], [0, 1.2]]), + np.array([[0.,5.]]) + ] + assert all([np.array_equal(x,y) for x,y in zip(res,answer)]) + + # Test one cell has no points + X = np.array([[0, 0.01], [0, 1.], [0, 1.2], [0, 5.]]) + c = np.array([[0, 1.], [0, 5.], [7, 9]]) + res = _get_cells(X, c, withdiag=True, internal_p=2.) + print(res) + answer = [np.array([[0., 1.], [0, 1.2]]), + np.array([[0., 5.]]), + np.empty((0,2)), + np.array([[0, 0.01]])] + assert all([np.array_equal(x, y) for x, y in zip(res, answer)]) + + # Test input is empty + X = np.array([]) + c = np.array([[0, 1.], [0, 5.]]) + res = _get_cells(X, c, withdiag=True, internal_p=2.) + answer = [[]] * (c.shape[0] + 1) + assert all([np.array_equal(x, y) for x, y in zip(res, answer)]) + + # Test input wrong dimensions + X = np.array([[0,1,2],[4,5,6]]) + c = np.array([[0, 1.], [0, 5.]]) + try: + _get_cells(X, c, withdiag=True, internal_p=2.) + except ValueError as e: + assert str(e) == "Input batch must be of shape (n x 2), not (2,3)" + + +def test_from_batches(): + d1 = np.array([[0,1], [0,2], [0,3]]) + d2 = np.array([[0,1], [0,3], [0,6]]) + d3 = np.array([[0,2], [0,5], [0,3]]) + d4 = np.array([[0,1], [0,1], [0,1]]) + d5 = np.array([[1,2], [1,4], [1,8]]) + pdiagset = [d1, d2, d3, d4, d5] + n = len(pdiagset) + # test batches for odd number of diagrams + batch_size = 2 + batches = np.array_split(np.arange(0, n, dtype=int), n // batch_size + (n % batch_size != 0)) + assert all([np.array_equal(x,y) for x,y in zip(batches, [np.array([0,1]), np.array([2,3]), np.array([4])])]) + # Test getting batch + res = _from_batch(pdiagset, batches[0]) + answer = np.array([[0,1], [0,2], [0,3], [0,1], [0,3], [0,6]]) + assert np.array_equal(res, answer) + res = _from_batch(pdiagset, batches[-1]) + answer = np.array([[1,2], [1,4], [1,8]]) + assert np.array_equal(res, answer) + + d6 = np.array([]) + pdiagset = [d1, d2, d3, d4, d5, d6] + n = len(pdiagset) + batch_size = 2 + batches = np.array_split(np.arange(0, n, dtype=int), n // batch_size + (n % batch_size != 0)) + assert all([np.array_equal(x, y) for x, y in zip(batches, [np.array([0, 1]), + np.array([2, 3]), + np.array([4, 5])])]) + # Test getting batch + res = _from_batch(pdiagset, batches[1]) + answer = np.array([[0,2], [0,5], [0,3], [0,1], [0,1], [0,1]]) + assert np.array_equal(res, answer) + # Test when one of the diagram is empty with wrong shape (get ignored in concat) + res = _from_batch(pdiagset, batches[-1]) + answer = np.array([[1,2], [1,4], [1,8]]) + assert np.array_equal(res, answer) + + d7 = np.empty((0,2)) + d8 = np.array([[0,1],[0,42]]) + pdiagset = pdiagset + [d7, d8] + n = len(pdiagset) + batch_size = 3 + batches = np.array_split(np.arange(0, n, dtype=int), n // batch_size + (n % batch_size != 0)) + print(batches) + assert all([np.array_equal(x, y) for x, y in zip(batches, [np.array([0, 1, 2]), + np.array([3, 4, 5]), + np.array([6, 7])])]) + + res = _from_batch(pdiagset, batches[-1]) + answer = np.array([[0,1], [0,42]]) + assert np.array_equal(res, answer) + +def test_init_c(): + d1 = np.array([[0, 0.001], [0, 1], [0, 2], [0, 3], [1, 1.01]]) + d2 = np.array([[0, 1], [0, 3], [0, 6]]) + d3 = np.array([[0, 2], [0, 5], [0, 3]]) + d4 = np.array([[0, 1], [0, 1], [0, 1]]) + d5 = np.array([[1, 2], [1, 4], [1, 8]]) + pdiagset = [d1, d2, d3, d4, d5] + k = 2 + res = _init_c(pdiagset, k=k, internal_p=2) + answer = np.array([[0, 2], [0, 3]]) + assert np.array_equal(res, answer) + + +def test_quantization(): + # test empty pdiagset + pdiagset = [] + try: + quantization(pdiagset) + except ValueError as e: + assert str(e) == "Input pdiagset is empty." + + # Test quantization on a vanilla example + # Two clusters of points, around (0,1) and (0,3) ; and points close to the diagonal. + d1 = np.array([[0, 1.001], [0, 3], [2, 2.001], [3, 3.001], [1, 1.01]]) + d2 = np.array([[0, 1], [0, 3.001], [0, 0.001]]) + d3 = np.array([[0, 0.999], [0, 3.002], [0, 2.998]]) + d4 = np.array([[0, 0.003], [0, 1.001], [0,3.004], [4, 4.01]]) + pdiagset = [d1, d2, d3, d4] + c_final = quantization(pdiagset) + answer = np.array([[0,1], [0,3]]) + my_tol = 2*1e-3 # result is something like 3.0015, so a bit greater than 1e-3. + assert np.linalg.norm(c_final - answer) < my_tol + + # Same example but with empty diagrams in addition + # Two clusters of points, around (0,1) and (0,3) ; and points close to the diagonal. + d1 = np.array([[0, 1.001], [0, 3], [2, 2.001], [3, 3.001], [1, 1.01]]) + d2 = np.array([[0, 1], [0, 3.001], [0, 0.001]]) + d3 = np.array([[0, 0.999], [0, 3.002], [0, 2.998]]) + d4 = np.array([[0, 0.003], [0, 1.001], [0,3.004], [4, 4.01]]) + # Test with two different likely encoding of the empty diagram. + d5 = np.empty((0,2)) + d6 = np.array([]) + pdiagset = [d1, d2, d3, d4, d5, d6] + c_final = quantization(pdiagset) + answer = np.array([[0,1], [0,3]]) + my_tol = 2*1e-3 # result is something like 3.0015, so a bit greater than 1e-3. + assert np.linalg.norm(c_final - answer) < my_tol \ No newline at end of file From 98a5b8414c6a94066587efe2a07f778b534d76f0 Mon Sep 17 00:00:00 2001 From: tlacombe Date: Fri, 15 Oct 2021 12:17:46 +0200 Subject: [PATCH 02/16] =?UTF-8?q?added=20header=20to=20quantization.py=20w?= =?UTF-8?q?ith=20Universit=C3=A9=20Gustave=20Eiffel=20copyright?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/python/gudhi/wasserstein/quantization.py | 18 ++++++++++++++---- 1 file changed, 14 insertions(+), 4 deletions(-) diff --git a/src/python/gudhi/wasserstein/quantization.py b/src/python/gudhi/wasserstein/quantization.py index 2b1bb6b2ac..537ae4674c 100644 --- a/src/python/gudhi/wasserstein/quantization.py +++ b/src/python/gudhi/wasserstein/quantization.py @@ -1,12 +1,18 @@ +# This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT. +# See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details. +# Author(s): Theo Lacombe +# +# Copyright (C) 2019 Université Gustave Eiffel +# +# Modification(s): +# - YYYY/MM Author: Description of the modification + + import numpy as np import scipy.spatial.distance as sc import warnings -############################## -### Quantization algorithm ### -############################## - def _dist_to_diag(X, internal_p): return ((X[:, 1] - X[:, 0]) * 2 ** (1. / internal_p - 1)) @@ -122,6 +128,10 @@ def _init_c(pdiagset, k, internal_p=2): return c0 +##################### +### Main method ### +##################### + def quantization(pdiagset, k=2, c0=None, batch_size=1, order=2., internal_p=2.): """ This quantization algorithm takes a list of diagrams ``pdiagset``, an integer ``k`` From f865e8c25b9e7e83ebc9d761c09008705f23d0e7 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Th=C3=A9o=20Lacombe?= Date: Wed, 10 Nov 2021 16:26:40 +0100 Subject: [PATCH 03/16] Update biblio/bibliography.bib Co-authored-by: Vincent Rouvreau <10407034+VincentRouvreau@users.noreply.github.com> --- biblio/bibliography.bib | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/biblio/bibliography.bib b/biblio/bibliography.bib index f0a8f1b1a9..e77460b25f 100644 --- a/biblio/bibliography.bib +++ b/biblio/bibliography.bib @@ -82,7 +82,8 @@ @article{divolLacombe2021quantization title={Estimation and Quantization of Expected Persistence Diagrams}, author={Divol, Vincent and Lacombe, Th{\'e}o}, journal={ICML 2021}, - year={2021} + year={2021}, + url = {https://arxiv.org/abs/2105.04852} } @inproceedings{Garland, From 59dee6199873022edac9d164532eac4bd73f1ad1 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Th=C3=A9o=20Lacombe?