{ "cells": [ { "cell_type": "markdown", "id": "88a0fa30-76a1-4ec1-990a-3a26b31fd4e4", "metadata": {}, "source": [ "# MNIST classification with stabilized ICA and multinomial logistic regression \n", "\n", "In this jupyter notebook we illustrate the integration of stabilized-ica into standard scikit-learn Machine Learning pipelines. We apply stabilized-ica and fit a multinomial logistic regression on the MNIST digits classification task.\n", "\n", "**Note :** Applying ICA and its stabilized-version to images simply means that we consider each image to be a linear combination of independent basis images (i.e ICA sources). These basis images contain sparse and local patterns linked to edges and curves." ] }, { "cell_type": "code", "execution_count": 1, "id": "1a62367a-6832-4f31-af77-75660ebd8000", "metadata": {}, "outputs": [], "source": [ "%load_ext autoreload\n", "%autoreload 2\n", "\n", "import time\n", "import matplotlib.pyplot as plt\n", "import numpy as np" ] }, { "cell_type": "markdown", "id": "68345126-6dcf-4f87-8d14-062e302fd070", "metadata": {}, "source": [ "## 0. Load MNIST data" ] }, { "cell_type": "code", "execution_count": 2, "id": "b27365a3-be7b-4b1c-b3a7-1ba1ab260f21", "metadata": {}, "outputs": [], "source": [ "from sklearn.datasets import fetch_openml\n", "from sklearn.model_selection import train_test_split\n", "from sklearn.utils import check_random_state" ] }, { "cell_type": "markdown", "id": "c2f0c535-b1e7-410f-a2a9-3735ee3d0875", "metadata": {}, "source": [ "We download the MNIST data set from the open platform [openml.org](https://www.openml.org/) using the tool of scikit-learn [sklearn.datasets.fetch_openml](https://scikit-learn.org/stable/modules/generated/sklearn.datasets.fetch_openml.html). It contains a dataset of 70000 samples and 784 features which correspond to the grey level of each pixel (i.e 28x28 flattened images). Each image is associated with a class label (from '0' to '9') which corresponds to the handwritten digit that it contains." ] }, { "cell_type": "code", "execution_count": 3, "id": "74bc45c3-0049-492f-9096-ba18f702eaa4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Loading time (min): 00:23.27\n" ] } ], "source": [ "# Load data from https://www.openml.org/d/554\n", "start = time.time()\n", "X, y = fetch_openml(\"mnist_784\", version=1, return_X_y=True, as_frame=False)\n", "end = time.time()\n", "\n", "minutes, seconds = divmod(end - start, 60)\n", "print(\"Loading time (min): \" + \"{:0>2}:{:05.2f}\".format(int(minutes),seconds))" ] }, { "cell_type": "markdown", "id": "fffa9903-af46-4f0c-9f85-0df5c0a04f71", "metadata": {}, "source": [ "We split the dataset into a training set of 60000 samples and a test set of 10000 samples. " ] }, { "cell_type": "code", "execution_count": 4, "id": "7d28826a-8d93-4de5-a082-2eace69e1225", "metadata": {}, "outputs": [], "source": [ "random_state = check_random_state(0) #fix the seed for reproducibility\n", "\n", "X_train, X_test, y_train, y_test = train_test_split(X,\n", " y.astype('int'),\n", " test_size=1/7.0,\n", " shuffle=True,\n", " random_state=random_state)" ] }, { "cell_type": "markdown", "id": "8fd6b7df-58ed-41a7-9656-61a2ddd939cd", "metadata": {}, "source": [ "Finally, we can check that the 10 classes are roughly equally distributed in the training set as well as in the test set." ] }, { "cell_type": "code", "execution_count": 5, "id": "7eaf454c-6837-4c93-befe-1dbae76872ec", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Frequency of classes - Test data')" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1,2, figsize=(20, 6))\n", "axes[0].hist(y_train);\n", "axes[0].set_title('Frequency of classes - Training data', fontsize=16)\n", "\n", "axes[1].hist(y_test);\n", "axes[1].set_title('Frequency of classes - Test data', fontsize=16)" ] }, { "cell_type": "markdown", "id": "d3792907-0d52-4876-a9ff-484bfc2030e2", "metadata": {}, "source": [ "## 1. Select the number of ICA components to