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1, X.shape[1])) + X_weighted = X * np.sqrt(row_w[:, None]) + U, s, Vt = np.linalg.svd(X_weighted, full_matrices=False) + V = Vt.T + U = U[:, :ncp] + V = V[:, :ncp] + s = s[:ncp] + mult = np.sign(np.sum(V, axis=0)) + mult[mult == 0] = 1 + U *= mult + V *= mult + U /= np.sqrt(row_w[:, None]) + return s, U, V + +# --- MIMCA Class --- + +class MIMCA(BaseEstimator, TransformerMixin): + """ + Multiple Imputation using Multiple Correspondence Analysis (MCA) + in a scikit-learn compatible estimator. + + Parameters + ---------- + ncp : int, default=2 + Number of principal components to retain. + method : str, default="Regularized" + Imputation method. Either "Regularized" or "EM". + row_w : Optional[np.ndarray], default=None + Row weights. If None, uniform weights are used. + coeff_ridge : float, default=1 + Regularization coefficient for Regularized MCA. + threshold : float, default=1e-6 + Convergence threshold. + maxiter : int, default=1000 + Maximum number of iterations. + debug : bool, default=False + If True, print internal debug information. + """ + + def __init__( + self, + ncp: int = 2, + method: str = "Regularized", + row_w: Optional[np.ndarray] = None, + coeff_ridge: float = 1, + threshold: float = 1e-6, + maxiter: int = 1000, + debug: bool = False, + ) -> None: + self.ncp = ncp + self.method = method + self.row_w = row_w + self.coeff_ridge = coeff_ridge + self.threshold = threshold + self.maxiter = maxiter + self.debug = debug + + def fit(self, X: pd.DataFrame, y: Optional[pd.DataFrame] = None) -> MIMCA: + self._is_fitted = True + return self + + def transform(self, X: pd.DataFrame) -> pd.DataFrame: + """ + Transform the dataset by imputing missing values using MCA. + + Returns + ------- + pd.DataFrame + The complete dataset with missing values imputed. + """ + res = imputeMCA( + X, + ncp=self.ncp, + method=self.method, + row_w=self.row_w, + coeff_ridge=self.coeff_ridge, + threshold=self.threshold, + maxiter=self.maxiter, + debug=self.debug, + ) + return res["completeObs"] + + def fit_transform(self, X: pd.DataFrame, y: Optional[pd.DataFrame] = None) -> pd.DataFrame: + """ + Fit and transform the data. + """ + return self.fit(X, y).transform(X) + + def impute_indicator(self, X: pd.DataFrame) -> pd.DataFrame: + """ + Return the imputed disjunctive (indicator) matrix. + """ + res = imputeMCA( + X, + ncp=self.ncp, + method=self.method, + row_w=self.row_w, + coeff_ridge=self.coeff_ridge, + threshold=self.threshold, + maxiter=self.maxiter, + debug=self.debug, + ) + return res["tab_disj"] + + def estimate_ncp( + self, + X: pd.DataFrame, + ncp_min: int = 0, + ncp_max: int = 5, + method_cv: str = "Kfold", + nbsim: int = 100, + pNA: float = 0.05, + ind_sup: Optional[np.ndarray] = None, + quanti_sup: Optional[np.ndarray] = None, + quali_sup: Optional[np.ndarray] = None, + seed: Optional[int] = None, + verbose: bool = True, + ) -> Dict[str, Any]: + """ + Estimate the optimal number of components (ncp) using cross-validation. + + Parameters + ---------- + X : pd.DataFrame + Input dataset. + ncp_min : int, default=0 + Minimum number of components to test. + ncp_max : int, default=5 + Maximum number of components to test. + method_cv : str, default="Kfold" + Cross-validation method: "Kfold" or "loo". + nbsim : int, default=100 + Number of simulations (for Kfold). + pNA : float, default=0.05 + Proportion of missing values to simulate. + ind_sup, quanti_sup, quali_sup : Optional[np.ndarray] + Indices of supplementary individuals or variables (if any). + seed : Optional[int] + Random seed. + verbose : bool, default=True + If True, show progress. + + Returns + ------- + Dict[str, Any] + Dictionary with keys: + - "ncp": optimal number of components. + - "criterion": list of CV error values for each tested ncp. + """ + return estim_ncpMCA( + X, + ncp_min=ncp_min, + ncp_max=ncp_max, + method=self.method, + method_cv=method_cv, + nbsim=nbsim, + pNA=pNA, + ind_sup=ind_sup, + quanti_sup=quanti_sup, + quali_sup=quali_sup, + threshold=self.threshold, + verbose=verbose, + seed=seed + ) + +# --- Core imputation function (with debug prints) --- + +def imputeMCA( + don: pd.DataFrame, + ncp: int = 2, + method: str = "Regularized", + row_w: Optional[np.ndarray] = None, + coeff_ridge: float = 1, + threshold: float = 1e-6, + seed: Optional[int] = None, + maxiter: int = 1000, + debug: bool = False +) -> Dict[str, pd.DataFrame]: + """ + Impute missing values in a dataset using MCA. + + Parameters + ---------- + don : pd.DataFrame + Input dataset with missing values. + ncp : int, default=2 + Number of principal components. + method : str, default="Regularized" + Either "Regularized" or "EM". + row_w : Optional[np.ndarray], default=None + Row weights; if None, uniform weights are used. + coeff_ridge : float, default=1 + Regularization coefficient. + threshold : float, default=1e-6 + Convergence threshold. + seed : Optional[int] + Random seed. + maxiter : int, default=1000 + Maximum iterations. + debug : bool, default=False + If True, print debug information. + + Returns + ------- + Dict[str, pd.DataFrame] + A dictionary with: + - "tab_disj": the imputed disjunctive table. + - "completeObs": the reconstructed categorical DataFrame. + """ + don = pd.DataFrame(don).copy() + # Convert non-numeric columns to categorical + for col in don.columns: + if not pd.api.types.is_numeric_dtype(don[col]) or don[col].dtype == "bool": + don[col] = don[col].astype("category") + new_categories = don[col].cat.categories.astype(str) + don[col] = don[col].cat.rename_categories(new_categories) + else: + unique_vals = don[col].dropna().unique() + if set(unique_vals).issubset({0, 1}): + don[col] = don[col].astype("category") + new_categories = don[col].cat.categories.astype(str) + don[col] = don[col].cat.rename_categories(new_categories) + if row_w is None: + row_w = np.ones(len(don)) / len(don) + else: + row_w = np.array(row_w, dtype=float) + row_w /= row_w.sum() + + tab_disj_NA_df = tab_disjonctif_NA(don) + tab_disj_comp = tab_disjonctif_prop(don, seed=seed, row_w=row_w) + hidden = tab_disj_NA_df.isna() # mask for missing cells + tab_disj_rec_old = tab_disj_comp.copy() + method = method.lower() + nbiter = 0 + continue_flag = True + + while continue_flag: + nbiter += 1 + # Compute weighted column means normalized by number of original variables. + M = tab_disj_comp.apply(lambda col: moy_p(col.values, row_w)) / don.shape[1] + M = M.replace(0, np.finfo(float).eps).fillna(np.finfo(float).eps) + col_means = tab_disj_comp.apply(lambda col: moy_p(col.values, row_w)) + col_means = col_means.replace(0, np.finfo(float).eps) + # Center and scale. + Z = tab_disj_comp.div(col_means, axis=1) + Z = Z.subtract(Z.apply(lambda col: moy_p(col.values, row_w), axis=0), axis=1) + Zscale = Z.multiply(np.sqrt(M), axis=1) + + # Full SVD on Zscale. + s_full, U_full, V_full = np.linalg.svd(Zscale.values, full_matrices=False) + s_full = np.array(s_full) + + if method == "em": + moyeig = 0 + else: + if len(s_full) > ncp: + tail_vals = s_full[ncp:] + moyeig = np.mean(tail_vals**2) if tail_vals.size > 0 else 0 + moyeig = min(float(moyeig * coeff_ridge), float((s_full[ncp]**2).item())) + else: + moyeig = 0 + + if debug: + print(f"Iteration {nbiter}") + print("s_full:", s_full) + print("Selected singular values (first ncp):", s_full[:ncp]) + print("Computed moyeig:", moyeig) + + U = U_full[:, :ncp] + V = V_full[:ncp, :].T + lambda_vals = s_full[:ncp] + eig_shrunk = (lambda_vals**2 - moyeig) / (lambda_vals + 1e-15) + eig_shrunk = np.maximum(eig_shrunk, 0) + + if ncp > 0: + rec = U @ np.diag(eig_shrunk) @ V.T + else: + rec = np.zeros_like(Zscale.values) + + tab_disj_rec = pd.DataFrame(rec, index=tab_disj_comp.index, columns=tab_disj_comp.columns) + # Reverse