RIDGE_CLASSIFY

Ridge classification converts the target labels to \{-1, 1\} (for binary) and treats the task as a regression problem with L2 regularization. The weights w are found by minimizing the penalized squared error:

\min_{w} \|Xw - y\|^2 + \alpha \|w\|^2

The predicted class is the one with the largest linear decision score. It is a fast baseline for dense tabular classification tasks when calibrated probabilities are not required.

This wrapper accepts rows as samples and a target supplied as a single row or single column. It returns training accuracy together with predicted labels, class counts, decision scores, and fitted coefficient arrays.

Excel Usage

=RIDGE_CLASSIFY(data, target, alpha, ridge_solver, fit_intercept, tol, random_state)

data (list[list], required): 2D array of numeric feature data with rows as samples and columns as features.
target (list[list], required): Target labels as a single row, single column, or scalar when only one sample is present.
alpha (float, optional, default: 1): L2 regularization strength applied to the classifier.
ridge_solver (str, optional, default: “auto”): Linear algebra solver used to fit the classifier.
fit_intercept (bool, optional, default: true): Whether to include an intercept term in the linear decision function.
tol (float, optional, default: 0.0001): Convergence tolerance for iterative solvers.
random_state (int, optional, default: null): Integer seed for stochastic solvers. Leave blank for the estimator default.

Returns (dict): Excel data type containing training accuracy, predictions, decision scores, and fitted coefficient arrays.

Example 1: Fit ridge classification for two string-labeled classes

Inputs:

data		target	alpha	ridge_solver	fit_intercept	tol	random_state
0	0	cold	1	auto	true	0.0001	0
0	1	cold
1	0	cold
2	2	hot
2	3	hot
3	2	hot

Excel formula:

=RIDGE_CLASSIFY({0,0;0,1;1,0;2,2;2,3;3,2}, {"cold";"cold";"cold";"hot";"hot";"hot"}, 1, "auto", TRUE, 0.0001, 0)

Expected output:

Example 2: Flatten a single-row numeric target for ridge classification

Inputs:

data	target						alpha	ridge_solver	fit_intercept	tol	random_state
0	0	0	0	1	1	1	1	auto	true	0.0001	0
0.2
0.4
1.2
1.4
1.6

Excel formula:

=RIDGE_CLASSIFY({0;0.2;0.4;1.2;1.4;1.6}, {0,0,0,1,1,1}, 1, "auto", TRUE, 0.0001, 0)

Expected output:

Example 3: Fit ridge classification for three separated groups

Inputs:

data		target	alpha	ridge_solver	fit_intercept	tol	random_state
0	0	left	1	auto	true	0.0001	0
0.2	0.1	left
4	4	center
4.2	3.9	center
8	0	right
8.2	0.1	right

Excel formula:

=RIDGE_CLASSIFY({0,0;0.2,0.1;4,4;4.2,3.9;8,0;8.2,0.1}, {"left";"left";"center";"center";"right";"right"}, 1, "auto", TRUE, 0.0001, 0)

Expected output:

