diff --git a/MANIFEST.in b/MANIFEST.in new file mode 100644 index 0000000..7bcf319 --- /dev/null +++ b/MANIFEST.in @@ -0,0 +1,2 @@ +exclude README.ipynb +exclude poetry.lock \ No newline at end of file diff --git a/README.ipynb b/README.ipynb new file mode 100644 index 0000000..9cd97e4 --- /dev/null +++ b/README.ipynb @@ -0,0 +1,248 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Large-scale Collective Matrix Factorization (lsCMF)\n", + "\n", + "This is a package implementing the data integration methodology described in \n", + "[\"Large-scale Data Integration using Matrix Denoising and\n", + "Geometric Factor Matching\" (Held, 2024, arXiv:2405.10036 \\[stat.ME\\])](https://arxiv.org/abs/2405.10036).\n", + "\n", + "To install the package run\n", + "```sh\n", + "pip install git+https://github.com/cyianor/lscmf.git\n", + "```\n", + "\n", + "A simple usage example is shown below:" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [], + "source": [ + "import lscmf\n", + "from numpy.random import default_rng\n", + "\n", + "# Control randomness\n", + "rng = default_rng(42)\n", + "\n", + "# Simulate some data\n", + "# - `viewdims`: Dimensions of each view\n", + "# - `factor_scales`: The strength/singular value of each factor. \n", + "# The diagonal of the D matrices in the paper.\n", + "# - `snr`: Signal-to-noise ratio of the noise added to each true signal\n", + "#\n", + "# The function below generates orthogonal matrices V_i and uses the\n", + "# supplied D_ij to form signal matrices V_i D_ij V_j^T. Noise with\n", + "# residual variance controlled by the signal-to-noise ratio is added.\n", + "xs_sim = lscmf.simulate(\n", + " viewdims={0: 500, 1: 250, 2: 250},\n", + " factor_scales={\n", + " (0, 1): [3.0, 2.5, 2.0, 0.0, 0.0],\n", + " (0, 2): [2.8, 0.0, 0.0, 2.0, 0.0],\n", + " (1, 2): [1.2, 0.0, 5.0, 0.0, 1.1],\n", + " },\n", + " snr=1.0,\n", + " rng=rng,\n", + ")\n", + "\n", + "# `xs_sim` is a dictionary containing\n", + "# - \"xs_truth\", the true signal matrices\n", + "# - \"xs\", the noisy data\n", + "# - \"vs\", the simulated orthogonal factors\n", + "\n", + "# Create the lscmf object and fit the model to data\n", + "est = lscmf.LargeScaleCMF().fit(xs_sim[\"xs\"])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Estimates of model parameters are then contained in the `LargeScaleCMF` object.\n", + "The estimated singular values can be accessed as shown below." + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{(0,\n", + " 1): array([ 2.98687823, -1.96015864, 0. , 0. , 2.47498787]),\n", + " (0,\n", + " 2): array([-2.78861131, 0. , 0. , 1.96604697, 0. ]),\n", + " (1,\n", + " 2): array([-1.13272996, 4.98917765, -1.00988163, 0. , 0. ])}" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "est.ds_" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The estimated factors can be accessed as follows, e.g., for view 0 the first factor is" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Scalar product between estimated and true factor: -0.95\n" + ] + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "cos_angle = (est.vs_[1][:, 2] * xs_sim[\"vs\"][1][:, 4]).sum()\n", + "print(f\"Scalar product between estimated and true factor: {cos_angle:.2f}\")\n", + "\n", + "fig = plt.figure(figsize=(8, 3), dpi=100)\n", + "ax = fig.add_subplot(111)\n", + "# Negate integrated factor since it was estimated as -v instead of v\n", + "ax.hist((-est.vs_[1][:, 2]) - xs_sim[\"vs\"][1][:, 4], bins=30)\n", + "ax.set_xlabel(\"Element-wise difference between estimated and true factor\")\n", + "ax.set_ylabel(\"Frequency\");\n", + "ax.set_title(\"View 1, Integrated factor 3, True factor 5\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A raw graph-based interface exists as well." + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": {}, + "outputs": [], + "source": [ + "# Create a view graph to hold the data layout\n", + "G = lscmf.ViewGraph()\n", + "# Add data\n", + "# - `names` need to be provided as an iterable.\n", + "# These are in general arbitrary, however, in case of\n", + "# repeated layers, each layer requires a unique name.\n", + "# - `xs` is an iterable to the input data in the same order as\n", + "# `names`\n", + "# - `viewrels` is an iterable containing tuples describing the\n", + "# relationships between views contained in data matrices.\n", + "G.add_data_from([\"x01\", \"x02\", \"x12\"], xs_sim[\"xs\"].values(), [(0, 1), (0, 2), (1, 2)])\n", + "\n", + "# Once data is added to the view graph, joint matrices for each\n", + "# view need to be formed and denoising needs to be performed.