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josevalim committed May 7, 2024
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7 changes: 2 additions & 5 deletions lib/scholar/manifold/mds.ex
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defmodule Scholar.Manifold.MDS do
@moduledoc """
TSNE (t-Distributed Stochastic Neighbor Embedding) is a nonlinear dimensionality reduction technique.
## References
* [t-SNE: t-Distributed Stochastic Neighbor Embedding](http://www.jmlr.org/papers/volume9/vandermaaten08a/vandermaaten08a.pdf)
Multidimensional scaling (MDS) seeks a low-dimensional representation of the data
in which the distances respect well the distances in the original high-dimensional space.
"""
import Nx.Defn
import Scholar.Shared
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2 changes: 1 addition & 1 deletion notebooks/cv_gradient_boosting_tree.livemd
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# Using cross-validation with gradient boosting trees
# Cross-validation with gradient boosting trees

```elixir
Mix.install([
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2 changes: 1 addition & 1 deletion notebooks/hierarchical_clustering.livemd
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# Hierarchical Clustering
# Hierarchical clustering

```elixir
app_root = Path.join(__DIR__, "..")
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2 changes: 1 addition & 1 deletion notebooks/k_means.livemd
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<!-- livebook:{"persist_outputs":true} -->

# K-means clustering
# k-means clustering

```elixir
Mix.install([
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2 changes: 1 addition & 1 deletion notebooks/k_nearest_neighbors.livemd
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<!-- livebook:{"persist_outputs":true} -->

# K-Nearest Neighbors
# k-nearest neighbors

```elixir
Mix.install([
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2 changes: 1 addition & 1 deletion notebooks/linear_regression.livemd
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<!-- livebook:{"persist_outputs":true} -->

# Linear Regression in Practice
# Linear regression in practice

```elixir
Mix.install([
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6 changes: 4 additions & 2 deletions notebooks/mds.livemd
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# MDS
# Multidimensional scaling (MDS)

```elixir
Mix.install([
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## Swiss Roll

Multidimensional scaling (MDS) seeks a low-dimensional representation of the data in which the distances respect well the distances in the original high-dimensional space.

The first example demonstrating MDS will use so-called Swiss Roll dataset. It's call as such because it resembles a popular sponge cake. Let's have a look on this dataset.

| ![Skewness](https://scikit-learn.org/stable/_images/sphx_glr_plot_swissroll_001.png) |
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Let's look how one of the images look like

```elixir
image =
image =
Nx.reshape(digits_data[[1234, ..]], {image_height, image_width})
|> Nx.as_type({:u, 8})

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