diff --git a/rdas/AS.ipynb b/rdas/AS.ipynb
new file mode 100644
index 0000000..2d3814a
--- /dev/null
+++ b/rdas/AS.ipynb
@@ -0,0 +1,10223 @@
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+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "955e580d",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import plotly.express as px\n",
+ "import plotly.graph_objects as go\n",
+ "\n",
+ "import numpy as np\n",
+ "\n",
+ "from sklearn.datasets import make_s_curve, make_circles"
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+ "id": "c72b7800",
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+ "source": [
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+ "n_samples = 100\n",
+ "\n",
+ "X, y = make_circles(n_samples=n_samples, noise=0.1, random_state=42)\n",
+ "X = np.hstack([X, y.reshape(-1, 1)])\n",
+ "\n",
+ "fig = go.Figure(data=[go.Scatter3d(x=X[:, 0], y=X[:, 1], z=X[:, 2],\n",
+ " mode='markers')])\n",
+ "\n",
+ "fig.update_layout(\n",
+ " title=f\"Circles. N_samples: {n_samples}; Noise: {noise_mc}\",\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "593f3b42",
+ "metadata": {},
+ "source": [
+ "# Dataset Generator"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "id": "1b5c896b",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import random\n",
+ "\n",
+ "class DatasetGenerator:\n",
+ " def __init__(self, dim_of_space, dim_of_manifold):\n",
+ " self.dim_of_space = dim_of_space\n",
+ " self.dim_of_manifold = dim_of_manifold\n",
+ "\n",
+ " def generate_dataset_in_subspace(self, n_samples, seed_value=42):\n",
+ " \"\"\"\n",
+ " Generate a dataset that lies along a low-dimensional subspace within a high-dimensional space.\n",
+ "\n",
+ " Parameters:\n",
+ " - num_samples: Number of data points to generate.\n",
+ " - dim_of_space: Dimension of the high-dimensional space (L).\n",
+ " - dim_of_subspace: Dimension of the low-dimensional subspace (l).\n",
+ "\n",
+ " Returns:\n",
+ " - dataset: NumPy array with shape (num_samples, dim_of_space)\n",
+ " \"\"\"\n",
+ " np.random.seed(seed_value)\n",
+ " # Generate a random orthonormal basis for the subspace\n",
+ " basis = np.linalg.qr(np.random.randn(self.dim_of_space, self.dim_of_manifold))[0]\n",
+ " # Generate random coefficients for the linear combination\n",
+ " coefficients = np.random.randn(n_samples, self.dim_of_manifold)\n",
+ " # Compute the dataset by projecting random points onto the subspace\n",
+ " dataset = np.dot(coefficients, basis.T)\n",
+ "\n",
+ " return dataset\n",
+ "\n",
+ " def generate_lines_planes(self, n_samples, scale, noise, line_params):\n",
+ " \"\"\"\n",
+ " Generate a dataset of straight lines in either a 2D plane or 3D space.\n",
+ "\n",
+ " Parameters:\n",
+ " - n_samples: Number of samples in the dataset.\n",
+ " - plane: If True, generate lines in a 2D plane. If False, generate lines in 3D space.\n",
+ "\n",
+ " Returns:\n",
+ " - dataset: NumPy array with shape (n_samples, dim_of_space)\n",
+ " \"\"\"\n",
+ " if self.dim_of_space not in [2, 3]:\n",
+ " raise ValueError(\"dim_of_space must be either 2 or 3.\")\n",
+ " dataset = np.zeros((n_samples, self.dim_of_space))\n",
+ " if self.dim_of_space == 2:\n",
+ " k, b = line_params\n",
+ " else:\n",
+ " if self.dim_of_manifold == 2: # plane in 3D space\n",
+ " a, b, c = line_params\n",
+ " if self.dim_of_manifold == 1:\n",
+ " p_0, p_1, p_2, x_0, y_0, z_0 = line_params\n",
+ "\n",
+ " for i in range(n_samples):\n",
+ " eps = noise * np.random.normal()\n",
+ " # Generate random parameters for the line\n",
+ " if self.dim_of_space == 2:\n",
+ " x = scale * np.random.rand()\n",
+ " y = k * x + b + eps\n",
+ " dataset[i] = [x, y]\n",
+ " else:\n",
+ " if self.dim_of_manifold == 2:\n",