= Date: Wed, 10 Nov 2021 16:27:10 +0100 Subject: [PATCH 04/16] Update src/python/gudhi/wasserstein/quantization.py Co-authored-by: Vincent Rouvreau <10407034+VincentRouvreau@users.noreply.github.com> --- src/python/gudhi/wasserstein/quantization.py | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/python/gudhi/wasserstein/quantization.py b/src/python/gudhi/wasserstein/quantization.py index 537ae4674c..fc557c845b 100644 --- a/src/python/gudhi/wasserstein/quantization.py +++ b/src/python/gudhi/wasserstein/quantization.py @@ -140,8 +140,8 @@ def quantization(pdiagset, k=2, c0=None, batch_size=1, order=2., internal_p=2.): expected persistence diagram underneath the diagrams in ``pdiagset``. The codebook is iteratively updated by going through (batches of) persistence diagrams. - :param pdiagset: A list of ``numpy.array`` of shape (n x 2) (``n`` can variate) representing a - set of persistence diagrams that we want to quantize. + :param pdiagset: a set of persistence diagrams that we want to quantize. + :type pdiagset: list of n x 2 numpy arrays :param k: number of centroids. Default is ``2``. A naive heuristic is used to initialize the codebook. Not used if an initial codebook ``c0`` has been provided. :type k: ``int`` From 60844d4420c9f9580904c8cde5c7c00ca9fd4769 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Th=C3=A9o=20Lacombe?= Date: Wed, 10 Nov 2021 16:27:37 +0100 Subject: [PATCH 05/16] Adding "Since GUDHI 3.5" in the file. Co-authored-by: Vincent Rouvreau <10407034+VincentRouvreau@users.noreply.github.com> --- src/python/doc/wasserstein_distance_user.rst | 3 +++ 1 file changed, 3 insertions(+) diff --git a/src/python/doc/wasserstein_distance_user.rst b/src/python/doc/wasserstein_distance_user.rst index def5b50227..42997ca189 100644 --- a/src/python/doc/wasserstein_distance_user.rst +++ b/src/python/doc/wasserstein_distance_user.rst @@ -196,6 +196,9 @@ The output is: Quantization ------------ +:Since: GUDHI 3.5.0 +:Requires: `SciPy `_ + The quantization problem consists, given a measure :math:`\mu` (e.g. a persistence diagram) and a budget :math:`k`, in finding a measure :math:`\nu` supported on :math:`k` points that is the best approximation possible of :math:`\mu` ; the :math:`k`-means problem is a particular example of quantization problem. From 797b7cf2f71074dddc2d298ac6adc1b35f284ff0 Mon Sep 17 00:00:00 2001 From: tlacombe Date: Wed, 10 Nov 2021 16:42:22 +0100 Subject: [PATCH 06/16] updated wasserstein/__init__.py --- src/python/gudhi/wasserstein/__init__.py | 1 + 1 file changed, 1 insertion(+) diff --git a/src/python/gudhi/wasserstein/__init__.py b/src/python/gudhi/wasserstein/__init__.py index ed225ba491..8173666d40 100644 --- a/src/python/gudhi/wasserstein/__init__.py +++ b/src/python/gudhi/wasserstein/__init__.py @@ -1 +1,2 @@ from .wasserstein import wasserstein_distance +from .quantization import quantization From 892b351f2e48e6c6be887235fc512251766269e5 Mon Sep 17 00:00:00 2001 From: tlacombe Date: Wed, 10 Nov 2021 16:55:17 +0100 Subject: [PATCH 07/16] changed tutorials : one tutorial per section, at the end of the section --- src/python/doc/wasserstein_distance_user.rst | 20 ++++++++++++++------ 1 file changed, 14 insertions(+), 6 deletions(-) diff --git a/src/python/doc/wasserstein_distance_user.rst b/src/python/doc/wasserstein_distance_user.rst index 42997ca189..3294a95a1c 100644 --- a/src/python/doc/wasserstein_distance_user.rst +++ b/src/python/doc/wasserstein_distance_user.rst @@ -193,6 +193,16 @@ The output is: [0.7375 0.7625 ] [0.2375 0.2625 ]] + + +Tutorial +******** + +This +`notebook `_ +presents the concept of barycenter, or Fréchet mean, of a family of persistence diagrams. + + Quantization ------------ @@ -255,12 +265,10 @@ an improvment over using vanilla :math:`k`-mean (Lloyd algorithm) to quantize pe [0. 