machine-learning-with-rust/DBSCAN.pdf

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":dep ndarray = \"0.15.6\""
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":dep linfa = { version = \"0.6.1\" }\n",
"// clustering is a separate crate\n",
":dep linfa-clustering = { version = \"0.6.1\" }"
]
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"// apt install libfontconfig-dev on Ubuntu 22.04 LTS\n",
":dep plotters = { version = \"^0.3.4\", default_features = false, features = [\"evcxr\", \"all_series\"] }\n",
"extern crate plotters;\n",
"// Import all the plotters prelude functions\n",
"use plotters::prelude::*;"
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":dep rand = \"0.8.5\""
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"source": [
"// Import the linfa prelude and KMeans algorithm\n",
"use linfa::prelude::*;\n",
"use linfa_clustering::Dbscan;\n",
"// We'll build our dataset on our own using ndarray and rand\n",
"use ndarray::prelude::*;\n",
"// Import the plotters crate to create the scatter plot\n",
"use plotters::prelude::*;"
]
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"use rand::prelude::*;\n",
"use std::f32;"
]
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"// Creates random points contained in an approximately square area\n",
"pub fn create_square(center_point: [f32; 2], edge_length: f32, num_points: usize) -> Array2<f32> {\n",
" // We\n",
" let mut data: Array2<f32> = Array2::zeros((num_points, 2));\n",
" let mut rng = rand::thread_rng();\n",
" for i in 0..num_points {\n",
" let x = rng.gen_range(-edge_length * 0.5..edge_length * 0.5); // generates a float between 0 and 1\n",
" let y = rng.gen_range(-edge_length * 0.5..edge_length * 0.5);\n",
" data[[i, 0]] = center_point[0] + x;\n",
" data[[i, 1]] = center_point[1] + y;\n",
" }\n",
"\n",
" data\n",
"}"
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"// Creates a circle of random points\n",
"pub fn create_circle(center_point: [f32; 2], radius: f32, num_points: usize) -> Array2<f32> {\n",
" let mut data: Array2<f32> = Array2::zeros((num_points, 2));\n",
" let mut rng = rand::thread_rng();\n",
" for i in 0..num_points {\n",
" let theta = rng.gen_range(0.0..2.0 * f32::consts::PI);\n",
" let r = rng.gen_range(0.0..radius);\n",
" let x = r * f32::cos(theta);\n",
" let y = r * f32::sin(theta);\n",
"\n",
" data[[i, 0]] = center_point[0] + x;\n",
" data[[i, 1]] = center_point[1] + y;\n",
" }\n",
"\n",
" data\n",
"}"
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"// Creates a line y = m*x + b with some noise\n",
"pub fn create_line(m: f64, b: f64, num_points: usize, min_max: [f64; 2]) -> Array2<f64> {\n",
" let mut data: Array2<f64> = Array2::zeros((num_points, 2));\n",
"\n",
" let mut rng = rand::thread_rng();\n",
" for i in 0..num_points {\n",
" let var_y = rng.gen_range(-0.5..0.5f64);\n",
" data[[i, 0]] = rng.gen_range(min_max[0]..min_max[1]);\n",
" data[[i, 1]] = (m * data[[i, 0]]) + b + var_y;\n",
" }\n",
"\n",
" data\n",
"}"
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"// Creates a quadratic y = m*x^2 + b with some noise\n",
"pub fn create_curve(m: f64, pow: f64, b: f64, num_points: usize, min_max: [f64; 2]) -> Array2<f64> {\n",
" let mut data: Array2<f64> = Array2::zeros((num_points, 2));\n",
"\n",
" let mut rng = rand::thread_rng();\n",
" for i in 0..num_points {\n",
" let var_y = rng.gen_range(-0.5..0.5f64);\n",
