From 061e626160c3944cd7ba58ad3be5146368712135 Mon Sep 17 00:00:00 2001 From: cchatzis Date: Fri, 21 Nov 2025 12:53:12 +0100 Subject: [PATCH 1/3] Added replicability example notebook --- docs/refs.bib | 24 ++- docs/sg_execution_times.rst | 61 ++++++++ examples/plot_replicability_analysis.py | 200 ++++++++++++++++++++++++ setup.cfg | 1 + 4 files changed, 285 insertions(+), 1 deletion(-) create mode 100644 docs/sg_execution_times.rst create mode 100644 examples/plot_replicability_analysis.py diff --git a/docs/refs.bib b/docs/refs.bib index 664ca1a..f42fa15 100644 --- a/docs/refs.bib +++ b/docs/refs.bib @@ -240,4 +240,26 @@ @article{jackson1980principal pages={201--213}, year={1980}, publisher={Taylor \& Francis} -} \ No newline at end of file +} + +@article{reprref1, + author={Adali, Tülay and Kantar, Furkan and Akhonda, Mohammad Abu Baker Siddique and Strother, Stephen and Calhoun, Vince D. and Acar, Evrim}, + journal={IEEE Signal Processing Magazine}, + title={Reproducibility in Matrix and Tensor Decompositions: Focus on model match, interpretability, and uniqueness}, + year={2022}, + volume={39}, + number={4}, + pages={8-24}, + keywords={Problem-solving;Reproducibility of results;Data models;Matrix decomposition}, + doi={10.1109/MSP.2022.3163870}} + +@article{reprref2, + title={Characterizing human postprandial metabolic response using multiway data analysis}, + author={Yan, Shi and Li, Lu and Horner, David and Ebrahimi, Parvaneh and Chawes, Bo and Dragsted, Lars O and Rasmussen, Morten A and Smilde, Age K and Acar, Evrim}, + journal={Metabolomics}, + volume={20}, + number={3}, + pages={50}, + year={2024}, + publisher={Springer} +} diff --git a/docs/sg_execution_times.rst b/docs/sg_execution_times.rst new file mode 100644 index 0000000..b5f3b63 --- /dev/null +++ b/docs/sg_execution_times.rst @@ -0,0 +1,61 @@ + +:orphan: + +.. _sphx_glr_sg_execution_times: + + +Computation times +================= +**02:50.968** total execution time for 9 files **from all galleries**: + +.. container:: + + .. raw:: html + + + + + + + + .. list-table:: + :header-rows: 1 + :class: table table-striped sg-datatable + + * - Example + - Time + - Mem (MB) + * - :ref:`sphx_glr_auto_examples_plot_replicability_analysis.py` (``../examples/plot_replicability_analysis.py``) + - 02:50.968 + - 0.0 + * - :ref:`sphx_glr_auto_examples_plot_bike_plotly.py` (``../examples/plot_bike_plotly.py``) + - 00:00.000 + - 0.0 + * - :ref:`sphx_glr_auto_examples_plot_core_consistency.py` (``../examples/plot_core_consistency.py``) + - 00:00.000 + - 0.0 + * - :ref:`sphx_glr_auto_examples_plot_labelled_decompositions.py` (``../examples/plot_labelled_decompositions.py``) + - 00:00.000 + - 0.0 + * - :ref:`sphx_glr_auto_examples_plot_optimisation_diagnostic.py` (``../examples/plot_optimisation_diagnostic.py``) + - 00:00.000 + - 0.0 + * - :ref:`sphx_glr_auto_examples_plot_outlier_detection.py` (``../examples/plot_outlier_detection.py``) + - 00:00.000 + - 0.0 + * - :ref:`sphx_glr_auto_examples_plot_selecting_aminoacids_components.py` (``../examples/plot_selecting_aminoacids_components.py``) + - 00:00.000 + - 0.0 + * - :ref:`sphx_glr_auto_examples_plot_split_half_analysis.py` (``../examples/plot_split_half_analysis.py``) + - 00:00.000 + - 0.0 + * - :ref:`sphx_glr_auto_examples_plot_working_with_xarray.py` (``../examples/plot_working_with_xarray.py``) + - 00:00.000 + - 0.0 diff --git a/examples/plot_replicability_analysis.py b/examples/plot_replicability_analysis.py new file mode 100644 index 0000000..54428a6 --- /dev/null +++ b/examples/plot_replicability_analysis.py @@ -0,0 +1,200 @@ +""" +.. _replicability_analysis: + +Replicability analysis +---------------- + +This example