3.00125]] -Tutorials ---------- +Tutorial +******** -This -`notebook `_ -presents the concept of barycenter, or Fréchet mean, of a family of persistence diagrams. This `notebook `_ -presents the concept of quantization, or codebooks, of a family of persistence diagrams. \ No newline at end of file +presents the concept of quantization, or codebooks, of a family of persistence diagrams. + From a7f0f111c8f0b37a0c9ecf1375c441611b98f007 Mon Sep 17 00:00:00 2001 From: tlacombe Date: Wed, 1 Dec 2021 11:50:34 +0100 Subject: [PATCH 08/16] updated date in copyright --- src/python/gudhi/wasserstein/quantization.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/python/gudhi/wasserstein/quantization.py b/src/python/gudhi/wasserstein/quantization.py index fc557c845b..94940573ec 100644 --- a/src/python/gudhi/wasserstein/quantization.py +++ b/src/python/gudhi/wasserstein/quantization.py @@ -2,7 +2,7 @@ # See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details. # Author(s): Theo Lacombe # -# Copyright (C) 2019 Université Gustave Eiffel +# Copyright (C) 2021 Université Gustave Eiffel # # Modification(s): # - YYYY/MM Author: Description of the modification From 6fcba580c038a0f054482994d4d4f95a1934c22a Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Th=C3=A9o=20Lacombe?= Date: Sun, 16 Jan 2022 22:48:17 +0100 Subject: [PATCH 09/16] Update src/python/doc/wasserstein_distance_user.rst Co-authored-by: Marc Glisse --- src/python/doc/wasserstein_distance_user.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/python/doc/wasserstein_distance_user.rst b/src/python/doc/wasserstein_distance_user.rst index 3294a95a1c..96cac6702b 100644 --- a/src/python/doc/wasserstein_distance_user.rst +++ b/src/python/doc/wasserstein_distance_user.rst @@ -212,7 +212,7 @@ Quantization The quantization problem consists, given a measure :math:`\mu` (e.g. a persistence diagram) and a budget :math:`k`, in finding a measure :math:`\nu` supported on :math:`k` points that is the best approximation possible of :math:`\mu` ; the :math:`k`-means problem is a particular example of quantization problem. -The output of a quantization algorithm is often referred to a codebook; it consists of :math:`k` points (centroids) +The output of a quantization algorithm is often referred to as a codebook; it consists of :math:`k` points (centroids) optimally positioned to summarize the input measure :math:`\mu`. If one has access to a sample of measures instead, one may perform online quantization: given a sample From f21abce3cbc23952f5997be2efa3a8d63e019ace Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Th=C3=A9o=20Lacombe?= Date: Sun, 16 Jan 2022 22:50:14 +0100 Subject: [PATCH 10/16] Update src/python/doc/wasserstein_distance_user.rst Co-authored-by: Marc Glisse --- src/python/doc/wasserstein_distance_user.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/python/doc/wasserstein_distance_user.rst b/src/python/doc/wasserstein_distance_user.rst index 96cac6702b..4fb7ece926 100644 --- a/src/python/doc/wasserstein_distance_user.rst +++ b/src/python/doc/wasserstein_distance_user.rst @@ -245,7 +245,7 @@ This example outputs a codebook for a set of diagrams with two proeminent modes Diagrams, as often, also contain points near the diagonal. As we compare the codebook and the input diagrams using the standard :math:`2`-Wasserstein metric between persistence diagram (which maps points to the diagonal rather than any centroids if it reduces the matching cost), those points do not influence the centroids positions, -an improvment over using vanilla :math:`k`-mean (Lloyd algorithm) to quantize persistence diagrams. +an improvement over using vanilla :math:`k`-mean (Lloyd algorithm) to quantize persistence diagrams. .. testcode:: From cc8d8c1c6b45d04c135eecb4ac8c042b6cd15032 Mon Sep 17 00:00:00 2001 From: theo Date: Tue, 17 May 2022 15:46:01 +0200 Subject: [PATCH 11/16] added _utils.py file in gudhi/wasserstein with some global functions. --- src/python/gudhi/wasserstein/_utils.py | 0 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 src/python/gudhi/wasserstein/_utils.py diff --git a/src/python/gudhi/wasserstein/_utils.py b/src/python/gudhi/wasserstein/_utils.py new file mode 100644 index 0000000000..e69de29bb2 From 231a3ca17efa345733e6c79fa5bb0bc0b3fb01c7 Mon Sep 17 00:00:00 2001 From: theo Date: Tue, 17 May 2022 15:46:24 +0200 Subject: [PATCH 12/16] changed standard distances to Wasserstein distances --- src/python/doc/wasserstein_distance_user.