+ " x = scale * np.random.rand(self.dim_of_space - 1)\n",
+ " y = a * x[0] + b * x[1] + c + eps\n",
+ " dataset[i] = [x[0], x[1], y]\n",
+ " if self.dim_of_manifold == 1:\n",
+ " t = scale * np.random.rand()\n",
+ " x = x_0 + p_0 * t + noise * np.random.normal()\n",
+ " y = y_0 + p_1 * t + noise * np.random.normal()\n",
+ " z = z_0 + p_2 * t + noise * np.random.normal()\n",
+ " dataset[i] = [x, y, z]\n",
+ " return dataset\n"
+ ]
+ },
+ {
+ "cell_type": "code",
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+ "source": [
+ "# Example usage:\n",
+ "dim_of_space = 3\n",
+ "dim_of_manifold = 2\n",
+ "n_samples = 100\n",
+ "\n",
+ "plane_generator = DatasetGenerator(dim_of_space, dim_of_manifold)\n",
+ "X = plane_generator.generate_lines_planes(n_samples, scale=100, noise=100, line_params = [10,7,30])\n",
+ "\n",
+ "\n",
+ "fig = go.Figure(data=[go.Scatter3d(x=X[:, 0], y=X[:, 1], z=X[:, 2],\n",
+ " mode='markers')])\n",
+ "\n",
+ "fig.update_layout(\n",
+ " title=f\"Plane. N_samples: {n_samples}; Noise: {noise_mc}\",\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a2a7eb53",
+ "metadata": {},
+ "source": [
+ "# PDF"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "id": "5d6a6397",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "from sklearn.neighbors import KernelDensity\n",
+ "from scipy.optimize import approx_fprime\n",
+ "\n",
+ "class KDEProbabilityDensityFunction:\n",
+ " def __init__(self, data, kernel='gaussian'):\n",
+ " self.data = data\n",
+ " self.kernel = kernel\n",
+ " self.kde_model = self._fit_kde()\n",
+ "\n",
+ " def _fit_kde(self):\n",
+ " kde_model = KernelDensity(kernel=self.kernel)\n",
+ " kde_model.fit(self.data)\n",
+ " return kde_model\n",
+ "\n",
+ " def value(self, x):\n",
+ " # Reshape x to match the input dimensions\n",
+ " x = np.array(x).reshape(1, -1)\n",
+ " return np.exp(self.kde_model.score_samples(x))\n",
+ "\n",
+ " def grad(self, x, epsilon=1e-5):\n",
+ " x = np.array(x)\n",
+ "\n",
+ " def func(x):\n",
+ " return np.log(self.value(x))\n",
+ "\n",
+ " # Use numerical approximation for gradient\n",
+ " gradient = approx_fprime(x, func, epsilon)\n",
+ " return gradient"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "aec18b70",
+ "metadata": {},
+ "source": [
+ "# Active subspace"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "id": "c9e9ebd4",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "dataset = plane_generator.generate_lines_planes(1000, scale=100, noise=10, line_params = [10,7,30])\n",
+ "\n",
+ "X, y = make_circles(n_samples=n_samples, noise=0.1, random_state=42)\n",
+ "dataset = np.hstack([X, y.reshape(-1, 1)])\n",
+ "\n",
+ "dataset, t = make_s_curve(n_samples=100, noise=0.2, random_state=42)\n",
+ "\n",
+ "kde_pdf = KDEProbabilityDensityFunction(dataset, kernel='gaussian')\n",
+ "\n",
+ "point = np.ones(dataset.shape[1])\n",
+ "pdf_value = kde_pdf.value(point)\n",
+ "pdf_gradient = kde_pdf.grad(point)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "id": "2b424855",
+ "metadata": {},
+ "outputs": [
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+ "fig = go.Figure(data=[go.Scatter3d(x=dataset[:, 0], y=dataset[:, 1], z=dataset[:, 2],\n",
+ " mode='markers')])\n",
+ "fig.update_layout(\n",
+ " title=f\"Dataset\",\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "id": "765df221",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from typing import Callable\n",
+ "import numpy as np\n",
+ "\n",
+ "def check_input(X):\n",
+ " # X : ndarray of input samples\n",
+ "\n",
+ " assert len(X.shape) == 2 and type(X) == np.ndarray, 'X should be a 2d numpy array'\n",
+ " N, d = X.shape\n",
+ " return X, N, d\n",
+ "\n",
+ "def get_n(S, eps=1e-8):\n",
+ " ediff = np.fabs(np.diff(S.reshape((S.size,))))\n",