extract" ] }, { "cell_type": "code", "execution_count": 6, "id": "aa3d8982-9639-4af3-be25-bad71b3c9bb9", "metadata": {}, "outputs": [], "source": [ "from sica.base import MSTD, StabilizedICA\n", "from sklearn.decomposition import PCA" ] }, { "cell_type": "markdown", "id": "0b9c6233-4155-46c4-9b18-6ceb279599a8", "metadata": {}, "source": [ "Here we want to get more insights about the appropriate number of ICA components we should select. Unfortunatly, there is no real consensus about how to select such a number. We can still run different tests:\n", "* Decompose the data set with PCA to estimate its intrinsic dimension (i.e what is the number of PCA components needed to retain 90% of the variance ?).\n", "* Study the stability of ICA components for different orders of decomposition (we want to find a trade-off between a sufficiently large number of components and a satisfying overall stability of the components).\n", "* Test the quality of the reconstruction of several unseen images with the ICA features (for different order of decomposition).\n", "\n", "**Note 1:** We perform these tests on the training set alone to avoid any risk of data leakage. \n", "\n", "**Note 2:** In the following we will center the expression of each pixel to avoid PCA and ICA capturing a component which simply separates the background pixels (i.e those on the side of the images) from the foreground pixels (i.e those in the center of the images)." ] }, { "cell_type": "code", "execution_count": 7, "id": "7ac0de3b-a4c3-4a5a-8834-c8d97740522f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Cumulative explained variance')" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pca = PCA(n_components=0.9).fit((X_train-X_train.mean(axis=0)).T)\n", "\n", "fig, ax = plt.subplots(figsize=(10,6))\n", "ax.plot(np.cumsum(pca.explained_variance_ratio_), '-o')\n", "ax.set_xlabel(\"Number of PCA components\", fontsize=14)\n", "ax.set_ylabel(\"Cumulative explained variance\", fontsize=14)" ] }, { "cell_type": "code", "execution_count": 8, "id": "dbfcd8c0-1f41-4933-b9d1-a8d7e153c7cb", "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "e0f3274190974ce2ae4525ebfeb81809", "version_major": 2, "version_minor": 0 }, "text/plain": [ " 0%| | 0/96 [00:00" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "MSTD(X_train - X_train.mean(axis=0), m = 5, M = 100, step = 1, n_runs=50)" ] }, { "cell_type": "code", "execution_count": 9, "id": "637c0393-6358-49d6-8e6a-f7f1f636ca63", "metadata": { "tags": [ "nbsphinx-thumbnail" ] }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#We first remove three images to test their reconstruction later with the ICA features extracted from\n", "#the remaining training data.\n", "X_new_train, X_new_test = train_test_split(X_train, shuffle=True, test_size = 10, stratify = y_train)\n", "\n", "#Here, we apply PCA with the maximum number of components to avoid repeating this step for each ICA decomposition\n", "X_w = PCA(n_components=100).fit_transform((X_new_train-X_new_train.mean(axis=0)).T).T\n", "\n", "fig, axes = plt.subplots(4, 7, figsize=(20,10))\n", "\n", "for j, n in enumerate([5, 10, 30, 60, 80, 100]):\n", " sICA = StabilizedICA(n_components=n, n_runs=100, plot=False, n_jobs=-1)\n", " sICA.fit(X_w[:n, :])\n", " A = sICA.transform(X_new_test - X_new_train.mean(axis=0))\n", " for i in range(4):\n", " axes[i, j].imshow((np.dot(A[i, :], sICA.S_) + X_new_train.mean(axis=0)).reshape((28,28)))\n", " axes[i, j].axis(\"off\")\n", " if i==0:\n", " axes[i, j].set_title(str(n) + \" components\")\n", "\n", "for i in range(4):\n", " axes[i, -1].imshow(X_new_test[i, :].reshape((28,28)))\n", " axes[i, -1].axis(\"off\")\n", " if i==0:\n", " axes[i, -1].set_title(\"True image\")" ] }, { "cell_type": "markdown", "id": "a5c764a5-1805-458b-ad4b-24b04b9679f2", "metadata": {}, "source": [ "Even with these different tests it is still difficult to select one single optimal number of independent sources. However we can make some interesting observations:\n", "* With PCA we observe that 60 to 80 components are enough to retain 80% to 90% of the variance.