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/python/doc/wasserstein_distance_user.rst b/src/python/doc/wasserstein_distance_user.rst index 4fb7ece926..1ea95905ce 100644 --- a/src/python/doc/wasserstein_distance_user.rst +++ b/src/python/doc/wasserstein_distance_user.rst @@ -225,7 +225,7 @@ The Figure below showcases the use of the online-quantization approach provided In this experiment, Rips persistence diagrams (in homology dimension 1) are built from random point clouds supported on different tori with some additional noise. Starting from an initial codebook ``c0``, centroids are iteratively updated as new diagrams are provided. -As we use the standard metrics between persistence diagrams (denoted here by :math:`\mathrm{OT}_2`), points in the +As we use the Wasserstein metrics between persistence diagrams (denoted here by :math:`\mathrm{OT}_2`), points in the diagrams that are close to the diagonal do not interfere in the codebook update process. Doing so, the final codebook is able to properly retrieve the two 1-dimensional features of the underlying points clouds (the two loops generating the tori). From 94e0df4d44a3d45e5dea6418f4a7c7ac3dfd6118 Mon Sep 17 00:00:00 2001 From: theo Date: Tue, 17 May 2022 15:46:47 +0200 Subject: [PATCH 13/16] refactor following the creation of _utils.py --- src/python/gudhi/wasserstein/wasserstein.py | 50 +++------------------ 1 file changed, 6 insertions(+), 44 deletions(-) diff --git a/src/python/gudhi/wasserstein/wasserstein.py b/src/python/gudhi/wasserstein/wasserstein.py index dc18806e02..90ff517d98 100644 --- a/src/python/gudhi/wasserstein/wasserstein.py +++ b/src/python/gudhi/wasserstein/wasserstein.py @@ -8,8 +8,8 @@ # - YYYY/MM Author: Description of the modification import numpy as np -import scipy.spatial.distance as sc import warnings +from _utils import _dist_to_diag, _build_dist_matrix try: import ot @@ -27,44 +27,6 @@ def _proj_on_diag(X): return np.array([Z , Z]).T -def _dist_to_diag(X, internal_p): - ''' - :param X: (n x 2) array encoding the points of a persistent diagram. - :param internal_p: Ground metric (i.e. norm L^p). - :returns: (n) array encoding the (respective orthogonal) distances of the points to the diagonal - - .. note:: - Assumes that the points are above the diagonal. - ''' - return (X[:, 1] - X[:, 0]) * 2 ** (1.0 / internal_p - 1) - - -def _build_dist_matrix(X, Y, order, internal_p): - ''' - :param X: (n x 2) numpy.array encoding the (points of the) first diagram. - :param Y: (m x 2) numpy.array encoding the second diagram. - :param order: exponent for the Wasserstein metric. - :param internal_p: Ground metric (i.e. norm L^p). - :returns: (n+1) x (m+1) np.array encoding the cost matrix C. - For 0 <= i < n, 0 <= j < m, C[i,j] encodes the distance between X[i] and Y[j], - while C[i, m] (resp. C[n, j]) encodes the distance (to the p) between X[i] (resp Y[j]) - and its orthogonal projection onto the diagonal. - note also that C[n, m] = 0 (it costs nothing to move from the diagonal to the diagonal). - ''' - Cxd = _dist_to_diag(X, internal_p)**order - Cdy = _dist_to_diag(Y, internal_p)**order - if np.isinf(internal_p): - C = sc.cdist(X,Y, metric='chebyshev')**order - else: - C = sc.cdist(X,Y, metric='minkowski', p=internal_p)**order - Cf = np.hstack((C, Cxd[:,None])) - Cdy = np.append(Cdy, 0) - - Cf = np.vstack((Cf, Cdy[None,:])) - - return Cf - - def _perstot_autodiff(X, order, internal_p): ''' Version of _perstot