desrcibes how replicability of patterns can be used to guide the component selection process for PARAFAC models :cite:p:`reprref1, reprref2`. + +This process evaluates the consistency of the uncovered patterns by fitting the model to different subsets of the data. The rationale is that if the appropriate number of components is used, the uncovered patterns should be consistent. This can be seen as a more strict extension of `split-half analysis `_ where a higher number of smaller subsets of the input are removed. +""" + +############################################################################### +# Imports and utilities +# ^^^^^^^^^^^^^^^^^^^^^ + +import matplotlib.pyplot as plt +import numpy as np +import tensorly as tl +from tensorly.decomposition import parafac + +import sklearn +from sklearn.model_selection import RepeatedKFold + +import tlviz + +rng = np.random.default_rng(1) + +############################################################################### +# To fit PARAFAC models, we need to solve a non-convex optimization problem, possibly with local minima. It is +# therefore useful to fit several models with the same number of components using many different random +# initialisations. + + +def fit_many_parafac(X, num_components, num_inits=5): + return [ + parafac( + X, + num_components, + n_iter_max=1000, + tol=1e-8, + init="random", + orthogonalise=True, + linesearch=True, + random_state=i, + ) + for i in range(num_inits) + ] + + +############################################################################### +# Creating simulated data +# ^^^^^^^^^^^^^^^^^^^^^^^ +# +# We start with some simulated data, since then, we know exactly how many components there are in the data. + +cp_tensor, dataset = tlviz.data.simulated_random_cp_tensor((30, 40, 25), 3, noise_level=0.3, labelled=True) + +############################################################################### +# The replicability analysis boils down to the following steps: +# +# 1. Split the data in a (user-chosen) mode into :math:`N` folds (user-chosen). +# 2. Create :math:`N` train subsets by subtracting each fold from the complete +# dataset. +# 3. Fit multiple initializations to each train subset and choose the *best* run +# according to lowest loss (total of :math:`N` *best* runs). +# 4. Repeat the above process :math:`M` times (user-chosen), to find a total of +# :math:`M N` *best* runs. +# 5. Compare, in terms of FMS, the factorization to evaluate the replicability +# of the uncovered patterns. + + +############################################################################### +# Splitting the data +# ^^^^^^^^^^^^^^^^^^ +# + +splits = 5 # N +repeats = 10 # M + +models = {} +split_indices = {} # Keeps track of which indices are used in each subset + +for rank in [2, 3, 4, 5]: + + print(f"{rank} components") + + rskf = RepeatedKFold(n_splits=splits, n_repeats=repeats, random_state=1) + + models[rank] = [] + split_indices[rank] = [] + + for train_index, _ in rskf.split(dataset): + + # Sort rows for consistent ordering (not necessary) + + sorted_train_index = sorted(train_index) + split_indices[rank].append(sorted_train_index) + train = dataset[sorted_train_index] + + train = train / tl.norm(train) # Normalize the tensor without leaking info from other folds + + current_models = fit_many_parafac(train.data, rank) + current_model = tlviz.multimodel_evaluation.get_model_with_lowest_error(current_models, train) + models[rank].append(current_model) + +############################################################################### +# Often, the mode one will be splitting within refers to different samples +# Depending on the use-case, it might be