\n", "* 60 to 80 components give fairly accurate reconstruction of the original images (meaning that not so much information has been lost with the ICA decomposition).\n", "* Looking at the stability plots we observe that, though the average stability decreases with the number of components it seems to slown down starting from ~50 components (meaning that the ratio of stable components to unstable ones does not change too much with the order of decomposition). \n", "\n", "In the following we will use **60 independent components** since it seems to be sufficiently large to capture relevant information and it is not too much affected by very unstable components." ] }, { "cell_type": "markdown", "id": "37d56a60-9253-4ec5-9692-bfc2fe690924", "metadata": {}, "source": [ "## 2. Build, train and test a classification pipeline" ] }, { "cell_type": "code", "execution_count": 10, "id": "3657cd34-6fd9-45ed-8625-1588cd5cca7a", "metadata": {}, "outputs": [], "source": [ "from sklearn.linear_model import LogisticRegression\n", "from sklearn.preprocessing import StandardScaler\n", "from sklearn.pipeline import Pipeline\n", "\n", "from sklearn.metrics import classification_report" ] }, { "cell_type": "markdown", "id": "2bf2094a-170a-44e5-8ec7-32a2b35e9899", "metadata": {}, "source": [ "Here we build a very simple Machine Learning classification pipeline with four steps:\n", "* 1. Center the expression of each pixel (remove a component which separates background from foreground)\n", "* 2. Apply stabilized ICA to reduce dimensionnality\n", "* 3. Standardize the transformed data set (mainly useful for feature importances analysis)\n", "* 4. Apply multinomial logistic regression" ] }, { "cell_type": "code", "execution_count": 11, "id": "ea0310ec-6651-4316-bc5a-c49cb22839e6", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Training time (min): 00:31.42\n" ] } ], "source": [ "pipe = Pipeline(steps=[('scaler', StandardScaler(with_std=False)),\n", " ('sICA' , StabilizedICA(n_components=60, n_runs=100)),\n", " ('scaler_bis', StandardScaler()),\n", " ('logistic', LogisticRegression(max_iter=2000))\n", " ]\n", " )\n", "\n", "start = time.time()\n", "pipe.fit(X_train, y_train)\n", "end = time.time()\n", "\n", "minutes, seconds = divmod(end - start, 60)\n", "print(\"Training time (min): \" + \"{:0>2}:{:05.2f}\".format(int(minutes),seconds)) " ] }, { "cell_type": "markdown", "id": "b7e556c5-1250-4e87-a1af-70ccfc2f8298", "metadata": {}, "source": [ "For each class we display the precision, the recall and the F1-score associated to the binary task one class vs all. We also compute their averages over the different classes (i.e macro-average)." ] }, { "cell_type": "code", "execution_count": 12, "id": "1a12bca2-b5d9-480d-972f-23ece98c3a69", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " precision recall f1-score support\n", "\n", " class 0 0.96 0.97 0.96 996\n", " class 1 0.95 0.97 0.96 1141\n", " class 2 0.90 0.88 0.89 1040\n", " class 3 0.91 0.87 0.89 1013\n", " class 4 0.88 0.92 0.90 962\n", " class 5 0.86 0.84 0.85 863\n", " class 6 0.94 0.95 0.94 989\n", " class 7 0.92 0.92 0.92 1064\n", " class 8 0.87 0.87 0.87 963\n", " class 9 0.86 0.87 0.87 969\n", "\n", " accuracy 0.91 10000\n", " macro avg 0.91 0.91 0.91 10000\n", "weighted avg 0.91 0.91 0.91 10000\n", "\n" ] } ], "source": [ "y_pred = pipe.predict(X_test)\n", "print(classification_report(y_test, y_pred, target_names=['class ' + str(i) for i in pipe['logistic'].classes_]))" ] }, { "cell_type": "code", "execution_count": 13, "id": "bf8aa035-7fd5-4fec-b6be-80c4ecb09dfe", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Accuracy micro-average: 0.9078\n" ] } ], "source": [ "print(\"Accuracy micro-average: \", pipe.score(X_test, y_test))" ] }, { "cell_type": "markdown", "id": "40d50183-7005-4f05-adea-f8e4006bb585", "metadata": {}, "source": [ "We obtain here a satisfying accuracy which is very close to the one we obtain by fitting a logistic regression on the 784 features. But with stabilized-ica as a preprocessing step the running time is much lower.