{"type":"Double","basicValue":1,"properties":{"accuracy":{"type":"Double","basicValue":1},"sample_count":{"type":"Double","basicValue":6},"feature_count":{"type":"Double","basicValue":2},"class_count":{"type":"Double","basicValue":3},"classes":{"type":"Array","elements":[[{"type":"String","basicValue":"center"}],[{"type":"String","basicValue":"left"}],[{"type":"String","basicValue":"right"}]]},"predictions":{"type":"Array","elements":[[{"type":"String","basicValue":"left"}],[{"type":"String","basicValue":"left"}],[{"type":"String","basicValue":"center"}],[{"type":"String","basicValue":"center"}],[{"type":"String","basicValue":"right"}],[{"type":"String","basicValue":"right"}]]},"prediction_counts":{"type":"Array","elements":[[{"type":"String","basicValue":"class"},{"type":"String","basicValue":"count"}],[{"type":"String","basicValue":"center"},{"type":"Double","basicValue":2}],[{"type":"String","basicValue":"left"},{"type":"Double","basicValue":2}],[{"type":"String","basicValue":"right"},{"type":"Double","basicValue":2}]]},"decision_scores":{"type":"Array","elements":[[{"type":"Double","basicValue":-0.992335},{"type":"Double","basicValue":1.00431},{"type":"Double","basicValue":-1.01198}],[{"type":"Double","basicValue":-0.943513},{"type":"Double","basicValue":0.930727},{"type":"Double","basicValue":-0.987214}],[{"type":"Double","basicValue":0.960875},{"type":"Double","basicValue":-0.955539},{"type":"Double","basicValue":-1.00534}],[{"type":"Double","basicValue":0.912022},{"type":"Double","basicValue":-0.980309},{"type":"Double","basicValue":-0.931713}],[{"type":"Double","basicValue":-0.992936},{"type":"Double","basicValue":-0.962803},{"type":"Double","basicValue":0.955739}],[{"type":"Double","basicValue":-0.944113},{"type":"Double","basicValue":-1.03639},{"type":"Double","basicValue":0.980501}]]},"coefficients":{"type":"Array","elements":[[{"type":"Double","basicValue":-0.0000750657},{"type":"Double","basicValue":0.488378}],[{"type":"Double","basicValue":-0.245889},{"type":"Double","basicValue":-0.244073}],[{"type":"Double","basicValue":0.245964},{"type":"Double","basicValue":-0.244304}]]},"intercepts":{"type":"Array","elements":[[{"type":"Double","basicValue":-0.992335}],[{"type":"Double","basicValue":1.00431}],[{"type":"Double","basicValue":-1.01198}]]}}}

Example 4: Fit ridge classification with boolean target labels

Inputs:

data	target	alpha	ridge_solver	fit_intercept	tol	random_state
0	false	1	auto	true	0.0001	0
0.3	false
0.6	false
1.4	true
1.7	true
2	true

Excel formula:

=RIDGE_CLASSIFY({0;0.3;0.6;1.4;1.7;2}, {FALSE;FALSE;FALSE;TRUE;TRUE;TRUE}, 1, "auto", TRUE, 0.0001, 0)

Expected output:

Python Code

import numpy as np
from sklearn.linear_model import RidgeClassifier as SklearnRidgeClassifier

def ridge_classify(data, target, alpha=1, ridge_solver='auto', fit_intercept=True, tol=0.0001, random_state=None):
    """
    Fit a ridge classifier and return training predictions with decision scores.

    See: https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.RidgeClassifier.html

    This example function is provided as-is without any representation of accuracy.

    Args:
        data (list[list]): 2D array of numeric feature data with rows as samples and columns as features.
        target (list[list]): Target labels as a single row, single column, or scalar when only one sample is present.
        alpha (float, optional): L2 regularization strength applied to the classifier. Default is 1.
        ridge_solver (str, optional): Linear algebra solver used to fit the classifier. Valid options: Auto, SVD, LSQR, SAG, SAGA. Default is 'auto'.
        fit_intercept (bool, optional): Whether to include an intercept term in the linear decision function. Default is True.
        tol (float, optional): Convergence tolerance for iterative solvers. Default is 0.0001.
        random_state (int, optional): Integer seed for stochastic solvers. Leave blank for the estimator default. Default is None.

    Returns:
        dict: Excel data type containing training accuracy, predictions, decision scores, and fitted coefficient arrays.
    """
    def py(value):
        return value.item() if isinstance(value, np.generic) else value

    def cell(value):
        value = py(value)
        if isinstance(value, bool):
            return {"type": "Boolean", "basicValue": bool(value)}
        if isinstance(value, (int, float)) and not isinstance(value, bool):
            return {"type": "Double", "basicValue": float(value)}
        return {"type": "String", "basicValue": str(value)}

    def col(values):
        return [[cell(value)] for value in values]