scaling and centering. + tab_disj_rec = tab_disj_rec.div(np.sqrt(M), axis=1).add(1.0) + tab_disj_rec = tab_disj_rec.multiply(col_means, axis=1) + + diff = tab_disj_rec - tab_disj_rec_old + diff.values[~hidden.values] = 0 + rel_change = np.sum((diff.values**2) * row_w[:, None]) + + if debug: + print("Relative change:", rel_change) + + tab_disj_comp.values[hidden.values] = tab_disj_rec.values[hidden.values] + tab_disj_rec_old = tab_disj_rec.copy() + continue_flag = (rel_change > threshold) and (nbiter < maxiter) + + completeObs = find_category(don, tab_disj_comp) + if debug: + print("Converged after", nbiter, "iterations") + return {"tab_disj": tab_disj_comp, "completeObs": completeObs} + +# --- CV Estimation Function --- + +def estim_ncpMCA( + don: pd.DataFrame, + ncp_min: int = 0, + ncp_max: int = 5, + method: str = "Regularized", + method_cv: str = "Kfold", + nbsim: int = 100, + pNA: float = 0.05, + ind_sup: Optional[np.ndarray] = None, + quanti_sup: Optional[np.ndarray] = None, + quali_sup: Optional[np.ndarray] = None, + threshold: float = 1e-4, + verbose: bool = True, + seed: Optional[int] = None, +) -> Dict[str, Any]: + """ + Estimate the optimal number of components (ncp) for MCA using cross-validation. + + Returns a dictionary with: + - "ncp": optimal number of components. + - "criterion": list of CV error values for each tested ncp. + """ + don = don.copy() + if ind_sup is not None: + don = don.drop(index=ind_sup) + if quanti_sup is not None or quali_sup is not None: + cols_to_drop = [] + if quanti_sup is not None: + cols_to_drop.extend(don.columns[list(quanti_sup)]) + if quali_sup is not None: + cols_to_drop.extend(don.columns[list(quali_sup)]) + don = don.drop(columns=cols_to_drop) + for col in don.columns: + if not pd.api.types.is_categorical_dtype(don[col]): + don[col] = don[col].astype("category") + vrai_tab = tab_disjonctif_NA(don) + criterion = [] + rng = np.random.default_rng(seed) if seed is not None else np.random.default_rng() + + if method_cv.lower() == "kfold": + res = np.full((ncp_max - ncp_min + 1, nbsim), np.nan) + for sim in range(nbsim): + max_attempts = 50 + for attempt in range(max_attempts): + donNA = don.copy() + total_cells = donNA.shape[0] * donNA.shape[1] + n_missing = int(np.floor(total_cells * pNA)) + idx = rng.choice(total_cells, n_missing, replace=False) + row_idx = idx // donNA.shape[1] + col_idx = idx % donNA.shape[1] + for r, c in zip(row_idx, col_idx): + donNA.iat[r, c] = np.nan + if all(donNA[col].nunique(dropna=True) == don[col].nunique(dropna=True) for col in don.columns): + break + else: + raise ValueError("Too many attempts to inject missing values without dropping categories.") + for nb in range(ncp_min, ncp_max + 1): + imputed = imputeMCA(donNA, ncp=nb, method=method, threshold=threshold, seed=seed) + tab_comp = imputed["tab_disj"] + numerator = ((tab_comp - vrai_tab)**2).sum().sum() + denom = tab_disjonctif_NA(donNA).isna().sum().sum() - vrai_tab.isna().sum().sum() + res[nb - ncp_min, sim] = numerator / denom if denom != 0 else np.nan + crit = np.nanmean(res, axis=1) + if np.all(np.isnan(crit)): + raise ValueError("All simulations resulted in NaN error") + opt_ncp = int(np.nanargmin(crit) + ncp_min) + criterion = crit.tolist() + return {"ncp": opt_ncp, "criterion": criterion} + elif method_cv.lower() == "loo": + criterion = [] + for nb in range(ncp_min, ncp_max + 1): + errors = [] + for i in range(don.shape[0]): + for col in don.columns: + if not pd.isna(don.at[don.index[i], col]): + donNA = don.copy() + donNA.at[don.index[i], col] = np.nan + if donNA[col].nunique(dropna=True) < don[col].nunique(dropna=True): + continue + imputed = imputeMCA(donNA, ncp=nb, method=method, threshold=threshold, seed=seed) + tab_comp = imputed["tab_disj"] + diff = (tab_comp - vrai_tab)**2 + errors.append(diff.to_numpy().sum()) + mean_err = np.nan if len(errors) == 0 else np.mean(errors) + criterion.append(mean_err) + if np.all(np.isnan(criterion)): + raise ValueError("All computations resulted in NaN errors") + opt_ncp = int(np.nanargmin(criterion) + ncp_min) + return {"ncp": opt_ncp, "criterion": criterion} + else: + raise ValueError("method_cv must be 'Kfold' or 'loo'") diff --git a/qolmat/imputations/mimca/estim_ncpMCA.py b/qolmat/imputations/mimca/estim_ncpMCA.py new file mode 100644 index 0000000..7c78232 --- /dev/null +++ b/qolmat/imputations/mimca/estim_ncpMCA.py @@ -0,0 +1,402 @@ +"""Estimate the optimal number of dimensions for MCA using CV or LOO.""" + + +import numpy as np +import pandas as pd +from tqdm import tqdm + + +def moy_p(V, weights): + """Compute the weighted mean of a vector, ignoring NaNs. + + Parameters + ---------- + V : array-like + Input vector with possible NaN values. + weights : array-like + Weights corresponding to each element in V. + + Returns + ------- + float + Weighted mean of non-NaN elements. + + """ + mask = ~np.isnan(V) + total_weight = np.sum(weights[mask]) + if total_weight == 0: + return 0.0 + return np.sum(V[mask] * weights[mask]) / total_weight + +def tab_disjonctif_NA(df): + """Create a disjunctive table for categorical variables, preserving NaNs. + + Parameters + ---------- + df : DataFrame + Input DataFrame with categorical and numeric variables. + + Returns + ------- + DataFrame + Disjunctive table with one-hot encoding, preserving NaNs. + + """ + df_encoded_list = [] + for col in df.columns: + if df[col].dtype.name == "category" or df[col].dtype == object: + df[col] = df[col].astype("category") + encoded = pd.get_dummies( + df[col], + prefix=col, + prefix_sep="_", + dummy_na=False, + dtype=float, + ) + categories = df[col].cat.categories.tolist() + col_names = [f"{col}_{cat}" for cat in categories] + encoded = encoded.reindex(columns=col_names, fill_value=0.0) + encoded[df[col].isna()] = np.nan + df_encoded_list.append(encoded) + else: + df_encoded_list.append(df[[col]]) + df_encoded = pd.concat(df_encoded_list, axis=1) + return df_encoded + +def prodna(data, noNA, rng): + """Introduce random missing values into a DataFrame. + + Parameters + ---------- + data : DataFrame + Input data. + noNA : float + Proportion of missing values to introduce. + rng : numpy.random.Generator + Random number generator. + + Returns + ------- + DataFrame + DataFrame with introduced missing values. + + """ + data = data.copy() + n_rows, n_cols = data.shape + total_values = n_rows * n_cols + n_missing = int(np.floor(total_values * noNA)) + missing_indices = rng.choice(total_values, n_missing, replace=False) + row_indices = missing_indices // n_cols + col_indices = missing_indices % n_cols + for i in range(n_missing): + row = row_indices[i] + col = col_indices[i] + data.iloc[row, col] = np.nan + return data + +def find_category(df_original, tab_disj): + """Reconstruct original categorical variables from disjunctive table. + + Parameters + ---------- + df_original : DataFrame + Original DataFrame with categorical variables. + tab_disj : DataFrame + Disjunctive table after imputation. + + Returns + ------- + DataFrame + Reconstructed DataFrame with imputed categorical variables. + + """ + df_reconstructed = df_original.copy() + start_idx = 0 + for col in df_original.columns: + if df_original[col].dtype.name == "category" or df_original[col].dtype == object: # noqa: E501 + categories = df_original[col].cat.categories.tolist() + num_categories = len(categories) + sub_tab = tab_disj.iloc[:, start_idx : start_idx + num_categories] + max_indices = sub_tab.values.argmax(axis=1) + df_reconstructed[col] = [categories[idx] for idx in max_indices] + df_reconstructed[col].replace("__MISSING__", np.nan, inplace=True) + start_idx += num_categories + else: + start_idx += 1 + return df_reconstructed + +def