" data[[i, 0]] = rng.gen_range(min_max[0]..min_max[1]);\n",
" data[[i, 1]] = (m * data[[i, 0]].powf(pow)) + b + var_y;\n",
" }\n",
"\n",
" data\n",
"}"
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"// Creates a hollow circle of random points with a specified inner and outer diameter\n",
"pub fn create_hollow_circle(\n",
" center_point: [f32; 2],\n",
" radius: [f32; 2],\n",
" num_points: usize,\n",
") -> Array2<f32> {\n",
" assert!(radius[0] < radius[1]);\n",
" let mut data: Array2<f32> = Array2::zeros((num_points, 2));\n",
" let mut rng = rand::thread_rng();\n",
" for i in 0..num_points {\n",
" let theta = rng.gen_range(0.0..2.0 * f32::consts::PI);\n",
" let r = rng.gen_range(radius[0]..radius[1]);\n",
" let x = r * f32::cos(theta);\n",
" let y = r * f32::sin(theta);\n",
"\n",
" data[[i, 0]] = center_point[0] + x;\n",
" data[[i, 1]] = center_point[1] + y;\n",
" }\n",
"\n",
" data\n",
"}"
]
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"// Check the array has the correct shape for plotting (Two-dimensional, with 2 columns)\n",
"pub fn check_array_for_plotting(arr: &Array2<f32>) -> bool {\n",
" if (arr.shape().len() != 2) || (arr.shape()[1] != 2) {\n",
" panic!(\n",
" \"Array shape of {:?} is incorrect for 2D plotting!\",\n",
" arr.shape()\n",
" );\n",
" // false\n",
" } else {\n",
" true\n",
" }\n",
"}"
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" // The goal is to be able to find each of these as distinct, and exclude some of the noise\n",
"let circle: Array2<f32> = create_circle([5.0, 5.0], 1.0, 100); // Cluster 0\n",
"let donut_1: Array2<f32> = create_hollow_circle([5.0, 5.0], [2.0, 3.0], 400); // Cluster 1\n",
"let donut_2: Array2<f32> = create_hollow_circle([5.0, 5.0], [4.5, 4.75], 1000); // Cluster 2\n",
"let noise: Array2<f32> = create_square([5.0, 5.0], 10.0, 100); // Random noise\n",
"\n",
"\n",
"let data = ndarray::concatenate(\n",
" Axis(0),\n",
" &[circle.view(), donut_1.view(), donut_2.view(), noise.view()],\n",
" )\n",
" .expect(\"An error occurred while stacking the dataset\");\n",
"\n"
]
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]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"evcxr_figure((640, 240), |root| {\n",
" \n",
" root.fill(&WHITE).unwrap();\n",
"\n",
" let x_lim = 0.0..10.0f32;\n",
" let y_lim = 0.0..10.0f32;\n",
"\n",
" let mut ctx = ChartBuilder::on(&root)\n",
" .set_label_area_size(LabelAreaPosition::Left, 40) // Put in some margins\n",
" .set_label_area_size(LabelAreaPosition::Right, 40)\n",
" .set_label_area_size(LabelAreaPosition::Bottom, 40)\n",
" .caption(\"DBSCAN\", (\"sans-serif\", 25)) // Set a caption and font\n",
" .build_cartesian_2d(x_lim, y_lim)\n",
" .expect(\"Couldn't build our ChartBuilder\");\n",
" \n",
" let circle: Array2<f32> = create_circle([5.0, 5.0], 1.0, 100); // Cluster 0\n",
" let donut_1: Array2<f32> = create_hollow_circle([5.0, 5.0], [2.0, 3.0], 400); // Cluster 1\n",
" let donut_2: Array2<f32> = create_hollow_circle([5.0, 5.0], [4.5, 4.75], 1000); // Cluster 2\n",
" let noise: Array2<f32> = create_square([5.0, 5.0], 10.0, 100); // Random noise\n",
"\n",
" let data = ndarray::concatenate(\n",
" Axis(0),\n",
" &[circle.view(), donut_1.view(), donut_2.view(), noise.view()],\n",
" )\n",
" .expect(\"An error occurred while stacking the dataset\");\n",
"\n",
" // Compared to linfa's KMeans algorithm, the DBSCAN implementation can operate\n",
