diff --git a/docs/src/conf.py b/docs/src/conf.py index 732b4cdcc..63665e32e 100644 --- a/docs/src/conf.py +++ b/docs/src/conf.py @@ -60,6 +60,7 @@ "regression", "reconstruction", "neighbors", + "decomposition", ] sphinx_gallery_conf = { "filename_pattern": "/*", diff --git a/docs/src/getting-started.rst b/docs/src/getting-started.rst index 3f9dd1d1e..e4a2e4c8b 100644 --- a/docs/src/getting-started.rst +++ b/docs/src/getting-started.rst @@ -52,3 +52,17 @@ Notebook Examples :start-line: 4 .. include:: examples/pcovc/index.rst :start-line: 4 + +.. _getting_started-decomposition: + +Non-linear Dimensionality Reduction +----------------------------------- + +.. automodule:: skmatter.decomposition + :noindex: + +Notebook Examples +^^^^^^^^^^^^^^^^^ + +.. include:: examples/decomposition/index.rst + :start-line: 4 diff --git a/docs/src/index.rst b/docs/src/index.rst index b8e302e93..f8345172f 100644 --- a/docs/src/index.rst +++ b/docs/src/index.rst @@ -82,6 +82,23 @@ +
+
+
+
+ +.. only:: html + + :ref:`getting_started-decomposition` + +.. raw:: html + +
+

Non-linear dimensionality reduction using + Sketch-map algorithm with transfer functions.

+
+
+

diff --git a/docs/src/references/decomposition.rst b/docs/src/references/decomposition.rst index 483d5f7c4..df0706320 100644 --- a/docs/src/references/decomposition.rst +++ b/docs/src/references/decomposition.rst @@ -70,3 +70,17 @@ Kernel PCovC .. automethod:: inverse_transform .. automethod:: decision_function .. automethod:: score + +.. _SketchMap-api: + +SketchMap +--------- + +.. autoclass:: skmatter.decomposition.SketchMap + :show-inheritance: + :special-members: + + .. automethod:: fit + .. automethod:: transform + .. automethod:: fit_transform + .. automethod:: score diff --git a/examples/decomposition/README.rst b/examples/decomposition/README.rst new file mode 100644 index 000000000..baedd7448 --- /dev/null +++ b/examples/decomposition/README.rst @@ -0,0 +1,2 @@ +Decomposition +============= diff --git a/examples/decomposition/highd-landmarks b/examples/decomposition/highd-landmarks new file mode 100644 index 000000000..571522f4f --- /dev/null +++ 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b/examples/decomposition/sketchmap.py @@ -0,0 +1,59 @@ +#!/usr/bin/env python +# coding: utf-8 + +""" +Sketch-map example using pre-selected high-dimensional landmarks +================================================================== + +This example demonstrates a minimal, sphinx-gallery friendly usage of the `SketchMap` +estimator. It loads the provided landmark file, fits the estimator on the landmark set +(using per-sample `sample_weights`) and plots the resulting 2D embedding. + +note:: + + The example fits only the landmark set (callers that want a subset + should pre-select and pass that array to `fit`). +""" + +# %% +import numpy as np +from matplotlib import pyplot as plt +from matplotlib import cm + +from skmatter.decomposition import SketchMap + + +# %% +# +# Load example landmark data. The file included with the examples contains +# high-dimensional descriptors and the last column holds a per-sample weight. + +data_file = "highd-landmarks" +data = np.loadtxt(data_file) +X_land = data[:, :-1] +weights = data[:, -1] + + +# %% +# +# Fit SketchMap on the landmark set and provide `sample_weights`. We fit on the +# landmarks only here (no FPS or internal selection). + +sm = SketchMap(n_components=2, auto_histogram=True, preopt_steps=50, mixing_ratio=0.2) +sm.fit(X_land, sample_weights=weights) +T = sm.embedding_ + +# %% +# +# Plot the resulting embedding colored by the per-sample weight. + +cmap = cm.get_cmap("viridis") +fig, ax = plt.subplots(figsize=(6, 5)) +sc = ax.scatter(T[:, 0], T[:, 1], c=weights, s=40, cmap=cmap, edgecolor="k") +ax.set_title("Sketch-map embedding (example)") +ax.set_xlabel("Sketchmap 1") +ax.set_ylabel("Sketchmap 2") +cbar = fig.colorbar(sc, ax=ax) +cbar.set_label("landmark weight") +fig.tight_layout() +plt.show() diff --git