\n", "\n", "**Note :** This performance is still significantly lower than the ones obtained with non-linear models and convolutional neural networks (see [here](http://yann.lecun.com/exdb/mnist/) for a benchmark). " ] }, { "cell_type": "markdown", "id": "dfab2603-9a9d-4fb6-8a02-9eb0b4ed6852", "metadata": {}, "source": [ "## 3. Use stabilized-ica to interpret the classifier" ] }, { "cell_type": "markdown", "id": "b088b618-8dc9-4326-bc82-44c158b2e675", "metadata": {}, "source": [ "Multinomial logistic regression gives us a natural way of higlihting the important features for the classification by studying the feature weights associated to each class. " ] }, { "cell_type": "markdown", "id": "8c7975c8-716e-4fec-8d37-a1c854982b1b", "metadata": {}, "source": [ "### 3.1 Important features for the 0 digit\n", "\n", "We can select the most important ICA features for the 0 class (with negative and positive weights) and display their associate ICA sources." ] }, { "cell_type": "code", "execution_count": 14, "id": "145afaed-9075-4225-82e9-8bcda6f20fb2", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1,5, figsize = (20, 10))\n", "fig.suptitle(\"5 samples of the class 0\", fontsize=20, y=0.7)\n", "\n", "for i in range(5):\n", " axes[i].imshow(X[y=='0'][i, :].reshape((28,28)))\n", " axes[i].axis(\"off\")" ] }, { "cell_type": "code", "execution_count": 15, "id": "105cd25c-180d-463b-ad79-1a4f2504cc67", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(constrained_layout=True, figsize = (20, 10))\n", "subfigs = fig.subfigures(2, 1)\n", "\n", "subfigs[0].suptitle(\"10 most important positive ICA features\", fontsize=20, y=0.8)\n", "axs = subfigs[0].subplots(1, 10)\n", "for i, index in enumerate(np.flip(np.argsort(pipe['logistic'].coef_[0,:]))[:10]):\n", " axs[i].imshow(pipe['sICA'].S_[index, :].reshape((28,28)))\n", " axs[i].axis(\"off\")\n", " \n", "subfigs[1].suptitle(\"10 most important negative ICA features\", fontsize=20, y=0.8)\n", "axs = subfigs[1].subplots(1, 10)\n", "for i, index in enumerate(np.argsort(pipe['logistic'].coef_[0,:])[:10]):\n", " axs[i].imshow(pipe['sICA'].S_[index, :].reshape((28,28)))\n", " axs[i].axis(\"off\")" ] }, { "cell_type": "markdown", "id": "f47cd06f-64ad-4a72-9081-39b2cf2ee6a3", "metadata": {}, "source": [ "Here we can roughly see that the most important positive features highlight the edges of the circles forming the zero digits whereas the most important negative features rather focus on the center of the circle" ] }, { "cell_type": "markdown", "id": "e61af745-29af-4cb5-bfc9-4ea67c6c5bab", "metadata": {}, "source": [ "### 3.2 Weighted aggregation of the ICA sources\n", "\n", "For each digit we can aggregate the ICA sources weighting them with the coefficients of the logistic regression. It may give us an idea of the areas of the image the algorithm considers for predicting each class. \n", "\n", "**Note :** In order to improve the visualization we clip each aggregated image to [-std, +std] so that the extreme pixels are highlighted." ] }, { "cell_type": "code", "execution_count": 16, "id": "e0c30155-aa01-4737-96ec-b6936b232f3f", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig , axes = plt.subplots(2, 5, figsize=(20,10))\n", "axes = axes.flatten()\n", "\n", "for i in range(10):\n", " img = (pipe['sICA'].S_*pipe['logistic'].coef_[i,:].reshape(-1,1)).sum(axis=0)\n", " axes[i].imshow(np.clip(img, -img.std(), img.std()).reshape((28,28)))\n", " axes[i].axis(\"off\")" ] } ], "metadata": { "celltoolbar": "Tags", "kernelspec": { "display_name": "Python [conda env:sica_env]", "language": "python", "name": "conda-env-sica_env-py" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.13" } }, "nbformat": 4, "nbformat_minor": 5 }