This example shows the reconstruction of an image from a set of parallel projections, acquired along different angles. Such a dataset is acquired in computed tomography (CT). Without any prior information on the sample, the number of projections required to reconstruct the image is of the order of the linear size l of the image (in pixels). For simplicity we consider here a sparse image, where only pixels on the boundary of objects have a non-zero value. Such data could correspond for example

We want to compare the performance of the MiniBatchKMeans and KMeans: the MiniBatchKMeans is faster, but gives slightly different results (see Mini Batch K-Means). We will cluster a set of data, first with KMeans and then with MiniBatchKMeans, and plot the results. We will also plot the points that are labelled differently between the two algorithms. print(__doc__) import time import numpy as np import matplotlib.pyplot as plt from sklearn.cluster import MiniBatchKMeans, KMeans from sklearn

An illustration of dimensionality reduction on the S-curve dataset with various manifold learning methods. For a discussion and comparison of these algorithms, see the manifold module page For a similar example, where the methods are applied to a sphere dataset, see Manifold Learning methods on a severed sphere Note that the purpose of the MDS is to find a low-dimensional representation of the data (here 2D) in which the distances respect well the distances in the original high-dimensional spa

The Iris dataset represents 3 kind of Iris flowers (Setosa, Versicolour and Virginica) with 4 attributes: sepal length, sepal width, petal length and petal width. Principal Component Analysis (PCA) applied to this data identifies the combination of attributes (principal components, or directions in the feature space) that account for the most variance in the data. Here we plot the different samples on the 2 first principal components. Linear Discriminant Analysis (LDA) tries to identify attrib

Both kernel ridge regression (KRR) and SVR learn a non-linear function by employing the kernel trick, i.e., they learn a linear function in the space induced by the respective kernel which corresponds to a non-linear function in the original space. They differ in the loss functions (ridge versus epsilon-insensitive loss). In contrast to SVR, fitting a KRR can be done in closed-form and is typically faster for medium-sized datasets. On the other hand, the learned model is non-sparse and thus sl

Both kernel ridge regression (KRR) and Gaussian process regression (GPR) learn a target function by employing internally the ?kernel trick?. KRR learns a linear function in the space induced by the respective kernel which corresponds to a non-linear function in the original space. The linear function in the kernel space is chosen based on the mean-squared error loss with ridge regularization. GPR uses the kernel to define the covariance of a prior distribution over the target functions and use

This example illustrates the differences between univariate F-test statistics and mutual information. We consider 3 features x_1, x_2, x_3 distributed uniformly over [0, 1], the target depends on them as follows: y = x_1 + sin(6 * pi * x_2) + 0.1 * N(0, 1), that is the third features is completely irrelevant. The code below plots the dependency of y against individual x_i and normalized values of univariate F-tests statistics and mutual information. As F-test captures only linear dependency, i

Well calibrated classifiers are probabilistic classifiers for which the output of the predict_proba method can be directly interpreted as a confidence level. For instance a well calibrated (binary) classifier should classify the samples such that among the samples to which it gave a predict_proba value close to 0.8, approx. 80% actually belong to the positive class. LogisticRegression returns well calibrated predictions as it directly optimizes log-loss. In contrast, the other methods return b

An example showing how different online solvers perform on the hand-written digits dataset. Out: training SGD training ASGD training Perceptron training Passive-Aggressive I training Passive-Aggressive II training SAG # Author: Rob Zinkov <rob at zinkov dot com> # License: BSD 3 clause import numpy as np import matplotlib.pyplot as plt from sklearn import datasets from sklearn.model_selection import train_test_split from sklearn.linear_model import SGDClassifier, Perceptron fro

Compare randomized search and grid search for optimizing hyperparameters of a random forest. All parameters that influence the learning are searched simultaneously (except for the number of estimators, which poses a time / quality tradeoff). The randomized search and the grid search explore exactly the same space of parameters. The result in parameter settings is quite similar, while the run time for randomized search is drastically lower. The performance is slightly worse for the randomized s