that works on eagerpy tensors. @@ -321,14 +283,14 @@ def wasserstein_distance(X, Y, matching=False, order=1., internal_p=np.inf, enab P = ot.emd(a=a,b=b,M=M, numItermax=2000000) ot_cost = np.sum(np.multiply(P,M)) P[-1, -1] = 0 # Remove matching corresponding to the diagonal - match = np.argwhere(P) + the_match = np.argwhere(P) # Now we turn to -1 points encoding the diagonal - match[:,0][match[:,0] >= n] = -1 - match[:,1][match[:,1] >= m] = -1 + the_match[:,0][the_match[:,0] >= n] = -1 + the_match[:,1][the_match[:,1] >= m] = -1 # Finally incorporate the essential part matching if essential_matching is not None: - match = np.concatenate([match, essential_matching]) if essential_matching.size else match - return (ot_cost + essential_cost) ** (1./order) , match + match = np.concatenate([the_match, essential_matching]) if essential_matching.size else the_match + return (ot_cost + essential_cost) ** (1./order) , the_match if enable_autodiff: P = ot.emd(a=a, b=b, M=M, numItermax=2000000) From 57c5de67b7f5eba34d87db9241af0af31745dfcd Mon Sep 17 00:00:00 2001 From: theo Date: Tue, 17 May 2022 15:47:26 +0200 Subject: [PATCH 14/16] update quantization including final remarks... --- src/python/gudhi/wasserstein/_utils.py | 49 +++++++++++++++++++ src/python/gudhi/wasserstein/quantization.py | 51 +++++--------------- 2 files changed, 60 insertions(+), 40 deletions(-) diff --git a/src/python/gudhi/wasserstein/_utils.py b/src/python/gudhi/wasserstein/_utils.py index e69de29bb2..5eccbab509 100644 --- a/src/python/gudhi/wasserstein/_utils.py +++ b/src/python/gudhi/wasserstein/_utils.py @@ -0,0 +1,49 @@ +# This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT. +# See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details. +# Author(s): Theo Lacombe +# +# Copyright (C) 2021 Université Gustave Eiffel +# +# Modification(s): +# - YYYY/MM Author: Description of the modification + +import numpy as np +import scipy.spatial.distance as sc + + +def _dist_to_diag(X, internal_p): + """ + :param X: (n x 2) array encoding the points of a persistent diagram. + :param internal_p: Ground metric (i.e. norm L^p). + :returns: (n) array encoding the (respective orthogonal) distances of the points to the diagonal + + .. note:: + Assumes that the points are above the diagonal. + """ + return (X[:, 1] - X[:, 0]) * 2 ** (1.0 / internal_p - 1) + + +def _build_dist_matrix(X, Y, order, internal_p): + """ + :param X: (n x 2) numpy.array encoding the (points of the) first diagram. + :param Y: (m x 2) numpy.array encoding the second diagram. + :param order: exponent for the Wasserstein metric. + :param internal_p: Ground metric (i.e. norm L^p). + :returns: (n+1) x (m+1) np.array encoding the cost matrix C. + For 0 <= i < n, 0 <= j < m, C[i,j] encodes the distance between X[i] and Y[j], + while C[i, m] (resp. C[n, j]) encodes the distance (to the p) between X[i] (resp Y[j]) + and its orthogonal projection onto the diagonal. + note also that C[n, m] = 0 (it costs nothing to move from the diagonal to the diagonal). + """ + Cxd = _dist_to_diag(X, internal_p)**order + Cdy = _dist_to_diag(Y, internal_p)**order + if np.isinf(internal_p): + C = sc.cdist(X,Y, metric='chebyshev')**order + else: + C = sc.cdist(X,Y, metric='minkowski', p=internal_p)**order + Cf = np.hstack((C, Cxd[:,None])) + Cdy = np.append(Cdy, 0) + + Cf = np.vstack((Cf, Cdy[None,:])) + + return Cf \ No newline at end of file diff --git a/src/python/gudhi/wasserstein/quantization.py b/src/python/gudhi/wasserstein/quantization.py index 94940573ec..d3c91c31a2 100644 --- a/src/python/gudhi/wasserstein/quantization.py +++ b/src/python/gudhi/wasserstein/quantization.py @@ -9,41 +9,10 @@ import numpy as np -import scipy.spatial.distance as sc +from _utils import _dist_to_diag, _build_dist_matrix import warnings -def _dist_to_diag(X, internal_p): - return ((X[:, 1] - X[:, 0]) * 2 ** (1. / internal_p - 1)) - - -def _build_dist_matrix(X, Y, order=2., internal_p=2): - ''' - :param X: (n x 2) numpy.array encoding the (points of the) first diagram. - :param Y: (m x 2) numpy.array encoding the second diagram. - :param order: exponent for the Wasserstein metric. - :param internal_p: Ground metric (i.e. norm L^p). - :returns: (n+1) x (m+1) np.array encoding the cost matrix C. - For 0 <= i < n, 0 <= j < m, C[i,j] encodes the distance between X[i] and Y[j], - while C[i, m] (resp. C[n, j]) encodes the distance (to the p) between X[i] (resp Y[j]) - and its orthogonal projection onto the diagonal. - note also that C[n, m] = 0 (it costs nothing to move from the diagonal to the diagonal). - ''' - Cxd = _dist_to_diag(X, internal_p=internal_p)**order #((X[:, 1] - X[:,0]) * 2 ** (1./internal_p - 1))**order - Cdy = _dist_to_diag(Y, internal_p=internal_p)**order #((Y[:, 1] - Y[:,0]) * 2 ** (1./internal_p - 1))**order - if np.isinf(internal_p): - C = sc.cdist(X, Y, metric='chebyshev') ** order - else: - C = sc.cdist(X, Y, metric='minkowski', p=internal_p) ** order - - Cf = np.hstack((C, Cxd[:, None])) - Cdy = np.append(Cdy, 0) - - Cf = np.vstack((Cf, Cdy[None, :])) - - return Cf - - def _get_cells(X, c, withdiag, internal_p): """ Given a point cloud `X` and a codebook (set of centroids) `c`, @@ -77,7 +46,8 @@ def _get_cells(X, c, withdiag, internal_p): if X.shape[1] != 2: raise ValueError("Input batch must be of shape (n x 2), not (%s,%s)" %(X.shape)) - M = _build_dist_matrix(X, c, internal_p=internal_p) # Note: Order is useless here + M = _build_dist_matrix(X, c, order=2, internal_p=internal_p) # Note: Order is useless here + # we just need nearest neighbors. if withdiag: a = np.argmin(M[:-1, :], axis=1) @@ -106,6 +76,7 @@ def _from_batch(pdiagset, batches_indices): else: return np.array([]) + def _init_c(pdiagset, k, internal_p=2): """ A naive heuristic to initialize a codebook: we take the k points with largest distances to the diagonal @@ -132,7 +103,7 @@ def _init_c(pdiagset, k, internal_p=2): ### Main method ### ##################### -def quantization(pdiagset, k=2, c0=None, batch_size=1, order=2., internal_p=2.): +def quantization(pdiagset, k=2, init=None, batch_size=1, order=2., internal_p=2.): """ This quantization algorithm takes a list of diagrams ``pdiagset``, an integer ``k`` (or an initial codebook guess ``c0``) @@ -145,9 +116,9 @@ def quantization(pdiagset, k=2, c0=None, batch_size=1, order=2., internal_p=2.): :param k: number of centroids. Default is ``2``. A naive heuristic is used to initialize the codebook. Not used if an initial codebook ``c0`` has been provided. :type k: ``int`` - :param c0: If provided, overwrite the provided ``k`` (which is now ``c0.shape[0]``), and is used as an + :param init: If provided, overwrite the provided ``k`` (which is now ``c0.shape[0]``), and is used as an initialization for the algorithm. Default is ``None``. - :type c0: (n x 2) ``numpy.array``, or ``None``. + :type init: (n x 2) ``numpy.array``, or ``None``. :param batch_size: Size of batches used during the online exploration of the ``pdiagset``. Default is ``1``. :type batch_size: ``int`` @@ -174,13 +145,13 @@ def quantization(pdiagset, k=2, c0=None, batch_size=1, order=2., internal_p=2.): if not pdiagset: raise ValueError("Input pdiagset is empty.") # If no codebook has been provided, we propose an initialization. - if c0 is None: - c0 = _init_c(pdiagset, k) + if init is None: + init = _init_c(pdiagset, k) # Number of centroids in the codebook (updated in the case c0 was provided by the user). - k = c0.shape[0] + k = init.shape[0] # Variable that will store the centroid evolution. - c_current = c0.copy() + c_current = init.copy() # number of diagrams n = len(pdiagset) From 9e3eaa1efb9b20a9c262d4eed3b6bedaf49e627d Mon Sep 17 