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dev/_downloads/264f6891fa2130246a013d5f089e7b2e/plot_svm_kernels.ipynb

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"cell_type": "markdown",
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"We can see that the decision boundaries obtained with the sigmoid kernel\nappear curved and irregular. The decision boundary tries to separate the\nclasses by fitting a sigmoid-shaped curve, resulting in a complex boundary\nthat may not generalize well to unseen data. From this example it becomes\nobvious, that the sigmoid kernel has very specific use cases, when dealing\nwith data that exhibits a sigmoidal shape. In this example, careful fine\ntuning might find more generalizable decision boundaries. Because of it's\nspecificity, the sigmoid kernel is less commonly used in practice compared to\nother kernels.\n\n## Conclusion\nIn this example, we have visualized the decision boundaries trained with the\nprovided dataset. The plots serve as an intuitive demonstration of how\ndifferent kernels utilize the training data to determine the classification\nboundaries.\n\nThe hyperplanes and margins, although computed indirectly, can be imagined as\nplanes in the transformed feature space. However, in the plots, they are\nrepresented relative to the original feature space, resulting in curved\ndecision boundaries for the polynomial, RBF, and sigmoid kernels.\n\nPlease note that the plots do not evaluate the individual kernel's accuracy or\nquality. They are intended to provide a visual understanding of how the\ndifferent kernels use the training data.\n\nFor a comprehensive evaluation, fine-tuning of :class:`~sklearn.svm.SVC`\nparameters using techniques such as\n:class:`~sklearn.model_selection.GridSearchCV` is recommended to capture the\nunderlying structures within the data.\n\n"
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"We can see that the decision boundaries obtained with the sigmoid kernel\nappear curved and irregular. The decision boundary tries to separate the\nclasses by fitting a sigmoid-shaped curve, resulting in a complex boundary\nthat may not generalize well to unseen data. From this example it becomes\nobvious, that the sigmoid kernel has very specific use cases, when dealing\nwith data that exhibits a sigmoidal shape. In this example, careful fine\ntuning might find more generalizable decision boundaries. Because of its\nspecificity, the sigmoid kernel is less commonly used in practice compared to\nother kernels.\n\n## Conclusion\nIn this example, we have visualized the decision boundaries trained with the\nprovided dataset. The plots serve as an intuitive demonstration of how\ndifferent kernels utilize the training data to determine the classification\nboundaries.\n\nThe hyperplanes and margins, although computed indirectly, can be imagined as\nplanes in the transformed feature space. However, in the plots, they are\nrepresented relative to the original feature space, resulting in curved\ndecision boundaries for the polynomial, RBF, and sigmoid kernels.\n\nPlease note that the plots do not evaluate the individual kernel's accuracy or\nquality. They are intended to provide a visual understanding of how the\ndifferent kernels use the training data.\n\nFor a comprehensive evaluation, fine-tuning of :class:`~sklearn.svm.SVC`\nparameters using techniques such as\n:class:`~sklearn.model_selection.GridSearchCV` is recommended to capture the\nunderlying structures within the data.\n\n"
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dev/_downloads/6b00e458f3e282f1cc421f077b2fcad1/plot_spectral_biclustering.ipynb

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"cell_type": "markdown",
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"metadata": {},
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"## Generate sample data\nWe generate the sample data using the\n:func:`~sklearn.datasets.make_checkerboard` function. Each pixel within\n`shape=(300, 300)` represents with it's color a value from a uniform\ndistribution. The noise is added from a normal distribution, where the value\nchosen for `noise` is the standard deviation.\n\nAs you can see, the data is distributed over 12 cluster cells and is\nrelatively well distinguishable.\n\n"
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"## Generate sample data\nWe generate the sample data using the\n:func:`~sklearn.datasets.make_checkerboard` function. Each pixel within\n`shape=(300, 300)` represents with its color a value from a uniform\ndistribution. The noise is added from a normal distribution, where the value\nchosen for `noise` is the standard deviation.\n\nAs you can see, the data is distributed over 12 cluster cells and is\nrelatively well distinguishable.\n\n"
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dev/_downloads/8975399471ae75debd0b26fbe3013719/plot_svm_kernels.py

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# that may not generalize well to unseen data. From this example it becomes
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# obvious, that the sigmoid kernel has very specific use cases, when dealing
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# with data that exhibits a sigmoidal shape. In this example, careful fine
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# tuning might find more generalizable decision boundaries. Because of it's
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# tuning might find more generalizable decision boundaries. Because of its
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# specificity, the sigmoid kernel is less commonly used in practice compared to
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# other kernels.
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#
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dev/_downloads/ac19db97f4bbd077ccffef2736ed5f3d/plot_spectral_biclustering.py