a/src/skmatter/decomposition/__init__.py b/src/skmatter/decomposition/__init__.py index 2fd488c93..de7b9048e 100644 --- a/src/skmatter/decomposition/__init__.py +++ b/src/skmatter/decomposition/__init__.py @@ -44,6 +44,8 @@ from ._kernel_pcovr import KernelPCovR from ._kernel_pcovc import KernelPCovC +from ._sketchmap import SketchMap + __all__ = [ "_BasePCov", "_BaseKPCov", @@ -51,4 +53,5 @@ "PCovC", "KernelPCovR", "KernelPCovC", + "SketchMap", ] diff --git a/src/skmatter/decomposition/_sketchmap.py b/src/skmatter/decomposition/_sketchmap.py new file mode 100644 index 000000000..285f0bc3a --- /dev/null +++ b/src/skmatter/decomposition/_sketchmap.py @@ -0,0 +1,525 @@ +"""Complete Sketch-Map implementation in Python matching PyTorch version + +This implementation follows the two-stage optimization approach: +1. Pre-optimization with identity transform +2. Refinement with sigmoid transform +""" + +import warnings + +import numpy as np +from scipy import sparse +from scipy.optimize import minimize +from scipy.spatial.distance import pdist, squareform +from sklearn.base import BaseEstimator, TransformerMixin +from sklearn.utils.validation import check_is_fitted, validate_data + + +class SketchMap(TransformerMixin, BaseEstimator): + """Sketch-Map dimensionality reducer. + + Parameters + ---------- + n_components : int, default=2 + Dimensionality of the target embedding. + + sigma : float, default=None + Sigmoid parameter for both high and low dimensional transforms. + If None, estimated automatically from distance histogram. + + a_hd : float, default=2.0 + High-dimensional sigmoid exponent a. + + b_hd : float, default=6.0 + High-dimensional sigmoid exponent b. + + a_ld : float, default=2.0 + Low-dimensional sigmoid exponent a. + + b_ld : float, default=6.0 + Low-dimensional sigmoid exponent b. + + auto_histogram : bool, default=True + If True, estimate sigma from pairwise-distance histogram. + + preopt_steps : int, default=100 + Number of pre-optimization steps with identity transform. + + opt_steps : int, default=100 + Number of optimization steps with sigmoid transform. + + global_opt_steps : int, default=0 + Number of global optimization steps (not implemented). + + mixing_ratio : float, default=0.0 + Balance between direct (1.0) and transformed (0.0) stress. + + center : bool, default=True + If True, center the input data around origin. + + random_state : int or None + Random seed. + + verbose : int, default=0 + Verbosity level. + """ + + def __init__( + self, + n_components=2, + sigma=None, + a_hd=2.0, + b_hd=6.0, + a_ld=2.0, + b_ld=6.0, + auto_histogram=True, + preopt_steps=100, + opt_steps=100, + global_opt_steps=0, + mixing_ratio=0.0, + center=True, + random_state=None, + verbose=False, + ): + self.n_components = n_components + self.sigma = sigma + self.a_hd = a_hd + self.b_hd = b_hd + self.a_ld = a_ld + self.b_ld = b_ld + self.auto_histogram = auto_histogram + self.preopt_steps = preopt_steps + self.opt_steps = opt_steps + self.global_opt_steps = global_opt_steps + self.mixing_ratio = mixing_ratio + self.center = center + self.random_state = random_state + self.verbose = verbose + self._first_stress_call = True + + def _sigmoid_transform(self, distances, sigma, a, b): + """Apply xsigmoid transformation: 1-(1+(2^(a/b)-1)(x/s)^a)^(-b/a)""" + with np.errstate(divide="ignore", invalid="ignore"): + x = distances / sigma + A = 2 ** (a / b) - 1.0 + term = A * (x**a) + val = 1.0 - (1.0 + term) ** (-b / a) + val[distances <= 0.0] = 0.0 + return val + + def _sigmoid_derivative(self, distances, sigma, a, b): + """Derivative of sigmoid with respect to distance.""" + A = 2 ** (a / b) - 1.0 + out = np.zeros_like(distances, dtype=float) + pos = distances > 0.0 + + if np.any(pos): + r = distances[pos] + u = A * (r / sigma) ** a + pref = b * A * (r ** (a - 1.0)) / (sigma**a) + out[pos] = pref * (1.0 + u) ** (-b / a - 1.0) + + return out + + def _classical_mds(self, distances): + """Classical MDS initialization matching C++ implementation.""" + D = distances + + # Compute Gram matrix with centering as in C++ + M = -0.5 * (D**2) + M -= M.mean(axis=0, keepdims=True) # subtract column means + M -= M.mean(axis=1, keepdims=True) # subtract row means + + # Eigendecomposition + w, V = np.linalg.eigh(M) + + # Sort descending and take top n_components + idx = np.argsort(w)[::-1] + top_idx = idx[: self.n_components] + + top_eigenvalues = w[top_idx] + top_eigenvectors = V[:, top_idx] + + # Compute coordinates + coordinates = top_eigenvectors * np.sqrt(np.maximum(top_eigenvalues, 0.0)) + + # Align signs to match C++ convention: make max abs value positive + for i in range(self.n_components): + col = coordinates[:, i] + max_id = np.argmax(np.abs(col)) + if col[max_id] < 0: + coordinates[:, i] *= -1 + + return coordinates + + def _estimate_sigma(self, distances, n_bins=200): + """Estimate sigma from histogram of distances.""" + d = distances[np.triu_indices_from(distances, k=1)] + d = d[np.isfinite(d) & (d >= 0)] + + if d.size == 0: + raise ValueError("Empty distances array") + + hist, edges = np.histogram(d, bins=n_bins) + peak_idx = np.argmax(hist) + peak_val = hist[peak_idx] + + # Find where histogram drops below half peak + half_idx = np.where(hist[peak_idx + 1 :] <= peak_val * 0.5)[0] + + if half_idx.size > 0: + sigma = 0.5 * ( + edges[peak_idx + 1 + half_idx[0]] + edges[peak_idx + half_idx[0]] + ) + else: + sigma = float(np.median(d)) + + return sigma + + def _compute_stress(self, X_ld, D_hd, S_hd, W, mixing_ratio, use_transform=True): + """Compute sketch-map stress function. + + Parameters + ---------- + X_ld : array, shape (n*d,) or (n, d) + Low-dimensional coordinates (flattened or matrix) + D_hd : array, shape (n, n) + High-dimensional distances + S_hd : array, shape (n, n) + Transformed high-dimensional distances + W : array, shape (n, n) + Weight matrix + mixing_ratio : float + Balance between direct and transformed stress + use_transform : bool + Whether to apply sigmoid transform to low-dim distances + """ + # Handle both flat and matrix inputs + if X_ld.ndim == 1: + n = D_hd.shape[0] + X_ld_mat = X_ld.reshape((n, self.n_components)) + else: + X_ld_mat = X_ld + + # Low-dimensional distances + D_ld = squareform(pdist(X_ld_mat, metric="euclidean")) + + # Transform low-dimensional distances if requested + if use_transform: + S_ld = self._sigmoid_transform(D_ld, self.sigma_, self.a_ld, self.b_ld) + else: + S_ld = D_ld + + # Compute stress components + direct_stress = np.sum(W * (D_hd - D_ld) ** 2) + transformed_stress = np.sum(W * (S_hd - S_ld) ** 2) + + combined_stress = ( + mixing_ratio * direct_stress + (1 - mixing_ratio) * transformed_stress + ) + + # Debug logging on first call + if self.verbose and self._first_stress_call: + print("\n=== First Stress Calculation Debug ===") + print(f"High-dim distances (sample 3x3):\n{D_hd[:3, :3]}") + print(f"\nLow-dim distances (sample 3x3):\n{D_ld[:3, :3]}") + print(f"\nTransformed high-dim (sample 3x3):\n{S_hd[:3, :3]}") + print(f"Transformed low-dim (sample 3x3):\n{S_ld[:3, :3]}") + print(f"\nWeights (sample 3x3):\n{W[:3, :3]}") + print(f"Weight sum: {np.sum(W):.4f}") + print("\nStress components:") + print(f" Direct stress: {direct_stress:.4f}") + print(f" Transformed stress: {transformed_stress:.4f}") + print(f" Combined stress: {combined_stress:.4f}") + print(f" Mixing ratio: {mixing_ratio:.2f}") + print(f" Normalized stress: {combined_stress / np.sum(W):.6f}") + print("=" * 40 + "\n") + self._first_stress_call = False + + # Normalize by sum of weights + return combined_stress / np.sum(W) + + def _compute_gradient(self, X_ld, D_hd, S_hd, W, mixing_ratio, use_transform=True): + """Compute gradient of stress function.""" + # Handle both flat and matrix inputs + if X_ld.ndim == 1: + n = D_hd.shape[0] + X_ld_mat = X_ld.reshape((n, self.n_components)) + else: + X_ld_mat = X_ld + + # Pairwise differences + dif = X_ld_mat[:, None, :] - X_ld_mat[None, :, :] + D_ld = np.sqrt(np.sum(dif**2, axis=2)) + + # Transform