imputeMCA( + don, + ncp=2, + method="Regularized", + row_w=None, + coeff_ridge=1, + threshold=1e-6, + seed=None, + maxiter=1000, +): + """Impute missing values in a dataset using MCA. + + Parameters + ---------- + don : DataFrame + Input dataset with missing values. + ncp : int, optional + Number of principal components for MCA. Default is 2. + method : str, optional + Imputation method ('Regularized' or 'EM'). Default is 'Regularized'. + row_w : array-like, optional + Row weights. If None, uniform weights are applied. Default is None. + coeff_ridge : float, optional + Regularization coefficient for 'Regularized' MCA. Default is 1. + threshold : float, optional + Convergence threshold. Default is 1e-6. + seed : int, optional + Random seed for reproducibility. Default is None. + maxiter : int, optional + Maximum number of iterations for the imputation process. + + Returns + ------- + dict + Dictionary containing: + - "tab_disj": Disjunctive coded table after imputation. + - "completeObs": Complete dataset with missing values imputed. + + """ + don = pd.DataFrame(don) + don = don.copy() + for col in don.columns: + if not pd.api.types.is_numeric_dtype(don[col]) or don[col].dtype == "bool": # noqa: E501 + don[col] = don[col].astype("category") + new_categories = don[col].cat.categories.astype(str) + don[col] = don[col].cat.rename_categories(new_categories) # noqa: E501 + else: + unique_values = don[col].dropna().unique() + if set(unique_values).issubset({0, 1}): + don[col] = don[col].astype("category") + new_categories = don[col].cat.categories.astype(str) + don[col] = don[col].cat.rename_categories(new_categories) # noqa: E501 + if row_w is None: + row_w = np.ones(len(don)) / len(don) + else: + row_w = np.array(row_w, dtype=float) + row_w /= row_w.sum() + tab_disj_NA = tab_disjonctif_NA(don) + if ncp == 0: + tab_disj_comp_mean = tab_disj_NA.apply(lambda col: moy_p(col.values, row_w)) # noqa: E501 + tab_disj_comp = tab_disj_NA.fillna(tab_disj_comp_mean) + completeObs = find_category(don, tab_disj_comp) + return {"tab_disj": tab_disj_comp, "completeObs": completeObs} + tab_disj_comp = tab_disj_NA.copy() + hidden = tab_disj_NA.isna() + tab_disj_comp.fillna(tab_disj_comp.mean(), inplace=True) + tab_disj_rec_old = tab_disj_comp.copy() + nbiter = 0 + continue_flag = True + while continue_flag: + nbiter += 1 + M = tab_disj_comp.apply(lambda col: moy_p(col.values, row_w)) / don.shape[1] # noqa: E501 + M = M.replace({0: np.finfo(float).eps}) + M = M.fillna(np.finfo(float).eps) + tab_disj_comp_mean = tab_disj_comp.apply(lambda col: moy_p(col.values, row_w)) # noqa: E501 + tab_disj_comp_mean = tab_disj_comp_mean.replace({0: np.finfo(float).eps}) # noqa: E501 + Z = tab_disj_comp.div(tab_disj_comp_mean, axis=1) + Z_mean = Z.apply(lambda col: moy_p(col.values, row_w)) + Z = Z.subtract(Z_mean, axis=1) + Zscale = Z.multiply(np.sqrt(M), axis=1) + + U, s, Vt = np.linalg.svd(Zscale.values, full_matrices=False) + V = Vt.T + U = U[:, :ncp] + V = V[:, :ncp] + s = s[:ncp] + + if method.lower() == "em": + moyeig = 0 + else: + if len(s) > ncp: + moyeig = np.mean(s[ncp:] ** 2) + moyeig = min(moyeig * coeff_ridge, s[ncp - 1] ** 2) + else: + moyeig = 0 + eig_shrunk = (s ** 2 - moyeig) / s + eig_shrunk = np.maximum(eig_shrunk, 0) + rec = U @ np.diag(eig_shrunk) @ V.T + tab_disj_rec = pd.DataFrame( + rec, columns=tab_disj_comp.columns, index=tab_disj_comp.index + ) + tab_disj_rec = tab_disj_rec.div(np.sqrt(M), axis=1) + 1 + tab_disj_rec = tab_disj_rec.multiply(tab_disj_comp_mean, axis=1) + diff = tab_disj_rec - tab_disj_rec_old + diff_values = diff.values + hidden_values = hidden.values + diff_values[~hidden_values] = 0 + relch = np.sum((diff_values**2) * row_w[:, None]) + tab_disj_rec_old = tab_disj_rec.copy() + tab_disj_comp.values[hidden_values] = tab_disj_rec.values[hidden_values] # noqa: E501 + continue_flag = (relch > threshold) and (nbiter < maxiter) + completeObs = find_category(don, tab_disj_comp) + return {"tab_disj": tab_disj_comp, "completeObs": completeObs} + +def estim_ncpMCA( + don, + ncp_min=0, + ncp_max=5, + method="Regularized", + method_cv="Kfold", + nbsim=100, + pNA=0.05, + ind_sup=None, + quanti_sup=None, + quali_sup=None, + threshold=1e-4, + verbose=True, + seed=None +): + """Estimate the optimal number of dimensions for MCA using CV. + + Parameters + ---------- + don : DataFrame + Input data. + ncp_min : int, optional + Minimum number of components to test. Default is 0. + ncp_max : int, optional + Maximum number of components to test. Default is 5. + method : str, optional + Imputation method ('Regularized' or 'EM'). Default is 'Regularized'. + method_cv : str, optional + Cross-validation method ('Kfold' or 'loo'). Default is 'Kfold'. + nbsim : int, optional + Number of simulations for cross-validation. Default is 100. + pNA : float, optional + Proportion of missing values to simulate. Default is 0.05. + ind_sup : array-like, optional + Indices of supplementary individuals to exclude from the analysis. + Indices of supplementary quantitative variables to exclude. + quali_sup : array-like, optional + Indices of supplementary qualitative variables to exclude. + quanti_sup= array-like, optional + Indices of supplementary quantitative variables to exclude. + threshold : float, optional + Convergence threshold. Default is 1e-4. + verbose : bool, optional + Whether to print progress. Default is True. + seed : int, optional + Random seed for reproducibility. Default is None. + + Returns + ------- + dict + Dictionary containing: + - 'ncp': Optimal number of dimensions. + - 'criterion': List of criterion values for each dimension. + + """ + don = don.copy() + if ind_sup is not None: + don = don.drop(index=ind_sup) + if quanti_sup is not None or quali_sup is not None: + cols_to_drop = [] + if quanti_sup is not None: + cols_to_drop.extend(don.columns[quanti_sup]) + if quali_sup is not None: + cols_to_drop.extend(don.columns[quali_sup]) + don = don.drop(columns=cols_to_drop) + method = method.lower() + method_cv = method_cv.lower() + + for col in don.columns: + if not pd.api.types.is_categorical_dtype(don[col]): + don[col] = don[col].astype("category") + vrai_tab = tab_disjonctif_NA(don) + criterion = [] + if seed is not None: + rng = np.random.default_rng(seed) + else: + rng = np.random.default_rng() + + + if method_cv == "kfold": + res = np.full((ncp_max - ncp_min + 1, nbsim), np.nan) + for sim in range(nbsim): + max_attempts = 50 + for attempt in range(max_attempts): + donNA = don.copy() + total_cells = donNA.shape[0] * donNA.shape[1] + n_missing = int(np.floor(total_cells * pNA)) + idx = rng.choice(total_cells, n_missing, replace=False) + row_idx = idx // donNA.shape[1] + col_idx = idx % donNA.shape[1] + for r, c in zip(row_idx, col_idx): + donNA.iat[r, c] = np.nan + if all(donNA[col].nunique(dropna=True) == don[col].nunique(dropna=True) for col in don.columns): + break + else: + raise ValueError("Too many attempts to inject missing values without dropping categories.") + for nb in range(ncp_min, ncp_max + 1): + imputed = imputeMCA(donNA, ncp=nb, method=method, threshold=threshold, seed=seed) + tab_comp = imputed["tab_disj"] + numerator = ((tab_comp - vrai_tab)**2).sum().sum() + denom = tab_disjonctif_NA(donNA).isna().sum().sum() - vrai_tab.isna().sum().sum() + res[nb - ncp_min, sim] = numerator / denom if denom != 0 else np.nan + crit = np.nanmean(res, axis=1) + if np.all(np.isnan(crit)): + raise ValueError("All simulations resulted in NaN error") + opt_ncp = int(np.nanargmin(crit) + ncp_min) + criterion = crit.tolist() + return {"ncp": opt_ncp, "criterion": criterion} + + + elif method_cv == "loo": + criterion = [] + if verbose: + loop = tqdm(total=(ncp_max - ncp_min + 1) * don.shape[0], desc="LOO CV") # noqa: E501 + for nbaxes in range(ncp_min, ncp_max + 1): + errors = [] + for i in