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# --------------------
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# We generate the sample data using the
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# :func:`~sklearn.datasets.make_checkerboard` function. Each pixel within
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# `shape=(300, 300)` represents with it's color a value from a uniform
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# `shape=(300, 300)` represents with its color a value from a uniform
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# distribution. The noise is added from a normal distribution, where the value
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# chosen for `noise` is the standard deviation.
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#
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dev/_downloads/bc88e7ec572d6d2d2ff19cf0d75265c9/plot_agglomerative_clustering_metrics.py

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We add observation noise to these waveforms. We generate very sparse
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noise: only 6% of the time points contain noise. As a result, the
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l1 norm of this noise (ie "cityblock" distance) is much smaller than it's
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l1 norm of this noise (ie "cityblock" distance) is much smaller than its
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l2 norm ("euclidean" distance). This can be seen on the inter-class
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distance matrices: the values on the diagonal, that characterize the
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spread of the class, are much bigger for the Euclidean distance than for
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dev/_downloads/e7d5500e87a046a110ca0daebd702588/plot_agglomerative_clustering_metrics.ipynb

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"cell_type": "markdown",
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"\n# Agglomerative clustering with different metrics\n\nDemonstrates the effect of different metrics on the hierarchical clustering.\n\nThe example is engineered to show the effect of the choice of different\nmetrics. It is applied to waveforms, which can be seen as\nhigh-dimensional vector. Indeed, the difference between metrics is\nusually more pronounced in high dimension (in particular for euclidean\nand cityblock).\n\nWe generate data from three groups of waveforms. Two of the waveforms\n(waveform 1 and waveform 2) are proportional one to the other. The cosine\ndistance is invariant to a scaling of the data, as a result, it cannot\ndistinguish these two waveforms. Thus even with no noise, clustering\nusing this distance will not separate out waveform 1 and 2.\n\nWe add observation noise to these waveforms. We generate very sparse\nnoise: only 6% of the time points contain noise. As a result, the\nl1 norm of this noise (ie \"cityblock\" distance) is much smaller than it's\nl2 norm (\"euclidean\" distance). This can be seen on the inter-class\ndistance matrices: the values on the diagonal, that characterize the\nspread of the class, are much bigger for the Euclidean distance than for\nthe cityblock distance.\n\nWhen we apply clustering to the data, we find that the clustering\nreflects what was in the distance matrices. Indeed, for the Euclidean\ndistance, the classes are ill-separated because of the noise, and thus\nthe clustering does not separate the waveforms. For the cityblock\ndistance, the separation is good and the waveform classes are recovered.\nFinally, the cosine distance does not separate at all waveform 1 and 2,\nthus the clustering puts them in the same cluster.\n"
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"\n# Agglomerative clustering with different metrics\n\nDemonstrates the effect of different metrics on the hierarchical clustering.\n\nThe example is engineered to show the effect of the choice of different\nmetrics. It is applied to waveforms, which can be seen as\nhigh-dimensional vector. Indeed, the difference between metrics is\nusually more pronounced in high dimension (in particular for euclidean\nand cityblock).\n\nWe generate data from three groups of waveforms. Two of the waveforms\n(waveform 1 and waveform 2) are proportional one to the other. The cosine\ndistance is invariant to a scaling of the data, as a result, it cannot\ndistinguish these two waveforms. Thus even with no noise, clustering\nusing this distance will not separate out waveform 1 and 2.\n\nWe add observation noise to these waveforms. We generate very sparse\nnoise: only 6% of the time points contain noise. As a result, the\nl1 norm of this noise (ie \"cityblock\" distance) is much smaller than its\nl2 norm (\"euclidean\" distance). This can be seen on the inter-class\ndistance matrices: the values on the diagonal, that characterize the\nspread of the class, are much bigger for the Euclidean distance than for\nthe cityblock distance.\n\nWhen we apply clustering to the data, we find that the clustering\nreflects what was in the distance matrices. Indeed, for the Euclidean\ndistance, the classes are ill-separated because of the noise, and thus\nthe clustering does not separate the waveforms. For the cityblock\ndistance, the separation is good and the waveform classes are recovered.\nFinally, the cosine distance does not separate at all waveform 1 and 2,\nthus the clustering puts them in the same cluster.\n"
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dev/_downloads/scikit-learn-docs.zip

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