" // directly on an ndarray `Array2` data structure, so there's no need to convert it\n",
" // into the linfa-native `Dataset` first.\n",
" let min_points = 20;\n",
" let clusters = Dbscan::params(min_points)\n",
" .tolerance(0.6)\n",
" .transform(&data)\n",
" .unwrap();\n",
" // println!(\"{:#?}\", clusters);\n",
"\n",
"\n",
" let x_lim = 0.0..10.0f32;\n",
" let y_lim = 0.0..10.0f32;\n",
" \n",
"\n",
" ctx.configure_mesh().draw().unwrap();\n",
" let root_area = ctx.plotting_area();\n",
" // ANCHOR_END: configure_chart\n",
"\n",
" // ANCHOR: run_check_for_plotting;\n",
" // check_array_for_plotting(dataset: &Array2<f32>) -> bool {}\n",
" check_array_for_plotting(&circle); // Panics if that's not true\n",
" // ANCHOR_END: run_check_for_plotting\n",
"\n",
" // ANCHOR: plot_points\n",
" for i in 0..data.shape()[0] {\n",
" let coordinates = data.slice(s![i, 0..2]);\n",
"\n",
" let point = match clusters[i] {\n",
" Some(0) => Circle::new(\n",
" (coordinates[0], coordinates[1]),\n",
" 3,\n",
" ShapeStyle::from(&RED).filled(),\n",
" ),\n",
" Some(1) => Circle::new(\n",
" (coordinates[0], coordinates[1]),\n",
" 3,\n",
" ShapeStyle::from(&GREEN).filled(),\n",
" ),\n",
" Some(2) => Circle::new(\n",
" (coordinates[0], coordinates[1]),\n",
" 3,\n",
" ShapeStyle::from(&BLUE).filled(),\n",
" ),\n",
" // Making sure our pattern-matching is exhaustive\n",
" // Note that we can define a custom color using RGB\n",
" _ => Circle::new(\n",
" (coordinates[0], coordinates[1]),\n",
" 3,\n",
" ShapeStyle::from(&RGBColor(255, 255, 255)).filled(),\n",
" ),\n",
" };\n",
"\n",
" root_area\n",
" .draw(&point)\n",
" .expect(\"An error occurred while drawing the point!\");\n",
" }\n",
" \n",
" Ok(())\n",
"}).style(\"width:90%\")"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "a757a5d6-4105-4c76-a5bb-6ba1af81f3a6",
"metadata": {
"execution": {
"iopub.execute_input": "2023-05-11T15:50:54.720203Z",
"iopub.status.busy": "2023-05-11T15:50:54.719873Z",
"iopub.status.idle": "2023-05-11T15:50:55.771325Z",
"shell.execute_reply": "2023-05-11T15:50:55.771045Z"
},
"papermill": {
"duration": 1.056514,
"end_time": "2023-05-11T15:50:55.771413",
"exception": false,
"start_time": "2023-05-11T15:50:54.714899",
"status": "completed"
},
"tags": []
},
"outputs": [
{
"data": {
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"<div style=\"width:60%\"><svg width=\"640\" height=\"240\" viewBox=\"0 0 640 240\" xmlns=\"http://www.w3.org/2000/svg\">\n",
"<text x=\"320\" y=\"5\" dy=\"0.76em\" text-anchor=\"middle\" font-family=\"Arial\" font-size=\"16.129032258064516\" opacity=\"1\" fill=\"#000000\">\n",
"Hello Plotters Chart Context!\n",
"</text>\n",
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"</svg>\n",
"</div>"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"extern crate plotters;\n",
"use plotters::prelude::*;\n",
"evcxr_figure((640, 240), |root| {\n",
" // The following code will create a chart context\n",
" let mut chart = ChartBuilder::on(&root)\n",
" .caption(\"Hello Plotters Chart Context!\", (\"Arial\", 20).into_font())\n",
" .build_cartesian_2d(0f32..1f32, 0f32..1f32)?;\n",
" // Then we can draw a series on it!\n",
" chart.draw_series((1..10).map(|x|{\n",
" let x = x as f32/10.0;\n",
" Circle::new((x,x), 5, &RED)\n",
" }))?;\n",
" Ok(())\n",
"}).style(\"width:60%\")"
]
},
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