00:00:00 2001 From: theo Date: Tue, 17 May 2022 17:04:17 +0200 Subject: [PATCH 15/16] changed how funcs from _utils are imported. --- src/python/gudhi/wasserstein/quantization.py | 6 +++--- src/python/gudhi/wasserstein/wasserstein.py | 8 ++++---- 2 files changed, 7 insertions(+), 7 deletions(-) diff --git a/src/python/gudhi/wasserstein/quantization.py b/src/python/gudhi/wasserstein/quantization.py index d3c91c31a2..1ba9ec703f 100644 --- a/src/python/gudhi/wasserstein/quantization.py +++ b/src/python/gudhi/wasserstein/quantization.py @@ -9,7 +9,7 @@ import numpy as np -from _utils import _dist_to_diag, _build_dist_matrix +from gudhi import _utils import warnings @@ -46,7 +46,7 @@ def _get_cells(X, c, withdiag, internal_p): if X.shape[1] != 2: raise ValueError("Input batch must be of shape (n x 2), not (%s,%s)" %(X.shape)) - M = _build_dist_matrix(X, c, order=2, internal_p=internal_p) # Note: Order is useless here + M = _utils._build_dist_matrix(X, c, order=2, internal_p=internal_p) # Note: Order is useless here # we just need nearest neighbors. if withdiag: @@ -93,7 +93,7 @@ def _init_c(pdiagset, k, internal_p=2): """ dgm = pdiagset[0] - w = _dist_to_diag(dgm, internal_p) + w = _utils._dist_to_diag(dgm, internal_p) s = np.argsort(w) c0 = dgm[s[-k:]] # Elements in dgm with larger persistence are last return c0 diff --git a/src/python/gudhi/wasserstein/wasserstein.py b/src/python/gudhi/wasserstein/wasserstein.py index 90ff517d98..39789be1ed 100644 --- a/src/python/gudhi/wasserstein/wasserstein.py +++ b/src/python/gudhi/wasserstein/wasserstein.py @@ -9,7 +9,7 @@ import numpy as np import warnings -from _utils import _dist_to_diag, _build_dist_matrix +from gudhi import _utils try: import ot @@ -31,7 +31,7 @@ def _perstot_autodiff(X, order, internal_p): ''' Version of _perstot that works on eagerpy tensors. ''' - return _dist_to_diag(X, internal_p).norms.lp(order) + return _utils._dist_to_diag(X, internal_p).norms.lp(order) def _perstot(X, order, internal_p, enable_autodiff): @@ -52,7 +52,7 @@ def _perstot(X, order, internal_p, enable_autodiff): return _perstot_autodiff(ep.astensor(X), order, internal_p).raw else: - return np.linalg.norm(_dist_to_diag(X, internal_p), ord=order) + return np.linalg.norm(_utils._dist_to_diag(X, internal_p), ord=order) def _get_essential_parts(a): @@ -272,7 +272,7 @@ def wasserstein_distance(X, Y, matching=False, order=1., internal_p=np.inf, enab n = len(X) m = len(Y) - M = _build_dist_matrix(X, Y, order=order, internal_p=internal_p) + M = _utils._build_dist_matrix(X, Y, order=order, internal_p=internal_p) a = np.ones(n+1) # weight vector of the input diagram. Uniform here. a[-1] = m b = np.ones(m+1) # weight vector of the input diagram. Uniform here. From 48d790910ab00924d4a4305f79a77223d82a70cf Mon Sep 17 00:00:00 2001 From: theo Date: Tue, 17 May 2022 17:25:32 +0200 Subject: [PATCH 16/16] changed how funcs from _utils are imported bis. --- src/python/gudhi/wasserstein/quantization.py | 2 +- src/python/gudhi/wasserstein/wasserstein.py | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/src/python/gudhi/wasserstein/quantization.py b/src/python/gudhi/wasserstein/quantization.py index 1ba9ec703f..dbdc8e0e41 100644 --- a/src/python/gudhi/wasserstein/quantization.py +++ b/src/python/gudhi/wasserstein/quantization.py @@ -9,7 +9,7 @@ import numpy as np -from gudhi import _utils +from gudhi.wasserstein import _utils import warnings diff --git a/src/python/gudhi/wasserstein/wasserstein.py b/src/python/gudhi/wasserstein/wasserstein.py index 39789be1ed..84f8fbf8f4 100644 --- a/src/python/gudhi/wasserstein/wasserstein.py +++ b/src/python/gudhi/wasserstein/wasserstein.py @@ -9,7 +9,7 @@ import numpy as np import warnings -from gudhi import _utils +from gudhi.wasserstein import _utils try: import ot

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