Computes the row principal coordinates of a dataset. Same as calling `row_coordinates`. This is just for compatibility with scikit-le

Fit the model with X. The algorithm naturally fits and transforms at the same time, so this simply calls ``.fit_transform``

The column principal coordinates.

Returns the row principal coordinates. The row principal coordinates are obtained by projecting `X` on the right eigenvectors. Synon

The row principal coordinates.

Mapping of active group name → list of its columns in Z (output names). For numerical groups the output names are the original column names;

One-hot encode the input if needed, and align columns with the fitted indicator matrix.

Fit the model with X and return the aligned shapes. Parameters: X (array-like of shape (n_shapes, n_points, n_dim)): Matrix of

Extract the pre-scaled Z as a numpy array, in active-then-supplementary order.

Log-map quaternions to tangent space and return as DataFrame.

Extract quaternion array (n, 4) in scalar-first format from DataFrame.

Return the active columns of Z. Z is already pre-scaled, so this is a slice.

A faster way to fit/transform. This methods produces exactly the same result as calling `fit(X)` followed by `transform(X)`. It is ho

Returns the partial row principal coordinates.

Build the global pre-scaled Z block by applying each group's preprocessing. Active groups come first and supplementary groups are appended at

Build the standardized partial axes table and project onto global MFA axes. Returns (coord, labels, eig_ratios) where coord is the projected

Adjusted eigenvalues and total inertia for subset MCA with Greenacre correction. Ports the ``lambda = "adjusted"`` + ``subsetcat`` branch of

Return the cos2 for each column against the dimensions. The cos2 value gives an indicator of the accuracy of the column projection on the dim

Compute the Fréchet mean via iterative Riemannian gradient descent. Parameters ---------- points Quaternions (n,

Log map: compute rotation vectors of base^{-1} * points. Parameters ---------- base Base quaternion (4,) in scala

Returns the row principal coordinates.

Row principal coordinates in the MCA space.

Return the cos2 for each row against the dimensions. The cos2 value gives an indicator of the accuracy of the row projection on the dimension

Ensure quaternions are in the same hemisphere as the base. Quaternions q and -q represent the same rotation, so we pick the sign that

Apply the fitted per-group preprocessing to produce that group's Z block.

Return a column label's within-group portion (the group level removed). For MultiIndex columns ``(group, var)`` this is ``var``; for flat col

Column (category) principal coordinates in the MCA space.

Exp map: apply rotation vectors to base. Parameters ---------- base Base quaternion (4,) in scalar-first format (

Fit PGA to data. Parameters ---------- X Rotation data. A DataFrame with columns (qw, qx, qy, qz) or a

Fit the MCA on a categorical dataframe. The input is one-hot encoded into an indicator matrix (unless ``one_hot=False``), then corres

Transforms row projections back to their original space. In other words, return a dataset whose transform would be X.

Scree plot. References ---------- https://en.wikipedia.org/wiki/Scree_plot

Project rotation data onto principal geodesic components. Parameters ---------- X Rotation data (same format as f

Computes the row principal coordinates of a dataset.

Fit `data` to `reference` using procrustes analysis without scaling. Uses translation (mean-centering), reflection, and orthogonal rotation.

Return a summary of the eigenvalues and their importance.

Construct ellipse coordinates from two arrays of numbers. Args: X (1D array_like) Y (1D array_like) Returns: float:

Column coordinates from PCA in the tangent space.

Calculate correlations between variables and components. The correlation between a variable and a component estimates the information they sh

Correlations between variables and components. For quantitative variables, these are the signed Pearson correlations between each sta

Squared cosine similarities (cos2) of each column on each component.

Computes an SVD with k components.

Returns the percentage of explained inertia per principal component.

Returns the eigenvalues associated with each principal component.

Eigenvalues from PCA in the tangent space.

Returns the eigenvalues associated with each principal component.

Returns the eigenvalues associated with each principal component.

Return a summary of the eigenvalues and their importance.

Exponential map: project tangent vectors back to the manifold. Parameters ---------- base The base point on the m

Compute the Fréchet mean on the manifold. Parameters ---------- points Points on the manifold. weights

Returns the contribution of each group to each component. This is the sum of the variable contributions for all variables in the group.

Returns the coordinates of each group on each component. This is the group contribution scaled by the eigenvalue.