range(don.shape[0]): + donNA = don.copy() + for col in don.columns: + if not pd.isna(donNA.at[donNA.index[i], col]): + # Temporarily set the value to NaN + donNA.at[donNA.index[i], col] = np.nan + # Check if all categories are still represented + categories_complete = all( + donNA[col].nunique(dropna=True) == don[col].nunique(dropna=True) # noqa: E501 + for col in don.columns + ) + if not categories_complete: + # Skip this iteration if removing the value causes an issue + donNA.at[donNA.index[i], col] = don.at[don.index[i], col] # noqa: E501 + continue + # Impute missing values using MCA + imputed = imputeMCA( + donNA, + ncp=nbaxes, + method=method, + threshold=threshold, + seed=seed + ) + tab_disj_comp = imputed["tab_disj"] + vrai_tab = tab_disjonctif_NA(don) + numerator = ((tab_disj_comp - vrai_tab) ** 2).sum().sum() + denominator = 1 # Since we imputed one value + error = numerator / denominator + errors.append(error) + # Restore the original value + donNA.at[donNA.index[i], col] = don.at[don.index[i], col] + if verbose: + loop.update(1) + mean_error = np.mean(errors) + criterion.append(mean_error) + if verbose: + loop.close() + if np.all(np.isnan(criterion)): + raise ValueError("All computations resulted in NaN errors") + ncp = int(np.nanargmin(criterion) + ncp_min) + return {"ncp": ncp, "criterion": criterion} + else: + raise ValueError("method_cv must be 'kfold' or 'loo'") + + diff --git a/qolmat/imputations/mimca/imputer_mca.py b/qolmat/imputations/mimca/imputer_mca.py new file mode 100644 index 0000000..fb37146 --- /dev/null +++ b/qolmat/imputations/mimca/imputer_mca.py @@ -0,0 +1,183 @@ +import numpy as np # noqa: D100 +import pandas as pd + +from qolmat.utils.algebra import svdtriplet +from qolmat.utils.utils import ( + find_category, + moy_p, + tab_disjonctif_NA, + tab_disjonctif_prop, +) + + +def imputeMCA( + don, + ncp=2, + method="Regularized", + row_w=None, + coeff_ridge=1, + threshold=1e-6, + seed=None, + maxiter=1000, +): + """Impute missing values in a dataset using (MCA). + + Parameters + ---------- + don : DataFrame + Input dataset with missing values. + ncp : int, optional + Number of principal components for MCA. Default is 2. + method : str, optional + Imputation method ('Regularized' or 'EM'). Default is 'Regularized'. + row_w : array-like, optional + Row weights. If None, uniform weights are applied. Default is None. + coeff_ridge : float, optional + Regularization coefficient for 'Regularized' MCA. Default is 1. + threshold : float, optional + Convergence threshold. Default is 1e-6. + seed : int, optional + Random seed for reproducibility. Default is None. + maxiter : int, optional + Maximum number of iterations for the imputation process. + + Returns + ------- + dict + Dictionary containing: + - "tab_disj": Disjunctive coded table after imputation. + - "completeObs": Complete dataset with missing values imputed. + + """ + # Ensure the data is a DataFrame + don = pd.DataFrame(don) + don = don.copy() + + for col in don.columns: + if ( + not pd.api.types.is_numeric_dtype(don[col]) + or don[col].dtype == "bool" + ): # noqa: E501 + don[col] = don[col].astype("category") + # Convert categories to strings and rename them + new_categories = don[col].cat.categories.astype(str) + don[col] = don[col].cat.rename_categories(new_categories) + else: + unique_values = don[col].dropna().unique() + if set(unique_values).issubset({0, 1}): + don[col] = don[col].astype("category") + new_categories = don[col].cat.categories.astype(str) + don[col] = don[col].cat.rename_categories(new_categories) # noqa: E501 + + print("Data types after conversion:") + print(don.dtypes) + + # Handle row weights + if row_w is None: + row_w = np.ones(len(don)) / len(don) + else: + row_w = np.array(row_w, dtype=float) + row_w /= row_w.sum() + + # Initial imputation and creation of disjunctive tables + tab_disj_NA = tab_disjonctif_NA(don) + tab_disj_comp = tab_disjonctif_prop(don, seed=seed) + hidden = tab_disj_NA.isna() + tab_disj_rec_old = tab_disj_comp.copy() + + # Initialize iteration parameters + nbiter = 0 + continue_flag = True + + while continue_flag: + nbiter += 1 + + # Step 1: Compute weighted means M + M = ( + tab_disj_comp.apply(lambda col: moy_p(col.values, row_w)) + / don.shape[1] + ) # noqa: E501 + M = M.replace({0: np.finfo(float).eps}) + M = M.fillna(np.finfo(float).eps) + + if (M < 0).any(): + raise ValueError( + "Negative values encountered in M. Check data preprocessing." + ) # noqa: E501 + + print(f"Iteration {nbiter}:") + print("Weighted means (M):") + print(M.head()) + + # Step 2: Center and scale the data + tab_disj_comp_mean = tab_disj_comp.apply( + lambda col: moy_p(col.values, row_w) + ) # noqa: E501 + tab_disj_comp_mean = tab_disj_comp_mean.replace( + {0: np.finfo(float).eps} + ) # noqa: E501 + Z = tab_disj_comp.div(tab_disj_comp_mean, axis=1) + Z_mean = Z.apply(lambda col: moy_p(col.values, row_w)) + Z = Z.subtract(Z_mean, axis=1) + Zscale = Z.multiply(np.sqrt(M), axis=1) + + print("Centered and scaled data (Zscale):") + print(Zscale.head()) + + # Step 3: Perform weighted SVD + s, U, V = svdtriplet(Zscale.values, row_w=row_w, ncp=ncp) + print("Singular values (s):") + print(s) + print("Left singular vectors (U):") + print(U) + print("Right singular vectors (V):") + print(V) + + # Step 4: Regularization (Shrinking Eigenvalues) + if method.lower() == "em": + moyeig = 0 + else: + # Calculate moyeig based on R's imputeMCA logic + if len(s) > ncp: + moyeig = np.mean(s[ncp:] ** 2) + moyeig = min(moyeig * coeff_ridge, s[ncp] ** 2) + else: + moyeig = 0 + # Set to 0 when there are no additional singular values + eig_shrunk = (s[:ncp] ** 2 - moyeig) / s[:ncp] + eig_shrunk = np.maximum(eig_shrunk, 0) # Ensure non-negative + print("Shrunk eigenvalues (eig_shrunk):") + print(eig_shrunk) + + # Step 5: Reconstruct the data + rec = U @ np.diag(eig_shrunk) @ V.T + tab_disj_rec = pd.DataFrame( + rec, columns=tab_disj_comp.columns, index=tab_disj_comp.index + ) # noqa: E501 + tab_disj_rec = tab_disj_rec.div(np.sqrt(M), axis=1) + 1 + tab_disj_rec = tab_disj_rec.multiply(tab_disj_comp_mean, axis=1) + print("Reconstructed disjunctive table (tab_disj_rec):") + print(tab_disj_rec.head()) + + # Step 6: Compute difference and relative change + diff = tab_disj_rec - tab_disj_rec_old + diff_values = diff.values + hidden_values = hidden.values + # Zero out observed positions + diff_values[~hidden_values] = 0 + relch = np.sum((diff_values**2) * row_w[:, None]) + print(f"Relative Change: {relch}\n") + + # Step 7: Update for next iteration + tab_disj_rec_old = tab_disj_rec.copy() + tab_disj_comp.values[hidden_values] = tab_disj_rec.values[ + hidden_values + ] # noqa: E501 + + # Step 8: Check convergence + continue_flag = (relch > threshold) and (nbiter < maxiter) + + # Step 9: Reconstruct categorical data + completeObs = find_category(don, tab_disj_comp) + + return {"tab_disj": tab_disj_comp, "completeObs": completeObs} diff --git a/qolmat/imputations/mimca/mimca.py b/qolmat/imputations/mimca/mimca.py new file mode 100644 index 0000000..260eee0 --- /dev/null +++ b/qolmat/imputations/mimca/mimca.py @@ -0,0 +1,689 @@ +import numpy as np +import pandas as pd +from tqdm import tqdm +from qolmat.utils.algebra import svdtriplet +from qolmat.utils.utils import ( + find_category, + moy_p, + tab_disjonctif_NA, + tab_disjonctif_prop, +) + +def moy_p(V, weights): + """Compute the weighted mean of a vector, ignoring NaNs. + + Parameters + ---------- + V : array-like + Input vector with possible NaN values. + weights : array-like + Weights corresponding to each element in V. + + Returns + ------- + float + Weighted mean of non-NaN elements. + + """ + mask = ~np.isnan(V) + total_weight = np.sum(weights[mask]) + if total_weight == 0: + return 0.0 + return np.sum(V[mask] * weights[mask]) / total_weight + + +def tab_disjonctif_NA(df) -> pd.DataFrame: + """Create a disjunctive table for categorical variables, preserving NaNs. + + Parameters + ---------- + df : DataFrame + Input DataFrame with categorical and numeric variables. + + Returns + ------- + DataFrame + Disjunctive table with one-hot encoding, preserving NaNs. + + """ + df_encoded_list = [] + for col in df.columns: + if df[col].dtype.name == "category" or df[col].dtype == object: + df[col] = df[col].astype("category") + encoded = pd.get_dummies( + df[col], + prefix=col, + prefix_sep="_", + dummy_na=False, + dtype=float, + ) + categories = df[col].cat.categories.tolist() + col_names = [f"{col}_{cat}" for cat in categories] + encoded = encoded.reindex(columns=col_names, fill_value=0.0) + encoded[df[col].isna()] = np.nan + df_encoded_list.append(encoded) + else: + df_encoded_list.append(df[[col]]) + df_encoded = pd.concat(df_encoded_list, axis=1) + return df_encoded + + +def prodna(data, noNA, rng): + """Introduce random missing values into a DataFrame. + + Parameters + ---------- + data : DataFrame + Input data. + noNA : float + Proportion of missing values to introduce. + rng : numpy.random.Generator + Random number generator. + + Returns + ------- + DataFrame + DataFrame with introduced missing values. + + """ + data = data.copy() + n_rows, n_cols = data.shape + total_values = n_rows * n_cols + n_missing = int(np.floor(total_values * noNA)) + missing_indices = rng.choice(total_values, n_missing, replace=False) + row_indices = missing_indices // n_cols + col_indices = missing_indices % n_cols + for i in range(n_missing): + row = row_indices[i] + col = col_indices[i] + data.iloc[row, col] = np.nan + return data + + +def find_category(df_original, tab_disj): + """Reconstruct original categorical variables from disjunctive table. + + Parameters + ---------- + df_original : DataFrame + Original DataFrame with categorical variables. + tab_disj : DataFrame + Disjunctive table after imputation. + + Returns + ------- + DataFrame + Reconstructed DataFrame with imputed categorical variables. + + """ + df_reconstructed = df_original.copy() + start_idx = 0 + for col in df_original.columns: + if ( + df_original[col].dtype.name == "category" + or df_original[col].dtype == object + ): # noqa: E501 + categories = df_original[col].cat.categories.tolist() + num_categories = len(categories) + sub_tab = tab_disj.iloc[:, start_idx : start_idx + num_categories] + max_indices = sub_tab.values.argmax(axis=1) + df_reconstructed[col] = [categories[idx] for idx in max_indices] + df_reconstructed[col] = df_reconstructed[col].astype("category") + start_idx += num_categories + else: + start_idx += 1 + return df_reconstructed + + +def imputeMCA( + don, + ncp=2, + method="Regularized", + row_w=None, + coeff_ridge=1, + threshold=1e-6, + seed=None, + maxiter=1000, +): + """Impute missing values in a dataset using (MCA). + + Parameters + ---------- + don : DataFrame + Input dataset with missing values. + ncp : int, optional + Number of principal components for MCA. Default is 2. + method : str, optional + Imputation method ('Regularized' or 'EM'). Default is 'Regularized'. + row_w : array-like, optional + Row weights. If None, uniform weights are applied. Default is None. + coeff_ridge : float, optional + Regularization coefficient for 'Regularized' MCA. Default is 1. + threshold : float, optional + Convergence threshold. Default is 1e-6. + seed : int, optional + Random seed for reproducibility. Default is None. + maxiter : int, optional + Maximum number of iterations for the imputation process. + + Returns + ------- + dict + Dictionary containing: + - "tab_disj": Disjunctive coded table after imputation. + - "completeObs": Complete dataset with missing values imputed. + + """ + don = pd.DataFrame(don) + don = don.copy() + for col in don.columns: + if ( + not pd.api.types.is_numeric_dtype(don[col]) + or don[col].dtype == "bool" + ): # noqa: E501 + don[col] = don[col].astype("category") + new_categories = don[col].cat.categories.astype(str) + don[col] = don[col].cat.rename_categories(new_categories) # noqa: E501 + else: + unique_values = don[col].dropna().unique() + if set(unique_values).issubset({0, 1}): + don[col] = don[col].astype("category") + new_categories = don[col].cat.categories.astype(str) + don[col] = don[col].cat.rename_categories(new_categories) # noqa: E501 + if row_w is None: + row_w = np.ones(len(don)) / len(don) + else: + row_w = np.array(row_w, dtype=float) + row_w /= row_w.sum() + tab_disj_NA = tab_disjonctif_NA(don) + if ncp == 0: + tab_disj_comp_mean = tab_disj_NA.apply( + lambda col: moy_p(col.values, row_w) + ) # noqa: E501 + tab_disj_comp = tab_disj_NA.fillna(tab_disj_comp_mean) + completeObs = find_category(don, tab_disj_comp) + return {"tab_disj": tab_disj_comp, "completeObs": completeObs} + tab_disj_comp = tab_disj_NA.copy() + hidden = tab_disj_NA.isna() + tab_disj_comp.fillna(tab_disj_comp.mean(), inplace=True) + tab_disj_rec_old = tab_disj_comp.copy() + nbiter = 0 + continue_flag = True + while continue_flag: + nbiter += 1 + # 1. Compute weighted category proportions (M) + M = tab_disj_comp.apply(lambda col: moy_p(col.values, row_w)) / don.shape[1] + M = M.replace(0, np.finfo(float).eps).fillna(np.finfo(float).eps) + if (M < 0).any(): + raise ValueError("Negative values in M – check data or reduce ncp.") + # 2. Center and scale the completed disjunctive table + col_means = tab_disj_comp.apply(lambda col: moy_p(col.values, row_w)) + col_means = col_means.replace(0, np.finfo(float).eps) + Z = tab_disj_comp.div(col_means, axis=1) # divide by means + Z = Z.subtract(Z.apply(lambda col: moy_p(col.values, row_w)), axis=1) # center + Zscale = Z.multiply(np.sqrt(M), axis=1) # scale by sqrt(M) + # 3. Weighted SVD on Zscale (apply row weights via svdtriplet) + # Perform full SVD (all components) to get entire spectrum + ncp_svd = min(Zscale.shape[0], Zscale.shape[1]) + s, U, V = svdtriplet(Zscale.values, row_w=row_w, ncp=ncp_svd) + # `s` = array of singular values (length = rank), U = left singular vectors, V = right singular vectors + s = np.array(s) + # 4. Compute regularization term (moyeig) as in missMDA + Ncol = Zscale.shape[1] # number of indicator columns (incl. all categories) + n_vars = don.shape[1] # number of original categorical variables + if method == "em": + moyeig = 0 + else: + if len(s) > ncp: + # Exclude first ncp components and any structural zero eigenvalues + if don.shape[0] > (Ncol - n_vars): + # If number of individuals > (total dummies - variables), skip the last `n_vars` singular values + tail_vals = s[ncp: len(s) - n_vars] if len(s) - n_vars > ncp else np.array([]) + else: + # Otherwise skip none at the high-index end + tail_vals = s[ncp:] + moyeig = np.mean(tail_vals**2) if tail_vals.size > 0 else 0 + # Regularization: scale by coeff_ridge, cap at (ncp+1)th eigenvalue^2 + next_eig_sq = s[ncp]**2 + moyeig = min(moyeig * coeff_ridge, next_eig_sq) + else: + moyeig = 0 + # 5. Shrink the first ncp singular values and reconstruct + # (eig_shrunk = (lambda^2 - moyeig)/lambda for each singular value) + if len(s) >= 1: + lambda_vals = s[:min(ncp, len(s))] + eig_shrunk = (lambda_vals**2 - moyeig) / (lambda_vals + 1e-15) + eig_shrunk = np.maximum(eig_shrunk, 0) # no negative eigenvalues + else: + eig_shrunk = np.array([]) + # Use first `ncp` components for reconstruction + r = min(ncp, len(s), U.shape[1], V.shape[1]) + if r == 0: + rec = np.zeros_like(Zscale.values) + elif r == 1: + rec = np.outer(U[:, 0] * eig_shrunk[0], V[:, 0]) # outer product for rank-1 + else: + rec = U[:, :r] @ np.diag(eig_shrunk[:r]) @ V[:, :r].T + tab_disj_rec = pd.DataFrame(rec, index=tab_disj_comp.index, columns=tab_disj_comp.columns) + # Reverse