+ " n = np.argmax(ediff)+1\n",
+ "\n",
+ " return n\n",
+ "\n",
+ "def compute_AS(X: np.ndarray, kde_pdf) -> np.ndarray:\n",
+ " # X : ndarray - input samples\n",
+ " # f_deriv : Callable - function derivative\n",
+ "\n",
+ " X, N, d = check_input(X)\n",
+ "\n",
+ " G = 1/np.sqrt(N) * np.column_stack([kde_pdf.grad(x) for x in dataset])\n",
+ " U, S, Vh = np.linalg.svd(G)\n",
+ " \n",
+ " # print(S)\n",
+ " \n",
+ " return get_n(S)"
+ ]
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+ "id": "4ff1d51a",
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+ "2\n"
+ ]
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+ "source": [
+ "n = compute_AS(dataset, kde_pdf)\n",
+ "print(n)"
+ ]
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+ "new = np.array([U[:, :n].T @ x for x in dataset])\n",
+ "\n",
+ "px.scatter(x=new[:, 0], y=new[:, 1])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f423aad3",
+ "metadata": {},
+ "source": [
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+ "execution_count": 20,
+ "id": "73845bf2",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "n_samples = 1000\n",
+ "dim_of_space = 50\n",
+ "dim_of_manifold = 15\n",
+ "\n",
+ "# plane_generator = DatasetGenerator(dim_of_space, dim_of_manifold)\n",
+ "# dataset = plane_generator.generate_dataset_in_subspace(n_samples, seed_value=71)\n",
+ "\n",
+ "plane_generator = DatasetGenerator(3, 1)\n",
+ "dataset = plane_generator.generate_lines_planes(n_samples, scale = 100, noise=0.3, line_params = [1,2,3,4,5,6])\n",
+ "\n",
+ "fig = go.Figure(data=[go.Scatter3d(x=dataset[:, 0], y=dataset[:, 1], z=dataset[:, 2],\n",
+ " mode='markers')])\n",
+ "fig.update_layout(\n",
+ " title=f\"Dataset\",\n",
+ ")\n",
+ "\n",
+ "kde_pdf = KDEProbabilityDensityFunction(dataset, kernel='gaussian')\n",
+ "\n",
+ "point = np.ones(dataset.shape[1])\n",
+ "pdf_value = kde_pdf.value(point)\n",
+ "pdf_gradient = kde_pdf.grad(point)"
+ ]
+ },
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+ " mode='markers')])\n",
+ "fig.update_layout(\n",
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+ },
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+ "cell_type": "code",
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+ "def gen_n_points(dataset, n_points, eps_range=0.01):\n",
+ " n, m = dataset.shape\n",
+ " \n",
+ " sample = []\n",
+ "# random_point = dataset[np.random.randint(n)]\n",
+ " random_point = np.array([0, 0, 0])\n",
+ " \n",
+ " for i in range(n_points):\n",
+ " eps = np.random.uniform(-1*eps_range, eps_range, m)\n",
+ " nearby_point = random_point + eps\n",
+ " \n",
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+ " return np.array(sample)"
+ ]
+ },
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+}
diff --git a/rdas/AS.py b/rdas/AS.py
index e69de29..24c8f63 100644
--- a/rdas/AS.py
+++ b/rdas/AS.py
@@ -0,0 +1,26 @@
+from typing import Callable
+import numpy as np
+
+def check_input(X):
+ # X : ndarray of input samples
+
+ assert len(X.shape) == 2 and type(X) == np.ndarray, 'X should be a 2d numpy array'
+ N, d = X.shape
+ return X, N, d
+
+def get_n(S):
+ ediff = np.fabs(np.diff(S.reshape((S.size,))))
+ n = np.argmax(ediff)+1
+
+ return n
+
+def compute_AS(X: np.ndarray, kde_pdf) -> np.ndarray:
+ # X : ndarray - input samples
+ # f_deriv : Callable - function derivative
+
+ X, N, d = check_input(X)
+
+ G = 1/np.sqrt(N) * np.column_stack([kde_pdf.grad(x) for x in X])
+ U, S, Vh = np.linalg.svd(G)
+
+ return get_n(S)
\ No newline at end of file
diff --git a/rdas/Manifold.ipynb b/rdas/Manifold.ipynb
new file mode 100644
index 0000000..af4c712
--- /dev/null
+++ b/rdas/Manifold.ipynb
@@ -0,0 +1,10227 @@
+{