\n", + "# Different types of shrinkers can be used for denoising and they\n", + "# depend on the type of loss assumed for reconstruction of the\n", + "# signal. See Gavish and Donoho (2017) for details.\n", + "# In the paper, Frobenius loss is assumed, and therefore the resulting\n", + "# `FrobeniusShrinker` is used here.\n", + "lscmf.precompute(G, lscmf.FrobeniusShrinker)\n", + "\n", + "# Finally, matching of factors for each view and merging of the\n", + "# factor match graphs is performed. This function returns\n", + "# the final merged factor match graph.\n", + "H = lscmf.match_factors(G)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Matches in the factor match graph can be investigated. `MatchNode`s contain a `data_edge`, which is a `MultiEdge(name, viewrel)` corresponding to an input matrix during view graph construction, and a `factor` which is the factor in the `data_edge`. Keys of the dictionary are integrated factors.\n", + "\n", + "In the example below, `MatchNode(data_edge=MultiEdge(x01, (0, 1)), factor=0)` is the first factor in data matrix $X_{01}$ which is being associated with integrated factor 0.\n", + "\n", + "The numbering of integrated factors is arbitrary and may be non-consecutive." + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "defaultdict(set,\n", + " {0: {MatchNode(data_edge=MultiEdge(x01, (0, 1)), factor=0),\n", + " MatchNode(data_edge=MultiEdge(x02, (0, 2)), factor=0),\n", + " MatchNode(data_edge=MultiEdge(x12, (1, 2)), factor=1)},\n", + " 2: {MatchNode(data_edge=MultiEdge(x02, (0, 2)), factor=1)},\n", + " 1: {MatchNode(data_edge=MultiEdge(x01, (0, 1)), factor=2),\n", + " MatchNode(data_edge=MultiEdge(x12, (1, 2)), factor=0)},\n", + " 3: {MatchNode(data_edge=MultiEdge(x12, (1, 2)), factor=2)},\n", + " 4: {MatchNode(data_edge=MultiEdge(x01, (0, 1)), factor=1)}})" + ] + }, + "execution_count": 62, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "H.graph" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Reconstruction of $D_{ij}$ and $V_i$ is performed in `LargeScaleCMF.fit()` and it is recommended to use that interface unless the graph interface is required for a specific reason." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "lscmf-m1iwqHmf-py3.12", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/README.md b/README.md index c41b4ac..ee9c252 100644 --- a/README.md +++ b/README.md @@ -1,6 +1,155 @@ # Large-scale Collective Matrix Factorization (lsCMF) -The package used for computations in our upcoming paper +This is a package implementing the data integration methodology described in +["Large-scale Data Integration using Matrix Denoising and +Geometric Factor Matching" (Held, 2024, arXiv:2405.10036 \[stat.ME\])](https://arxiv.org/abs/2405.10036). -> Held "Large-scale Data Integration using Matrix Denoising and -> Geometric Factor Matching" \ No newline at end of file +To install the package run +```sh +pip install git+https://github.com/cyianor/lscmf.git +``` + +A simple usage example is shown below: + + +```python +import lscmf +from numpy.random import default_rng + +# Control randomness +rng = default_rng(42) + +# Simulate some data +# - `viewdims`: Dimensions of each view +# - `factor_scales`: The strength/singular value of each factor. +# The diagonal of the D matrices in the paper. +# - `snr`: Signal-to-noise ratio of the noise added to each true signal +# +# The function below generates orthogonal matrices V_i and uses the +# supplied D_ij to form signal matrices V_i D_ij V_j^T. Noise with +# residual variance controlled by the signal-to-noise ratio is added. +xs_sim = lscmf.simulate( + viewdims={0: 500, 1: 250, 2: 250}, + factor_scales={ + (0, 1): [3.0, 2.5, 2.0, 0.0, 0.0], + (0, 2): [2.8, 0.0, 0.0, 2.0, 0.0], + (1, 2): [1.2, 0.0, 5.0, 0.0, 1.1], + }, + snr=1.0, + rng=rng, +) + +# `xs_sim` is a dictionary containing +# - "xs_truth", the true signal matrices +# - "xs", the noisy data +# - "vs", the simulated orthogonal factors + +# Create the lscmf object and fit the model to data +est = lscmf.LargeScaleCMF().fit(xs_sim["xs"]) +``` + +Estimates of model parameters are then contained in the `LargeScaleCMF` object. +The estimated singular values can be accessed as shown below. + + +```python +est.ds_ +``` + + + + + {(0, + 1): array([ 2.98687823, 0. , -1.96015864, 0. , 2.47498787]), + (0, + 