deemed reasonable to retain the +# distributions of some properties in each subset. For this goal, +# `RepeatedStratifiedKFold `_ +# can be used. +# +# Each subset might require certain pre-processing. It is important to pre-process +# each subset in isolation to avoid leaking information from the omitted part of the input. +# For example, in this case we normalize each subset to unit norm independently. +# Also, notice that ``for train_index, _ in rskf.split(dataset):`` is embarrassingly parallel. + +############################################################################### +# Computing and plotting factor similarity +# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +# Here, we are skipping the mode we split (``mode=0``). + +replicability_stability = {} +for rank in [2, 3, 4, 5]: + replicability_stability[rank] = [] + for i, cp_i in enumerate(models[rank]): + for j, cp_j in enumerate(models[rank]): + if i < j: # include every pair only once and omit i == j + fms = tlviz.factor_tools.factor_match_score(cp_i, cp_j, consider_weights=False, skip_mode=0) + replicability_stability[rank].append(fms) + +ranks = sorted(replicability_stability.keys()) +data = [np.ravel(replicability_stability[r]) for r in ranks] + +fig, ax = plt.subplots() +ax.axhline(0.9, linestyle="--", color="gray") +ax.boxplot(data, positions=ranks) +ax.set_xlabel("Number of components") +ax.set_ylabel("Replicability stability") +plt.show() + +############################################################################### +# Here, we can observe that over-estimating the number of components +# results in not replicable patterns, indicated by low FMS. + +############################################################################### +# Computing and plotting factor similarity (alt.) +# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +# There is an alternative way to estimate the replicability of the uncovered patterns +# that includes the mode we are splitting within. When comparing two factorizations in +# terms of FMS, we can include the previously skipped factor by using only the indices +# presend in both subsets. + +replicability_stability_alt = {} +for rank in [2, 3, 4, 5]: + replicability_stability_alt[rank] = [] + for i, cp_i in enumerate(models[rank]): + for j, cp_j in enumerate(models[rank]): + if i < j: # include every pair only once and omit i == j + + weights_i, (A_i, B_i, C_i) = cp_i + weights_j, (A_j, B_j, C_j) = cp_j + + indices_subset_i = sorted(split_indices[rank][i]) + indices_subset_j = sorted(split_indices[rank][j]) + + common_indices = sorted(list(set(indices_subset_i).intersection(set(indices_subset_j)))) + + indices2use_i = [] + indices2use_j = [] + + for common_idx in common_indices: + indices2use_i.append(indices_subset_i.index(common_idx)) + indices2use_j.append(indices_subset_j.index(common_idx)) + + A_i = A_i[indices2use_i, :] + A_j = A_j[indices2use_j, :] + + fms = tlviz.factor_tools.factor_match_score( + (weights_i, (A_i, B_i, C_i)), (weights_j, (A_j, B_j, C_j)), consider_weights=False + ) + replicability_stability_alt[rank].append(fms) + +ranks = sorted(replicability_stability_alt.keys()) +data = [np.ravel(replicability_stability_alt[r]) for r in ranks] + +fig, ax = plt.subplots() +ax.axhline(0.9, linestyle="--", color="gray") +ax.boxplot(data, positions=ranks) +ax.set_xlabel("Number of components") +ax.set_ylabel("Replicability stability") +plt.show() + +############################################################################### +# ``common_indices`` contains the indices (e.g. samples) present in both subsets, +# but since the position of each index can change (e.g. sample no 3 is not guaranteeed at +# the