and derivatives + if use_transform: + S_ld = self._sigmoid_transform(D_ld, self.sigma_, self.a_ld, self.b_ld) + dS_dD = self._sigmoid_derivative(D_ld, self.sigma_, self.a_ld, self.b_ld) + else: + S_ld = D_ld + dS_dD = np.ones_like(D_ld) + + # Avoid division by zero + eps = np.finfo(float).eps + inv_D = 1.0 / (D_ld + eps) + + # Gradient matrix + M = ( + W + * ( + mixing_ratio * (D_ld - D_hd) + + (1 - mixing_ratio) * (S_ld - S_hd) * dS_dD + ) + * inv_D + ) + np.fill_diagonal(M, 0.0) + + row_sums = M.sum(axis=1) + G = (row_sums[:, None] * X_ld_mat) - (M @ X_ld_mat) + + # Normalize by sum of weights and apply factor of 2 + G = 2.0 * G / np.sum(W) + + return G.ravel() + + def _optimize( + self, X_init, D_hd, S_hd, W, mixing_ratio, n_steps, use_transform=True + ): + """Run L-BFGS-B optimization.""" + n = X_init.shape[0] + x0 = X_init.ravel() + + def objective(x): + return self._compute_stress(x, D_hd, S_hd, W, mixing_ratio, use_transform) + + def gradient(x): + return self._compute_gradient(x, D_hd, S_hd, W, mixing_ratio, use_transform) + + # Optimize + result = minimize( + objective, + x0, + method="L-BFGS-B", + jac=gradient, + options={"maxiter": n_steps, "disp": int(self.verbose)}, + ) + + return result.x.reshape((n, self.n_components)), result.fun + + def fit(self, X, y=None, sample_weights=None): + """Fit the Sketch-Map model following PyTorch two-stage approach. + + Stage 1: Pre-optimization with identity transform + Stage 2: Refinement with sigmoid transform + + Parameters + ---------- + X : array-like, shape (n_samples, n_features) + Training data. + + y : Ignored + Not used, present for API consistency. + + sample_weights : array-like, shape (n_samples,), optional + Per-sample weights. + + Returns + ------- + self : object + Returns the instance itself. + """ + X = validate_data(self, X, reset=True, dtype=np.float64) + self.X_ = X.copy() + + if sparse.issparse(X): + raise ValueError("Sparse input is not supported") + if np.any(~np.isfinite(X)): + raise ValueError("Input contains NaN or infinity") + + n_samples, n_features = X.shape + if n_samples < 2: + raise ValueError( + f"Found array with {n_samples} sample(s) (shape={X.shape}) while a " + "minimum of 2 is required." + ) + self.n_samples_ = n_samples + self.n_features_ = n_features + + if self.verbose: + print(f"Fitting Sketch-Map with {n_samples} samples, {n_features} features") + if sample_weights is not None: + print( + f"Using sample weights: min={np.min(sample_weights):.4f}, " + f"max={np.max(sample_weights):.4f}, " + f"mean={np.mean(sample_weights):.4f}" + ) + + X_work = X.copy() + if self.center: + if self.verbose: + print("Centering the data") + X_work = X_work - X_work.mean(axis=0, keepdims=True) + + # Compute pairwise distances + if self.verbose: + print("Computing pairwise distances...") + D_hd = squareform(pdist(X_work, metric="euclidean")) + + # Estimate or set sigma + if self.auto_histogram and self.sigma is None: + self.sigma_ = self._estimate_sigma(D_hd) + if self.verbose: + print(f"Estimated sigma: {self.sigma_:.4f}") + else: + self.sigma_ = self.sigma if self.sigma is not None else 1.0 + + # Transform high-dimensional distances (for stage 2) + S_hd = self._sigmoid_transform(D_hd, self.sigma_, self.a_hd, self.b_hd) + + # Setup weight matrix: W_ij = w_i * w_j + if sample_weights is not None: + w = np.asarray(sample_weights) + if w.shape[0] != n_samples: + raise ValueError( + f"sample_weights must have length {n_samples}, got {w.shape[0]}" + ) + W = np.outer(w, w) + if self.verbose: + print(f"Weight matrix: sum={np.sum(W):.4f}, shape={W.shape}") + else: + W = np.ones_like(D_hd) + if self.verbose: + print("Using uniform weights") + + # Reset debug flag + self._first_stress_call = True + + # Initialize with classical MDS + if self.verbose: + print("Initializing with classical MDS...") + X_ld = self._classical_mds(D_hd) + + # Stage 1: Pre-optimization with identity transform + if self.preopt_steps > 0: + if self.verbose: + print("\n=== Stage 1: Pre-optimization with identity transform ===") + print(f"Running {self.preopt_steps} optimization steps...") + + X_ld, stress = self._optimize( + X_ld, + D_hd, + D_hd, + W, # Use D_hd for both (identity) + self.mixing_ratio, + self.preopt_steps, + use_transform=False, + ) + + if self.verbose: + print(f"Pre-optimization stress: {stress:.6f}") + + # Stage 2: Refinement with sigmoid transform + if self.opt_steps > 0: + if self.verbose: + print("\n=== Stage 2: Refinement with sigmoid transform ===") + print(f"Running {self.opt_steps} optimization steps...") + + # Reset debug flag for second stage + self._first_stress_call = True + + X_ld, stress = self._optimize( + X_ld, + D_hd, + S_hd, + W, + self.mixing_ratio, + self.opt_steps, + use_transform=True, + ) + + if self.verbose: + print(f"Final stress: {stress:.6f}") + + # Note: Global optimization not implemented + if self.global_opt_steps > 0: + warnings.warn("Global optimization not yet implemented, skipping") + + self.embedding_ = X_ld + self.stress_ = stress + + if self.verbose: + print("\nSketch-Map fitting complete!") + + return self + + def fit_transform(self, X, y=None, sample_weights=None): + """Fit the model and return the embedding. + + Parameters + ---------- + X : array-like, shape (n_samples, n_features) + Training data. + + y : Ignored + Not used, present for API consistency. + + sample_weights : array-like, shape (n_samples,), optional + Per-sample weights. + + Returns + ------- + X_new : array, shape (n_samples, n_components) + Embedded coordinates. + """ + self.fit(X, y, sample_weights=sample_weights) + return self.embedding_ + + def transform(self, X): + """Project data to the embedding space. + + Only supports in-sample transformation (same data used for fit). + """ + check_is_fitted(self, ["embedding_", "X_"]) + X = validate_data(self, X, reset=False) + + # Allow in-sample transformation (full or subset) by matching rows. + indices = [] + for row in X: + matches = np.all(np.isclose(self.X_, row, rtol=1e-8, atol=1e-12), axis=1) + if not np.any(matches): + warnings.warn( + "SketchMap.transform only supports in-sample rows. " + "Out-of-sample projection is not implemented.", + UserWarning, + ) + indices.append(int(np.argmax(matches))) + + return self.embedding_[indices] + + def predict(self, X): + """Project data to the embedding space (alias for transform). + + Currently only supports in-sample transformation (same data used for fit). + Out-of-sample projection is not implemented. + """ + return self.transform(X) + + def score(self, X, y=None): + """Return the negative stress as a score. + + Parameters + ---------- + X : array-like + Ignored, present for API consistency. + y : array-like + Ignored, present for API consistency. + + Returns + ------- + score : float + Negative of the final stress value. + """ + check_is_fitted(self, ["stress_"]) + X = validate_data(self, X, reset=False) + return -self.stress_ diff --git a/tests/test_check_estimators.py b/tests/test_check_estimators.py index 1683b53f3..20cd262d9 100644 --- a/tests/test_check_estimators.py +++ b/tests/test_check_estimators.py @@ -1,6 +1,6 @@ from sklearn.utils.estimator_checks import parametrize_with_checks -from skmatter.decomposition import KernelPCovR, PCovC, PCovR +from skmatter.decomposition import KernelPCovR, PCovC, PCovR, SketchMap from skmatter.feature_selection import CUR as fCUR from skmatter.feature_selection import FPS as fFPS from skmatter.feature_selection import PCovCUR as fPCovCUR @@ -11,15 +11,16 @@ @parametrize_with_checks( [ - KernelPCovR(mixing=0.5), - PCovR(mixing=0.5), - PCovC(mixing=0.5), fCUR(), fFPS(), fPCovCUR(), fPCovFPS(), - Ridge2FoldCV(), KernelNormalizer(), + KernelPCovR(mixing=0.5), + PCovC(mixing=0.5), + PCovR(mixing=0.5), + Ridge2FoldCV(), + SketchMap(), StandardFlexibleScaler(), ] ) diff --git a/tests/test_sketchmap.py b/tests/test_sketchmap.py new file mode 100644 index 000000000..eb1ae458f --- /dev/null +++ b/tests/test_sketchmap.py @@ -0,0 +1 @@ +...