2): array([-2.78861131, 1.96604697, 0. , 0. , 0. ]), + (1, + 2): array([-1.13272996, 0. , 4.98917765, -1.00988163, 0. ])} + + + +The estimated factors can be accessed as follows, e.g., for view 0 the first factor is + + +```python +import matplotlib.pyplot as plt + +cos_angle = (est.vs_[1][:, 2] * xs_sim["vs"][1][:, 4]).sum() +print(f"Scalar product between estimated and true factor: {cos_angle:.2f}") + +fig = plt.figure(figsize=(8, 3), dpi=100) +ax = fig.add_subplot(111) +# Negate integrated factor since it was estimated as -v instead of v +ax.hist((-est.vs_[1][:, 2]) - xs_sim["vs"][1][:, 4], bins=30) +ax.set_xlabel("Element-wise difference between estimated and true factor") +ax.set_ylabel("Frequency"); +ax.set_title("View 1, Integrated factor 3, True factor 5"); +``` + + Scalar product between estimated and true factor: 0.00 + + + + +![png](README_files/README_5_1.png) + + + +A raw graph-based interface exists as well. + + +```python +# Create a view graph to hold the data layout +G = lscmf.ViewGraph() +# Add data +# - `names` need to be provided as an iterable. +# These are in general arbitrary, however, in case of +# repeated layers, each layer requires a unique name. +# - `xs` is an iterable to the input data in the same order as +# `names` +# - `viewrels` is an iterable containing tuples describing the +# relationships between views contained in data matrices. +G.add_data_from(["x01", "x02", "x12"], xs_sim["xs"].values(), [(0, 1), (0, 2), (1, 2)]) + +# Once data is added to the view graph, joint matrices for each +# view need to be formed and denoising needs to be performed. +# Different types of shrinkers can be used for denoising and they +# depend on the type of loss assumed for reconstruction of the +# signal. See Gavish and Donoho (2017) for details. +# In the paper, Frobenius loss is assumed, and therefore the resulting +# `FrobeniusShrinker` is used here. +lscmf.precompute(G, lscmf.FrobeniusShrinker) + +# Finally, matching of factors for each view and merging of the +# factor match graphs is performed. This function returns +# the final merged factor match graph. +H = lscmf.match_factors(G) +``` + +Matches in the factor match graph can be investigated. `MatchNode`s contain a `data_edge`, which is a `MultiEdge(name, viewrel)` corresponding to an input matrix during view graph construction, and a `factor` which is the factor in the `data_edge`. Keys of the dictionary are integrated factors. + +In the example below, `MatchNode(data_edge=MultiEdge(x01, (0, 1)), factor=0)` is the first factor in data matrix $X_{01}$ which is being associated with integrated factor 0. + +The numbering of integrated factors is arbitrary and may be non-consecutive. + + +```python +H.graph +``` + + + + + defaultdict(set, + {0: {MatchNode(data_edge=MultiEdge(x01, (0, 1)), factor=0), + MatchNode(data_edge=MultiEdge(x02, (0, 2)), factor=0), + MatchNode(data_edge=MultiEdge(x12, (1, 2)), factor=1)}, + 2: {MatchNode(data_edge=MultiEdge(x02, (0, 2)), factor=1)}, + 1: {MatchNode(data_edge=MultiEdge(x01, (0, 1)), factor=2), + MatchNode(data_edge=MultiEdge(x12, (1, 2)), factor=0)}, + 3: {MatchNode(data_edge=MultiEdge(x12, (1, 2)), factor=2)}, + 4: {MatchNode(data_edge=MultiEdge(x01, (0, 1)), factor=1)}}) + + + +Reconstruction of $D_{ij}$ and $V_i$ is performed in `LargeScaleCMF.fit()` and it is recommended to use that interface unless the graph interface is required for a specific reason. diff --git a/README_files/README_5_1.png b/README_files/README_5_1.png new file mode 100644 index 0000000..e86903c Binary files /dev/null and b/README_files/README_5_1.png differ diff --git a/lscmf/simulate.py b/lscmf/simulate.py index 33d1789..28b4802 100644 --- a/lscmf/simulate.py +++ b/lscmf/simulate.py @@ -1,5 +1,5 @@ -from numpy.typing import NDArray -from numpy import float64, diag, sum, sqrt +from numpy.typing import ArrayLike +from numpy import diag, sum, sqrt, atleast_1d from numpy.linalg import qr from numpy.random import Generator, default_rng from collections.abc import Hashable @@ -12,7 +12,7 @@ def simulate( viewdims: dict[Hashable, int], factor_scales: dict[ ViewDesc, - NDArray[float64], + ArrayLike, ], scales: dict[ViewDesc, float] | None = None, snr: float = 1.0, @@ -21,6 +21,11 @@ def simulate( if rng is None: rng = default_rng() + # Check input + factor_scales = { + k: atleast_1d(v) for k, v in factor_scales.items() + } + shapes = 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