scaling and centering to get back to indicator scale + tab_disj_rec = tab_disj_rec.div(np.sqrt(M), axis=1).add(1.0) + tab_disj_rec = tab_disj_rec.multiply(col_means, axis=1) + # 6. Compute weighted change on imputed cells + diff = tab_disj_rec - tab_disj_rec_old + diff.values[~hidden.values] = 0 # zero-out observed cells + rel_change = np.sum((diff.values**2) * row_w[:, None]) + # 7. Update and iterate + tab_disj_comp.values[hidden.values] = tab_disj_rec.values[hidden.values] + tab_disj_rec_old = tab_disj_rec.copy() + continue_flag = (rel_change > threshold) and (nbiter < maxiter) + # 8. Reconstruct categorical data from completed indicator matrix + completeObs = find_category(don, tab_disj_comp) + return {"tab_disj": tab_disj_comp, "completeObs": completeObs} + +def estim_ncpMCA( + don, + ncp_min=0, + ncp_max=5, + method="Regularized", + method_cv="Kfold", + nbsim=100, + pNA=0.05, + ind_sup=None, + quanti_sup=None, + quali_sup=None, + threshold=1e-4, + verbose=True, + seed=None, +): + """Estimate the optimal number of dimensions for MCA using CV. + + Parameters + ---------- + don : DataFrame + Input data. + ncp_min : int, optional + Minimum number of components to test. Default is 0. + ncp_max : int, optional + Maximum number of components to test. Default is 5. + method : str, optional + Imputation method ('Regularized' or 'EM'). Default is 'Regularized'. + method_cv : str, optional + Cross-validation method ('Kfold' or 'loo'). Default is 'Kfold'. + nbsim : int, optional + Number of simulations for cross-validation. Default is 100. + pNA : float, optional + Proportion of missing values to simulate. Default is 0.05. + ind_sup : array-like, optional + Indices of supplementary individuals to exclude from the analysis. + quanti_sup : array-like, optional + Indices of supplementary quantitative variables to exclude. + quali_sup : array-like, optional + Indices of supplementary qualitative variables to exclude. + Convergence threshold. Default is 1e-4. + verbose : bool, optional + Whether to print progress. Default is True. + seed : int, optional + Random seed for reproducibility. Default is None. + + Returns + ------- + dict + Dictionary containing: + - 'ncp': Optimal number of dimensions. + - 'criterion': List of criterion values dimensions. + + """ + don = don.copy() + if ind_sup is not None: + don = don.drop(index=ind_sup) + if quanti_sup is not None or quali_sup is not None: + cols_to_drop = [] + if quanti_sup is not None: + cols_to_drop.extend(don.columns[quanti_sup]) + if quali_sup is not None: + cols_to_drop.extend(don.columns[quali_sup]) + don = don.drop(columns=cols_to_drop) + method = method.lower() + method_cv = method_cv.lower() + for col in don.columns: + if not pd.api.types.is_categorical_dtype(don[col]): + don[col] = don[col].astype("category") + vrai_tab = tab_disjonctif_NA(don) + criterion = [] + if seed is not None: + rng = np.random.default_rng(seed) + else: + rng = np.random.default_rng() + if method_cv == "kfold": + res = np.full((ncp_max - ncp_min + 1, nbsim), np.nan) + if verbose: + sim_range = tqdm(range(nbsim), desc="Simulations") + else: + sim_range = range(nbsim) + for sim in sim_range: + compteur = 0 + max_attempts = 50 + while compteur < max_attempts: + donNA = prodna(don, pNA, rng) + categories_complete = all( + donNA[col].nunique(dropna=True) + == don[col].nunique(dropna=True) # noqa: E501 + for col in don.columns + ) + if categories_complete: + break + compteur += 1 + else: + raise ValueError( + "It is too difficult to suppress some cells.\n" + "Maybe several categories by only one individual. " + 'You should remove these variables or try with"loo".' + ) + for nbaxes in range(ncp_min, ncp_max + 1): + imputed = imputeMCA( + donNA, + ncp=nbaxes, + method=method, + threshold=threshold, + seed=seed, + ) + tab_disj_comp = imputed["tab_disj"] + numerator = ((tab_disj_comp - vrai_tab) ** 2).sum().sum() + denominator = ( + tab_disjonctif_NA(donNA).isna().sum().sum() + - vrai_tab.isna().sum().sum() + ) # noqa: E501 + if denominator == 0: + res[nbaxes - ncp_min, sim] = np.nan + else: + res[nbaxes - ncp_min, sim] = numerator / denominator + crit = np.nanmean(res, axis=1) + if np.all(np.isnan(crit)): + raise ValueError( + "All simulations resulted in NaN errors. Please check your data and parameters." + ) # noqa: E501 + ncp = int(np.nanargmin(crit) + ncp_min) + criterion = crit.tolist() + return {"ncp": ncp, "criterion": criterion} + elif method_cv == "loo": + # LOO cross-validation code (if needed) + pass + else: + raise ValueError("method_cv must be 'kfold' or 'loo'") + + +def imputeMCA_print( + don, + ncp, + method="Regularized", + row_w=None, + coeff_ridge=1, + threshold=1e-6, + seed=None, + maxiter=1000, + verbose=False, + print_msg="", +): + """Print progress during MCA imputation. + + Parameters + ---------- + don : DataFrame + Input dataset with missing values. + ncp : int + Number of principal components for MCA. + method : str, optional + Imputation method ('Regularized' or 'EM'). Default is 'Regularized'. + row_w : array-like, optional + Row weights. If None, uniform weights are applied. Default is None. + coeff_ridge : float, optional + Regularization coefficient for 'Regularized' MCA. Default is 1. + threshold : float, optional + Convergence threshold. Default is 1e-6. + seed : int, optional + Random seed for reproducibility. Default is None. + maxiter : int, optional + Maximum number of iterations for the imputation process. + verbose : bool, optional + Whether to print progress. Default is False. + print_msg : str, optional + Message to print during imputation. Default is ''. + + Returns + ------- + dict + Result of the MCA imputation. + + """ + if verbose: + print(f"{print_msg}...", end="", flush=True) + res = imputeMCA( + don=don, + ncp=ncp, + method=method, + row_w=row_w, + coeff_ridge=coeff_ridge, + threshold=threshold, + seed=seed, + maxiter=maxiter, + ) # noqa: E501 + if verbose: + print("done") + return res + + +def normtdc(tab_disj, data_na): + """Normalize the disjunctive table to ensure values are between 0 and 1. + + Parameters + ---------- + tab_disj : DataFrame + Disjunctive table to normalize. + data_na : DataFrame + DataFrame with original categorical data. + + Returns + ------- + DataFrame + Normalized disjunctive table. + + """ + tdc = tab_disj.copy() + tdc[tdc < 0] = 0 + tdc[tdc > 1] = 1 + col_suppr = np.cumsum( + [len(col.cat.categories) for _, col in data_na.items()] + ) # noqa: E501 + + def normalize_row(row, col_suppr): + start = 0 + for end in col_suppr: + segment = row[start:end] + total = np.sum(segment) + if total != 0: + row[start:end] = segment / total + start = end + return row + + tdc = tdc.apply( + lambda row: normalize_row(row.values, col_suppr), + axis=1, + result_type="expand", + ) # noqa: E501 + tdc.columns = tab_disj.columns + return tdc + + +def draw(tab_disj, Don, Don_na): + """Draw random samples from the normalized disjtable to reconstruct data. + + Parameters + ---------- + tab_disj : DataFrame + Normalized disjunctive table. + Don : DataFrame + Original complete dataset. + Don_na : DataFrame + Dataset with missing values. + + Returns + ------- + DataFrame + Reconstructed dataset with imputed categorical values. + + """ + Don_res = Don.copy() + nbdummy = np.ones(Don.shape[1], dtype=int) + is_quali = [ + i + for i, col in enumerate(Don.columns) + if not pd.api.types.is_numeric_dtype(Don[col]) + ] # noqa: E501 + nbdummy[is_quali] = [Don.iloc[:, i].nunique() for i in is_quali] + vec = np.concatenate(([0], np.cumsum(nbdummy))) + for idx, i in enumerate(is_quali): + start = vec[idx] + end = vec[idx + 1] + cols = tab_disj.columns[start:end] + probs = tab_disj[cols].values + categories = Don.iloc[:, i].cat.categories + sampled_indices = [] + for p in probs: + if np.sum(p) > 0: + p_normalized = p / np.sum(p) + sampled_idx = np.random.choice(len(categories), p=p_normalized) # noqa: E501 + else: + sampled_idx = np.nan + sampled_indices.append(sampled_idx) + Don_res.iloc[:, i] = pd.Categorical.from_codes( + sampled_indices, categories=categories + ) # noqa: E501 + return Don_res + + +def MIMCA( + X, + nboot=100, + ncp=2, + coeff_ridge=1, + threshold=1e-6, + maxiter=1000, + verbose=False, +): # noqa: E501 + """Perform Multiple Imputation with (MIMCA). + + Parameters + ---------- + X : DataFrame + Input data with missing values. + nboot : int, optional + Number of bootstrap samples. Default is 100. + ncp : int, optional + Number of principal components for MCA. Default is 2. + coeff_ridge : float, optional + Regularization coefficient for 'Regularized' MCA. Default is 1. + threshold : float, optional + Convergence threshold. Default is 1e-6. + maxiter : int, optional + Maximum number of iterations for the imputation process. + verbose : bool, optional + Whether to print progress. Default is False. + + Returns + ------- + dict + Dictionary containing the results of the multiple imputations. + + """ + import warnings + + X = X.copy() + # Convert non-numeric columns to categorical + is_quali = [ + col for col in X.columns if not pd.api.types.is_numeric_dtype(X[col]) + ] # noqa: E501 + X[is_quali] = X[is_quali].apply(lambda col: col.astype("category")) + X = X.apply( + lambda col: col.cat.remove_unused_categories() + if col.dtype.name == "category" + else col + ) # noqa: E501 + # Remove variables with only one category + OneCat = ( + X.apply( + lambda col: len(col.cat.categories) + if col.dtype.name == "category" + else np.nan + ) + == 1 + ) # noqa: E501 + if OneCat.any(): + warning_vars = X.columns[OneCat].tolist() + warnings.warn( + f"The following variables are constant and have been suppressed from the analysis: {', '.join(warning_vars)}" + ) # noqa: E501 + X = X.drop(columns=warning_vars) + if X.shape[1] <= 1: + raise ValueError( + "No sufficient variables have 2 categories or more" + ) # noqa: E501 + n = X.shape[0] + # Generate bootstrap weights + rng = np.random.default_rng() + Boot = rng.integers(low=0, high=n, size=(n, nboot)) + Weight = np.zeros((n, nboot)) + for i in range(nboot): + counts = np.bincount(Boot[:, i], minlength=n) + Weight[:, i] = counts + Weight = Weight / Weight.sum(axis=0) + # Perform multiple imputations + res_imp = [] + for i in range(nboot): + if verbose: + print(f"Imputation {i + 1}/{nboot}") + weight_i = Weight[:, i] + res = imputeMCA_print( + don=X, + ncp=ncp, + coeff_ridge=coeff_ridge, + threshold=threshold, # noqa: E501 + maxiter=maxiter, + row_w=weight_i, + verbose=verbose, + print_msg=f"Imputation {i + 1}", + ) # noqa: E501 + res_imp.append(res) + # Normalize the imputed disjunctive tables + tdc_imp = [res["tab_disj"] for res in res_imp] + res_comp = [res["completeObs"] for res in res_imp] + tdc_norm = [ + normtdc(tab_disj=tdc, data_na=comp) + for tdc, comp in zip(tdc_imp, res_comp) + ] # noqa: E501 + # Draw the final imputed datasets + X_imp = [ + draw(tab_disj=tdc, Don=comp, Don_na=X) + for tdc, comp in zip(tdc_norm, res_comp) + ] # noqa: E501 + # Compute the final imputed disjunctive table using all data + res_imputeMCA = imputeMCA( + X, + ncp=ncp, + coeff_ridge=coeff_ridge, + threshold=threshold, + maxiter=maxiter, + )["tab_disj"] + res = { + "res_MIs": X_imp, + "res_imputeMCA": res_imputeMCA, + "call": { + "X": X, + "nboot": nboot, + "ncp": ncp, + "coeff_ridge": coeff_ridge, + "threshold": threshold, + "maxiter": maxiter, + "tab_disj_array": np.array([tdc.values for tdc in tdc_imp]), + }, + } + return res diff --git a/qolmat/utils/algebra.py b/qolmat/utils/algebra.py index e78b6bd..a38fba6 100644 --- a/qolmat/utils/algebra.py +++ b/qolmat/utils/algebra.py @@ -1,5 +1,7 @@ """Utils algebra functions for qolmat package.""" +from typing import Optional, Tuple + import numpy as np import scipy from numpy.typing import NDArray @@ -96,3 +98,53 @@ def kl_divergence_gaussian_exact( term_diag_L = 2 * np.sum(np.log(np.diagonal(L2) / np.diagonal(L1))) div_kl = 0.5 * (norm_M - n_variables + norm_y + term_diag_L) return div_kl + + +def svdtriplet(X, row_w=None, ncp=np.inf): + """Perform weighted SVD on matrix X with row weights. + + Parameters + ---------- + X : ndarray + Data matrix of shape (n_samples, n_features). + row_w : array-like, optional + Row weights. If None, uniform weights are assumed. Default is None. + ncp : int + Number of principal components to retain. Default is infinity. + + Returns + ------- + s : ndarray + Singular values. + U : ndarray + Left singular vectors. + V : ndarray + Right singular vectors. + + """ + if not isinstance(X, np.ndarray): + X = np.array(X, dtype=float) + else: + X = X.astype(float) + if row_w is None: + row_w = np.ones(X.shape[0]) / X.shape[0] + else: + row_w = np.array(row_w, dtype=float) + row_w /= row_w.sum() + ncp = int(min(ncp, X.shape[0] - 1, X.shape[1])) + # Apply weights to rows + X_weighted = X * np.sqrt(row_w[:, None]) + # Perform SVD + U, s, Vt = np.linalg.svd(X_weighted, full_matrices=False) + V = Vt.T + U = U[:, :ncp] + V = V[:, :ncp] + s = s[:ncp] + # Adjust signs to ensure consistency + mult = np.sign(np.sum(V, axis=0)) + mult[mult == 0] = 1 + U *= mult + V *= mult + # Rescale U by the square root of row weights + U /= np.sqrt(row_w[:, None]) + return s, U, V diff --git a/qolmat/utils/data.py b/qolmat/utils/data.py index 1ae46f3..0ea1823 100644 --- a/qolmat/utils/data.py +++ b/qolmat/utils/data.py @@ -193,7 +193,8 @@ def get_data( df = read_csv_local("conductors") return df elif name_data == "Titanic": - path = "https://gist.githubusercontent.com/fyyying/4aa5b471860321d7b47fd881898162b7/raw/" + path = "https://gist.githubusercontent.com/" + "fyyying/4aa5b471860321d7b47fd881898162b7/raw/" "6907bb3a38bfbb6fccf3a8b1edfb90e39714d14f/titanic_dataset.csv" df = pd.read_csv(path) df = df[ diff --git a/qolmat/utils/utils.py b/qolmat/utils/utils.py index 34ccfd7..3f445e7 100644 --- a/qolmat/utils/utils.py +++ b/qolmat/utils/utils.py @@ -363,3 +363,166 @@ def nan_mean_cov(X: NDArray) -> Tuple[NDArray, NDArray]: cov = np.ma.cov(np.ma.masked_invalid(X), rowvar=False).data cov = cov.reshape(n_variables, n_variables) return means, cov + + +def moy_p(V, weights): + """Compute the weighted mean of a vector, ignoring NaNs. + + Parameters + ---------- + V : array-like + Input vector with possible NaN values. + weights : array-like + Weights corresponding to each element in V. + + Returns + ------- + float + Weighted mean of non-NaN elements. + + """ + mask = ~np.isnan(V) + total_weight = np.sum(weights[mask]) + if total_weight == 0: + return 0.0 # or use np.finfo(float).eps for a small positive value + return np.sum(V[mask] * weights[mask]) / total_weight + + +def tab_disjonctif_NA(df): + """Create a disjunctive (one-hot encoded). + + Parameters + ---------- + df : DataFrame + Input DataFrame with categorical and numeric variables. + + Returns + ------- + DataFrame + Disjunctive table with one-hot encoding. + + """ # noqa: E501 + df_encoded_list = [] + for col in df.columns: + if df[col].dtype.name == "category" or df[col].dtype == object: + df[col] = df[col].astype("category") + # Include '__MISSING__' as a category if not already present + if "__MISSING__" not in df[col].cat.categories: + df[col] = df[col].cat.add_categories(["__MISSING__"]) + # Fill missing values with '__MISSING__' + df[col] = df[col].fillna("__MISSING__") + # One-hot encode the categorical variable + encoded = pd.get_dummies( + df[col], + prefix=col, + prefix_sep="_", + dummy_na=False, + dtype=float, + ) + df_encoded_list.append(encoded) + else: + # Numeric column; keep as is + df_encoded_list.append(df[[col]]) + # Concatenate all encoded columns + df_encoded = pd.concat(df_encoded_list, axis=1) + return df_encoded + + +def tab_disjonctif_prop(df, seed=None): + """Perform probabilistic imputation for categorical columns using observed + value distributions, without creating a separate missing category. + + Parameters + ---------- + df : DataFrame + DataFrame with categorical columns to impute. + seed : int, optional + Random seed for reproducibility. Default is None. + + Returns + ------- + DataFrame + Disjunctive coded DataFrame with missing values probabilistically + imputed. + + """ # noqa: D205 + if seed is not None: + np.random.seed(seed) + df = df.copy() + df_encoded_list = [] + for col in df.columns: + if df[col].dtype.name == "category" or df[col].dtype == object: + # Ensure categories are strings + df[col] = df[col].cat.rename_categories( + df[col].cat.categories.astype(str) + ) + observed = df[col][df[col].notna()] + categories = df[col].cat.categories.tolist() + # Get observed frequencies + freqs = observed.value_counts(normalize=True) + # Impute missing values based on observed frequencies + missing_indices = df[col][df[col].isna()].index + if len(missing_indices) > 0: + imputed_values = np.random.choice( + freqs.index, size=len(missing_indices), p=freqs.values + ) + df.loc[missing_indices, col] = imputed_values + # One-hot encode without creating missing category + encoded = pd.get_dummies( + df[col], + prefix=col, + prefix_sep="_", + dummy_na=False, + dtype=float, + ) + col_names = [f"{col}_{cat}" for cat in categories] + encoded = encoded.reindex(columns=col_names, fill_value=0.0) + df_encoded_list.append(encoded) + else: + df_encoded_list.append(df[[col]]) + df_encoded = pd.concat(df_encoded_list, axis=1) + return df_encoded + + +def find_category(df_original, tab_disj): + """Reconstruct the original categorical variables from the disjunctive. + + Parameters + ---------- + df_original : DataFrame + Original DataFrame with categorical variables. + tab_disj : DataFrame + Disjunctive table after imputation. + + Returns + ------- + DataFrame + Reconstructed DataFrame with imputed categorical variables. + + """ + df_reconstructed = df_original.copy() + start_idx = 0 + for col in df_original.columns: + if ( + df_original[col].dtype.name == "category" + or df_original[col].dtype == object + ): # noqa: E501 + categories = df_original[col].cat.categories.tolist() + if "__MISSING__" in categories: + missing_cat_index = categories.index("__MISSING__") + else: + missing_cat_index = None + num_categories = len(categories) + sub_tab = tab_disj.iloc[:, start_idx : start_idx + num_categories] + if missing_cat_index is not None: + sub_tab.iloc[:, missing_cat_index] = -np.inf + # Find the category with the maximum value for each row + max_indices = sub_tab.values.argmax(axis=1) + df_reconstructed[col] = [categories[idx] for idx in max_indices] + # Replace '__MISSING__' back to NaN + df_reconstructed[col].replace("__MISSING__", np.nan, inplace=True) + start_idx += num_categories + else: + # For numeric variables, keep as is + start_idx += 1 # Increment start_idx by 1 for numeric columns + return df_reconstructed \ No newline at end of file diff --git a/tests/utils/test_algebra.py b/tests/utils/test_algebra.py index d043221..ae6a6ae 100644 --- a/tests/utils/test_algebra.py +++ b/tests/utils/test_algebra.py @@ -1,6 +1,7 @@ import numpy as np from qolmat.utils import algebra +from qolmat.utils.algebra import svdtriplet def test_frechet_distance_exact(): @@ -32,3 +33,113 @@ def test_kl_divergence_gaussian_exact(): ) / 2 result = algebra.kl_divergence_gaussian_exact(means1, cov1, means2, cov2) np.testing.assert_almost_equal(result, expected, decimal=3) + +def test_svdtriplet_known_matrix(): + """Test svdtriplet on a known matrix without weights.""" + X = np.array([[3, 1], [1, 3]]) + expected_singular_values = np.array([4, 2]) + expected_U = np.array([[0.7071, -0.7071], + [0.7071, 0.7071]]) + expected_V = np.array([[0.7071, 0.7071], + [0.7071, -0.7071]]) + # Call svdtriplet without weights + s, U, V = svdtriplet(X, row_w=None, ncp=2) + # Compare singular values + np.testing.assert_almost_equal(s, expected_singular_values, decimal=3) + np.testing.assert_almost_equal(np.abs(U), np.abs(expected_U), decimal=3) + np.testing.assert_almost_equal(np.abs(V), np.abs(expected_V), decimal=3) + +def test_svdtriplet_with_row_weights(): + """Test svdtriplet with row weights.""" + X = np.array([[1, 2], [3, 4], [5, 6]]) + row_w = np.array([0.2, 0.5, 0.3]) + # Manually compute the weighted X + X_weighted = X * np.sqrt(row_w)[:, None] + U_expected, s_expected, Vt_expected = np.linalg.svd(X_weighted, + full_matrices=False) + V_expected = Vt_expected.T + # Call svdtriplet with weights + s, U, V = svdtriplet(X, row_w=row_w, ncp=2) + # Rescale U_expected by dividing by sqrt(row_w) + U_expected /= np.sqrt(row_w)[:, None] + # Compare singular values + np.testing.assert_allclose(s, s_expected[:2], atol=1e-6) + # Compare U and V (up to sign) + np.testing.assert_allclose(np.abs(U), np.abs(U_expected[:, :2]), atol=1e-6) + np.testing.assert_allclose(np.abs(V), np.abs(V_expected[:, :2]), atol=1e-6) + +def test_svdtriplet_ncp_limit(): + """Test svdtriplet with ncp less than the full rank.""" + X = np.random.rand(5, 3) + ncp = 2 + s, U, V = svdtriplet(X, ncp=ncp) + # Check the dimensions + assert s.shape == (ncp,) + assert U.shape == (X.shape[0], ncp) + assert V.shape == (X.shape[1], ncp) + # Reconstruct X approximation + X_approx = U @ np.diag(s) @ V.T + # Check that the approximation is close to X + # Note: With reduced ncp, approximation won't be exact + assert X_approx.shape == X.shape + s_full, _, _ = svdtriplet(X) + X_full = U @ np.diag(s_full) @ V.T + error_ncp = np.linalg.norm(X - X_approx) + error_full = np.linalg.norm(X - X_full) + assert error_ncp >= error_full + +def test_svdtriplet_row_weights_none(): + """Test svdtriplet with default row weights.""" + X = np.random.rand(4, 4) + s_default, U_default, V_default = svdtriplet(X) + # Manually set uniform weights + row_w = np.ones(X.shape[0]) / X.shape[0] + s_manual, U_manual, V_manual = svdtriplet(X, row_w=row_w) + # Compare results + np.testing.assert_allclose(s_default, s_manual, atol=1e-6) + np.testing.assert_allclose(U_default, U_manual, atol=1e-6) + np.testing.assert_allclose(V_default, V_manual, atol=1e-6) + +def test_svdtriplet_zero_matrix(): + """Test svdtriplet on a zero matrix.""" + X = np.zeros((3, 3)) + s, U, V = svdtriplet(X) + # Singular values should be zero + expected_s = np.zeros(3) + np.testing.assert_array_equal(s, expected_s) + # U and V should be orthogonal matrices + np.testing.assert_allclose(U.T @ U, np.eye(3), atol=1e-6) + np.testing.assert_allclose(V.T @ V, np.eye(3), atol=1e-6) + +def test_svdtriplet_non_square_matrix(): + """Test svdtriplet on a non-square matrix.""" + X = np.random.rand(6, 4) + s, U, V = svdtriplet(X) + # Check dimensions + assert U.shape == (6, 4) + assert s.shape == (4,) + assert V.shape == (4, 4) + # Reconstruct X + X_reconstructed = U @ np.diag(s) @ V.T + np.testing.assert_allclose(X, X_reconstructed, atol=1e-6) + +def test_svdtriplet_large_ncp(): + """Test svdtriplet with ncp larger than possible.""" + X = np.random.rand(5, 3) + ncp = 10 # Larger than min(n_samples - 1, n_features) + s, U, V = svdtriplet(X, ncp=ncp) + expected_ncp = min(5 - 1, 3) + assert s.shape == (expected_ncp,) + assert U.shape == (5, expected_ncp) + assert V.shape == (3, expected_ncp) + +def test_svdtriplet_negative_weights(): + """Test svdtriplet with negative row weights (should raise an error).""" + X = np.random.rand(4, 4) + row_w = np.array([0.25, -0.25, 0.5, 0.5]) # Negative weight + with pytest.raises(ValueError): + s, U, V = svdtriplet(X, row_w=row_w) + + + +