third position in all subsets as the first and second sampled might be omitted) we need to +# utilize the indices in the original tensor input. +# +# Simialar results can be also observed here in terms of the replicability of the patterns. diff --git a/setup.cfg b/setup.cfg index 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z)mo;?Cr38EQxz55ebXv2{GE>)1@$9hxZ3EpmDCx%J@8eRWPoNa50nb^Rhbnt9@uN0 zN8i9Nop|t2gy}xm!)y$TcsUz@z=YYhgtbN_7R3a`Upei+CB6Th1Z-5|&$L(iv+&6A ziz2T{*gd$@4ZMhzs5fZU_I4WAI)Z3oVs2jP#&vP1zYl%mv~ItG>!f0|>`U1ItbL@@ zBekZZZ_1>F@h8NUM)o^jzd@9<+cddZ*Ti8jBDBI)a)AB=e6A#x5pjXE@vx)Qdk-}> zI*!U%irs}+H>gNpG0P{5yeI8SgPRKIiju& zJrg}HFz$HiHS$)D9gEw+FU|J0p#PX`(2$_XLCKr5H1U=2z;FrwukQ2;*MwGMEdnWS zS*J)m=RP~)Hc4FP3_Jo-6!z;<-`Pbi$>OAmul5fx-9!ze$ofHw_$(=8n^FN9{q(4z zWY4!o8ZspI1^41afFa}mKp-<%o!cBssaP{v!r$gvgpjLzXlS^VQdaz?g!PN$2>$hq z&H+H*MWmFG+Ml}Vn8kZVlm2rRq9FT+=Fn>`_ where a higher number of smaller subsets of the input are removed. +This process evaluates the consistency of the uncovered patterns by fitting the model to different subsets of the data. The rationale is that if the appropriate number of components is used, the uncovered patterns should be consistent. This can be seen as an extension of `split-half analysis `_ where a higher number of smaller subsets of the input are removed. """ ############################################################################### @@ -39,7 +39,6 @@ def fit_many_parafac(X, num_components, num_inits=5): n_iter_max=1000, tol=1e-8, init="random", - orthogonalise=True, linesearch=True, random_state=i, ) @@ -55,18 +54,22 @@ def fit_many_parafac(X, num_components, num_inits=5): cp_tensor, dataset = tlviz.data.simulated_random_cp_tensor((30, 40, 25), 3, noise_level=0.3, labelled=True) +############################################################################### +# .. figure:: /_static/notebook_figures/replicability.jpg +# Illustration of the replicability check, taken from :cite:p:`reprref3`. +# + ############################################################################### # The replicability analysis boils down to the following steps: # # 1. Split the data in a (user-chosen) mode into :math:`N` folds (user-chosen). -# 2. Create :math:`N` train subsets by subtracting each fold from the complete -# dataset. -# 3. Fit multiple initializations to each train subset and choose the *best* run +# 2. Create :math:`N` subsets by subtracting each fold from the complete dataset. +# 3. Fit multiple initializations to each subset and choose the *best* run # according to lowest loss (total of :math:`N` *best* runs). -# 4. Repeat the above process :math:`M` times (user-chosen), to find a total of -# :math:`M N` *best* runs. -# 5. Compare, in terms of FMS, the factorization to evaluate the replicability -# of the uncovered patterns. +# 4. Compare, in terms of FMS, the best runs across the different subsets +# to evaluate the replicability of the uncovered patterns (:math:`\binom{N}{2}` comparisons). +# 5. Repeat the above process :math:`M` times (user-chosen), to find a total of +# :math:`M \binom{N}{2}` comparisons. ############################################################################### @@ -86,22 +89,32 @@ def fit_many_parafac(X, num_components, num_inits=5): rskf = RepeatedKFold(n_splits=splits, n_repeats=repeats, random_state=1) - models[rank] = [] - split_indices[rank] = [] + models[rank] = {} + split_indices[rank] = {} - for train_index, _ in rskf.split(dataset): + for split_no, (train_index, _) in enumerate(rskf.split(dataset)): + repeat_no = split_no // splits # Sort rows for consistent ordering (not necessary) sorted_train_index = sorted(train_index) - split_indices[rank].append(sorted_train_index) train = dataset[sorted_train_index] - train = train / tl.norm(train) # Normalize the tensor without leaking info from other folds + train = train / tl.norm(train) # Pre-process the tensor without leaking info from other folds current_models = fit_many_parafac(train.data, rank) current_model = tlviz.multimodel_evaluation.get_model_with_lowest_error(current_models, train) - models[rank].append(current_model) + + if repeat_no not in models[rank].keys(): + models[rank][repeat_no] = [] + + models[rank][repeat_no].append(current_model) + + if repeat_no not in split_indices[rank].keys(): + split_indices[rank][repeat_no] = [] + + split_indices[rank][repeat_no].append(sorted_train_index) + ############################################################################### # Often, the mode one will be splitting within refers to different samples @@ -123,11 +136,12 @@ def fit_many_parafac(X, num_components, num_inits=5): replicability_stability = {} for rank in [2, 3, 4, 5]: replicability_stability[rank] = [] - for i, cp_i in enumerate(models[rank]): - for j, cp_j in enumerate(models[rank]): - if i < j: # include every pair only once and omit i == j - fms = tlviz.factor_tools.factor_match_score(cp_i, cp_j, consider_weights=False, skip_mode=0) - replicability_stability[rank].append(fms) + for repeat_no in models[rank].keys(): + for i, cp_i in enumerate(models[rank][repeat_no]): + for j, cp_j in enumerate(models[rank][repeat_no]): + if i < j: # include every pair only once and omit i == j + fms = tlviz.factor_tools.factor_match_score(cp_i, cp_j, consider_weights=False, skip_mode=0) + replicability_stability[rank].append(fms) ranks = sorted(replicability_stability.keys()) data = [np.ravel(replicability_stability[r]) for r in ranks] @@ -149,37 +163,38 @@ def fit_many_parafac(X, num_components, num_inits=5): # There is an alternative way to estimate the replicability of the uncovered patterns # that includes the mode we are splitting within. When comparing two factorizations in # terms of FMS, we can include the previously skipped factor by using only the indices -# presend in both subsets. +# present in both subsets. replicability_stability_alt = {} for rank in [2, 3, 4, 5]: replicability_stability_alt[rank] = [] - for i, cp_i in enumerate(models[rank]): - for j, cp_j in enumerate(models[rank]): - if i < j: # include every pair only once and omit i == j + for repeat_no in models[rank].keys(): + for i, cp_i in enumerate(models[rank][repeat_no]): + for j, cp_j in enumerate(models[rank][repeat_no]): + if i < j: # include every pair only once and omit i == j - weights_i, (A_i, B_i, C_i) = cp_i - weights_j, (A_j, B_j, C_j) = cp_j + weights_i, (A_i, B_i, C_i) = cp_i + weights_j, (A_j, B_j, C_j) = cp_j - indices_subset_i = sorted(split_indices[rank][i]) - indices_subset_j = sorted(split_indices[rank][j]) + indices_subset_i = sorted(split_indices[rank][repeat_no][i]) + indices_subset_j = sorted(split_indices[rank][repeat_no][j]) - common_indices = sorted(list(set(indices_subset_i).intersection(set(indices_subset_j)))) + common_indices = sorted(list(set(indices_subset_i).intersection(set(indices_subset_j)))) - indices2use_i = [] - indices2use_j = [] + indices2use_i = [] + indices2use_j = [] - for common_idx in common_indices: - indices2use_i.append(indices_subset_i.index(common_idx)) - indices2use_j.append(indices_subset_j.index(common_idx)) + for common_idx in common_indices: + indices2use_i.append(indices_subset_i.index(common_idx)) + indices2use_j.append(indices_subset_j.index(common_idx)) - A_i = A_i[indices2use_i, :] - A_j = A_j[indices2use_j, :] + A_i = A_i[indices2use_i, :] + A_j = A_j[indices2use_j, :] - fms = tlviz.factor_tools.factor_match_score( - (weights_i, (A_i, B_i, C_i)), (weights_j, (A_j, B_j, C_j)), consider_weights=False - ) - replicability_stability_alt[rank].append(fms) + fms = tlviz.factor_tools.factor_match_score( + (weights_i, (A_i, B_i, C_i)), (weights_j, (A_j, B_j, C_j)), consider_weights=False + ) + replicability_stability_alt[rank].append(fms) ranks = sorted(replicability_stability_alt.keys()) data = [np.ravel(replicability_stability_alt[r]) for r in ranks] @@ -194,7 +209,7 @@ def fit_many_parafac(X, num_components, num_inits=5): ############################################################################### # ``common_indices`` contains the indices (e.g. samples) present in both subsets, # but since the position of each index can change (e.g. sample no 3 is not guaranteeed at -# the third position in all subsets as the first and second sampled might be omitted) we need to +# the third position in all subsets as the first and second samples might be omitted) we need to # utilize the indices in the original tensor input. # -# Simialar results can be also observed here in terms of the replicability of the patterns. +# Similar results can be also observed here in terms of the replicability of the patterns. From a94cb43363928c53a1a7856e8c6c8fbe0b8c4acc Mon Sep 17 00:00:00 2001 From: cchatzis Date: Fri, 28 Nov 2025 20:48:05 +0100 Subject: [PATCH 3/3] Added new ref --- docs/refs.bib | 9 +++++++++ docs/sg_execution_times.rst | 4 ++-- examples/plot_replicability_analysis.py | 2 +- 3 files changed, 12 insertions(+), 3 deletions(-) diff --git a/docs/refs.bib b/docs/refs.bib index 5551dd0..5866e38 100644 --- a/docs/refs.bib +++ b/docs/refs.bib @@ -273,4 +273,13 @@ @article{reprref3 pages = {e3601}, doi = {https://doi.org/10.1002/cem.3601}, year = {2024} +} + +@article {reprref4, + author = {Erd{\H o}s, Bal{\'a}zs and Chatzis, Christos and Thorsen, Jonathan and Stokholm, Jakob and Smilde, Age K. and Rasmussen, Morten A. and Acar, Evrim}, + title = {Extracting host-specific developmental signatures from longitudinal microbiome data}, + elocation-id = {2025.11.22.689760}, + year = {2025}, + doi = {10.1101/2025.11.22.689760}, + journal = {bioRxiv} } \ No newline at end of file diff --git a/docs/sg_execution_times.rst b/docs/sg_execution_times.rst index b522a16..a66f7e1 100644 --- a/docs/sg_execution_times.rst +++ b/docs/sg_execution_times.rst @@ -6,7 +6,7 @@ Computation times ================= -**02:22.749** total execution time for 9 files **from all galleries**: +**01:57.453** total execution time for 9 files **from all galleries**: .. container:: @@ -33,7 +33,7 @@ Computation times - Time - Mem (MB) * - :ref:`sphx_glr_auto_examples_plot_replicability_analysis.py` (``../examples/plot_replicability_analysis.py``) - - 02:22.749 + - 01:57.453 - 0.0 * - :ref:`sphx_glr_auto_examples_plot_bike_plotly.py` (``../examples/plot_bike_plotly.py``) - 00:00.000 diff --git a/examples/plot_replicability_analysis.py b/examples/plot_replicability_analysis.py index 7a7c9ba..8d03f2a 100644 --- a/examples/plot_replicability_analysis.py +++ b/examples/plot_replicability_analysis.py @@ -161,7 +161,7 @@ def fit_many_parafac(X, num_components, num_inits=5): # Computing and plotting factor similarity (alt.) # ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ # There is an alternative way to estimate the replicability of the uncovered patterns -# that includes the mode we are splitting within. When comparing two factorizations in +# that includes the mode we are splitting within :cite:p:`reprref4`. When comparing two factorizations in # terms of FMS, we can include the previously skipped factor by using only the indices # present in both subsets.