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+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "955e580d",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import plotly.express as px\n",
+ "import plotly.graph_objects as go\n",
+ "\n",
+ "import numpy as np\n",
+ "\n",
+ "from sklearn.datasets import make_s_curve, make_circles"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c72b7800",
+ "metadata": {},
+ "source": [
+ "# S-curve"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "id": "444771b7",
+ "metadata": {
+ "scrolled": false
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+ "source": [
+ "n_samples = 100\n",
+ "\n",
+ "X, y = make_circles(n_samples=n_samples, noise=0.1, random_state=42)\n",
+ "X = np.hstack([X, y.reshape(-1, 1)])\n",
+ "\n",
+ "fig = go.Figure(data=[go.Scatter3d(x=X[:, 0], y=X[:, 1], z=X[:, 2],\n",
+ " mode='markers')])\n",
+ "\n",
+ "fig.update_layout(\n",
+ " title=f\"Circles. N_samples: {n_samples}; Noise: {noise_mc}\",\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cd328619",
+ "metadata": {},
+ "source": [
+ "# Dataset Generator"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "id": "d6b5cb0f",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import random\n",
+ "\n",
+ "class DatasetGenerator:\n",
+ " def __init__(self, dim_of_space, dim_of_manifold):\n",
+ " self.dim_of_space = dim_of_space\n",
+ " self.dim_of_manifold = dim_of_manifold\n",
+ "\n",
+ " def generate_dataset_in_subspace(self, n_samples, seed_value=42):\n",
+ " \"\"\"\n",
+ " Generate a dataset that lies along a low-dimensional subspace within a high-dimensional space.\n",
+ "\n",
+ " Parameters:\n",
+ " - num_samples: Number of data points to generate.\n",
+ " - dim_of_space: Dimension of the high-dimensional space (L).\n",
+ " - dim_of_subspace: Dimension of the low-dimensional subspace (l).\n",
+ "\n",
+ " Returns:\n",
+ " - dataset: NumPy array with shape (num_samples, dim_of_space)\n",
+ " \"\"\"\n",
+ " np.random.seed(seed_value)\n",
+ " # Generate a random orthonormal basis for the subspace\n",
+ " basis = np.linalg.qr(np.random.randn(self.dim_of_space, self.dim_of_manifold))[0]\n",
+ " # Generate random coefficients for the linear combination\n",
+ " coefficients = np.random.randn(n_samples, self.dim_of_manifold)\n",
+ " # Compute the dataset by projecting random points onto the subspace\n",
+ " dataset = np.dot(coefficients, basis.T)\n",
+ "\n",
+ " return dataset\n",
+ "\n",
+ " def generate_lines_planes(self, n_samples, scale, noise, line_params):\n",
+ " \"\"\"\n",
+ " Generate a dataset of straight lines in either a 2D plane or 3D space.\n",
+ "\n",
+ " Parameters:\n",
+ " - n_samples: Number of samples in the dataset.\n",
+ " - plane: If True, generate lines in a 2D plane. If False, generate lines in 3D space.\n",
+ "\n",
+ " Returns:\n",
+ " - dataset: NumPy array with shape (n_samples, dim_of_space)\n",
+ " \"\"\"\n",
+ " if self.dim_of_space not in [2, 3]:\n",
+ " raise ValueError(\"dim_of_space must be either 2 or 3.\")\n",
+ " dataset = np.zeros((n_samples, self.dim_of_space))\n",
+ " if self.dim_of_space == 2:\n",
+ " k, b = line_params\n",
+ " else:\n",
+ " if self.dim_of_manifold == 2: # plane in 3D space\n",
+ " a, b, c = line_params\n",
+ " if self.dim_of_manifold == 1:\n",
+ " p_0, p_1, p_2, x_0, y_0, z_0 = line_params\n",
+ "\n",
+ " for i in range(n_samples):\n",
+ " eps = noise * np.random.normal()\n",
+ " # Generate random parameters for the line\n",
+ " if self.dim_of_space == 2:\n",
+ " x = scale * np.random.rand()\n",
+ " y = k * x + b + eps\n",
+ " dataset[i] = [x, y]\n",
+ " else:\n",
+ " if self.dim_of_manifold == 2:\n",
+ " x = scale * np.random.rand(self.dim_of_space - 1)\n",
+ " y = a * x[0] + b * x[1] + c + eps\n",
+ " dataset[i] = [x[0], x[1], y]\n",
+ " if self.dim_of_manifold == 1:\n",
+ " t = scale * np.random.rand()\n",
+ " x = x_0 + p_0 * t + noise * np.random.normal()\n",
+ " y = y_0 + p_1 * t + noise * np.random.normal()\n",
+ " z = z_0 + p_2 * t + noise * np.random.normal()\n",
+ " dataset[i] = [x, y, z]\n",
+ " return dataset\n"
+ ]
+ },
+ {
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+ "# Example usage:\n",
+ "dim_of_space = 3\n",
+ "dim_of_manifold = 2\n",
+ "n_samples = 100\n",
+ "\n",
+ "plane_generator = DatasetGenerator(dim_of_space, dim_of_manifold)\n",
+ "X = plane_generator.generate_lines_planes(n_samples, scale=100, noise=100, line_params = [10,7,30])\n",
+ "\n",
+ "\n",
+ "fig = go.Figure(data=[go.Scatter3d(x=X[:, 0], y=X[:, 1], z=X[:, 2],\n",
+ " mode='markers')])\n",
+ "\n",
+ "fig.update_layout(\n",
+ " title=f\"Plane. N_samples: {n_samples}; Noise: {noise_mc}\",\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "94f16647",
+ "metadata": {},
+ "source": [
+ "# PDF"
+ ]
+ },
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+ "cell_type": "code",
+ "execution_count": 6,
+ "id": "a5180917",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "from sklearn.neighbors import KernelDensity\n",
+ "from scipy.optimize import approx_fprime\n",
+ "\n",
+ "class KDEProbabilityDensityFunction:\n",
+ " def __init__(self, data, kernel='gaussian'):\n",
+ " self.data = data\n",
+ " self.kernel = kernel\n",
+ " self.kde_model = self._fit_kde()\n",
+ "\n",
+ " def _fit_kde(self):\n",
+ " kde_model = KernelDensity(kernel=self.kernel)\n",
+ " kde_model.fit(self.data)\n",
+ " return kde_model\n",
+ "\n",
+ " def value(self, x):\n",
+ " # Reshape x to match the input dimensions\n",
+ " x = np.array(x).reshape(1, -1)\n",
+ " return np.exp(self.kde_model.score_samples(x))\n",
+ "\n",
+ " def grad(self, x, epsilon=1e-5):\n",
+ " x = np.array(x)\n",
+ "\n",
+ " def func(x):\n",
+ " return np.log(self.value(x))\n",
+ "\n",
+ " # Use numerical approximation for gradient\n",
+ " gradient = approx_fprime(x, func, epsilon)\n",
+ " return gradient"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "93c0ca50",
+ "metadata": {},
+ "source": [
+ "# Active subspace"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "id": "1f325271",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "dataset = plane_generator.generate_lines_planes(1000, scale=100, noise=10, line_params = [10,7,30])\n",
+ "\n",
+ "X, y = make_circles(n_samples=n_samples, noise=0.1, random_state=42)\n",
+ "dataset = np.hstack([X, y.reshape(-1, 1)])\n",
+ "\n",
+ "dataset, t = make_s_curve(n_samples=100, noise=0.2, random_state=42)\n",
+ "\n",
+ "kde_pdf = KDEProbabilityDensityFunction(dataset, kernel='gaussian')\n",
+ "\n",
+ "point = np.ones(dataset.shape[1])\n",
+ "pdf_value = kde_pdf.value(point)\n",
+ "pdf_gradient = kde_pdf.grad(point)"
+ ]
+ },
+ {
+ "cell_type": "code",
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+ "source": [
+ "fig = go.Figure(data=[go.Scatter3d(x=dataset[:, 0], y=dataset[:, 1], z=dataset[:, 2],\n",
+ " mode='markers')])\n",
+ "fig.update_layout(\n",
+ " title=f\"Dataset\",\n",
+ ")"
+ ]
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+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "id": "4e388e6d",
+ "metadata": {},
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+ "source": [
+ "from typing import Callable\n",
+ "import numpy as np\n",
+ "\n",
+ "def check_input(X):\n",
+ " # X : ndarray of input samples\n",
+ "\n",
+ " assert len(X.shape) == 2 and type(X) == np.ndarray, 'X should be a 2d numpy array'\n",
+ " N, d = X.shape\n",
+ " return X, N, d\n",
+ "\n",
+ "def get_n(S, eps=1e-8):\n",
+ " ediff = np.fabs(np.diff(S.reshape((S.size,))))\n",
+ " n = np.argmax(ediff)+1\n",
+ "\n",
+ " return n\n",
+ "\n",
+ "def compute_AS(X: np.ndarray, kde_pdf) -> np.ndarray:\n",
+ " # X : ndarray - input samples\n",
+ " # f_deriv : Callable - function derivative\n",
+ "\n",
+ " X, N, d = check_input(X)\n",
+ "\n",
+ " G = 1/np.sqrt(N) * np.column_stack([kde_pdf.grad(x) for x in X])\n",
+ " U, S, Vh = np.linalg.svd(G)\n",
+ " \n",
+ " # print(S)\n",
+ " \n",
+ " return U, S, get_n(S)"
+ ]
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+ "id": "466eb6a4",
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+ "name": "stdout",
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+ "text": [
+ "2\n"
+ ]
+ }
+ ],
+ "source": [
+ "U, S, n = compute_AS(dataset, kde_pdf)\n",
+ "print(n)"
+ ]
+ },
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+ "id": "80404984",
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+ "source": [
+ "new = np.array([U[:, :n].T @ x for x in dataset])\n",
+ "\n",
+ "px.scatter(x=new[:, 0], y=new[:, 1])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "22eac299",
+ "metadata": {},
+ "source": [
+ "# Sub-sample"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "id": "e8551cd7",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "n_samples = 1000\n",
+ "dim_of_space = 50\n",
+ "dim_of_manifold = 15\n",
+ "\n",
+ "# plane_generator = DatasetGenerator(dim_of_space, dim_of_manifold)\n",
+ "# dataset = plane_generator.generate_dataset_in_subspace(n_samples, seed_value=71)\n",
+ "\n",
+ "plane_generator = DatasetGenerator(3, 1)\n",
+ "dataset = plane_generator.generate_lines_planes(n_samples, scale = 100, noise=0.3, line_params = [1,2,3,4,5,6])\n",
+ "\n",
+ "fig = go.Figure(data=[go.Scatter3d(x=dataset[:, 0], y=dataset[:, 1], z=dataset[:, 2],\n",
+ " mode='markers')])\n",
+ "fig.update_layout(\n",
+ " title=f\"Dataset\",\n",
+ ")\n",
+ "\n",
+ "kde_pdf = KDEProbabilityDensityFunction(dataset, kernel='gaussian')\n",
+ "\n",
+ "point = np.ones(dataset.shape[1])\n",
+ "pdf_value = kde_pdf.value(point)\n",
+ "pdf_gradient = kde_pdf.grad(point)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "id": "a339bcbc",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "application/vnd.plotly.v1+json": {
+ "config": {
+ "plotlyServerURL": "https://plot.ly"
+ },
+ "data": [
+ {
+ "mode": "markers",
+ "type": "scatter3d",
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+ "source": [
+ "fig = go.Figure(data=[go.Scatter3d(x=dataset[:, 0], y=dataset[:, 1], z=dataset[:, 2],\n",
+ " mode='markers')])\n",
+ "fig.update_layout(\n",
+ " title=f\"Dataset\",\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "id": "04e047ae",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def gen_n_points(dataset, n_points, eps_range=0.01):\n",
+ " n, m = dataset.shape\n",
+ " \n",
+ " sample = []\n",
+ "# random_point = dataset[np.random.randint(n)]\n",
+ " random_point = np.array([0, 0, 0])\n",
+ " \n",
+ " for i in range(n_points):\n",
+ " eps = np.random.uniform(-1*eps_range, eps_range, m)\n",
+ " nearby_point = random_point + eps\n",
+ " \n",
+ " sample.append(nearby_point)\n",
+ " \n",
+ " \n",
+ " return np.array(sample)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "id": "5c035c27",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(array([[-0.47250682, 0.50933554, -0.71924586],\n",
+ " [-0.54447989, -0.81042833, -0.21621186],\n",
+ " [-0.69302161, 0.28945333, 0.66025588]]),\n",
+ " array([9.50200032e+00, 5.20163849e-03, 2.42486200e-03]),\n",
+ " 1)"
+ ]
+ },
+ "execution_count": 18,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "sample = gen_n_points(dataset, 5)\n",
+ "compute_AS(sample, kde_pdf)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "c50d3aea",
+ "metadata": {},
+ "outputs": [],
+ "source": []
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