    def mat(values):
        return [[cell(value) for value in row] for row in values]

    def parse_data(value):
        value = [[value]] if not isinstance(value, list) else value
        if not isinstance(value, list) or not value or not all(isinstance(row, list) and row for row in value):
            return None, "Error: data must be a non-empty 2D list"
        if len({len(row) for row in value}) != 1:
            return None, "Error: data must be a rectangular 2D list"
        data_np = np.array(value, dtype=float)
        if data_np.ndim != 2 or data_np.size == 0:
            return None, "Error: data must be a non-empty 2D list"
        if not np.isfinite(data_np).all():
            return None, "Error: data must contain only finite numeric values"
        return data_np, None

    def parse_target(value, sample_count):
        if not isinstance(value, list):
            labels = [value]
        elif not value:
            return None, "Error: target must be non-empty"
        elif all(not isinstance(item, list) for item in value):
            labels = value
        elif len(value) == 1:
            labels = value[0]
        elif all(isinstance(row, list) and len(row) == 1 for row in value):
            labels = [row[0] for row in value]
        else:
            return None, "Error: target must be a single row or column"

        if len(labels) != sample_count:
            return None, "Error: target length must match sample count"

        parsed = []
        classes = []
        for item in labels:
            item = py(item)
            if isinstance(item, str):
                if not item.strip():
                    return None, "Error: target labels must not be blank"
            elif isinstance(item, bool):
                item = bool(item)
            elif isinstance(item, (int, float)) and not isinstance(item, bool):
                if not np.isfinite(float(item)):
                    return None, "Error: target labels must be finite"
                item = float(item) if isinstance(item, float) else int(item)
            else:
                return None, "Error: target labels must be scalar string, boolean, or numeric values"
            parsed.append(item)
            if not any(type(existing) is type(item) and existing == item for existing in classes):
                classes.append(item)

        if len(classes) < 2:
            return None, "Error: target must contain at least 2 classes"
        return parsed, None

    def count_table(predictions, classes):
        rows = [[{"type": "String", "basicValue": "class"}, {"type": "String", "basicValue": "count"}]]
        for class_label in classes:
            count = sum(type(prediction) is type(class_label) and prediction == class_label for prediction in predictions)
            rows.append([cell(class_label), {"type": "Double", "basicValue": float(count)}])
        return rows

    def score_rows(values):
        values = np.asarray(values)
        return [[float(value)] for value in values.tolist()] if values.ndim == 1 else values.tolist()

    try:
        data_np, error = parse_data(data)
        if error:
            return error

        target_values, error = parse_target(target, data_np.shape[0])
        if error:
            return error

        solver_value = str(ridge_solver).strip().lower()
        if solver_value not in {"auto", "svd", "lsqr", "sag", "saga"}:
            return "Error: solver must be 'auto', 'svd', 'lsqr', 'sag', or 'saga'"
        if float(alpha) < 0:
            return "Error: alpha must be non-negative"
        if float(tol) <= 0:
            return "Error: tol must be greater than 0"

        fitted = SklearnRidgeClassifier(
            alpha=float(alpha),
            solver=solver_value,
            fit_intercept=bool(fit_intercept),
            tol=float(tol),
            random_state=None if random_state in (None, "") else int(random_state)
        ).fit(data_np, target_values)

        prediction_array = fitted.predict(data_np)
        predictions = [py(item) for item in prediction_array.tolist()]
        classes = [py(item) for item in fitted.classes_.tolist()]
        accuracy = float(np.mean([
            type(prediction) is type(actual) and prediction == actual
            for prediction, actual in zip(predictions, target_values)
        ]))

        return {
            "type": "Double",
            "basicValue": accuracy,
            "properties": {
                "accuracy": {"type": "Double", "basicValue": accuracy},
                "sample_count": {"type": "Double", "basicValue": float(data_np.shape[0])},
                "feature_count": {"type": "Double", "basicValue": float(data_np.shape[1])},
                "class_count": {"type": "Double", "basicValue": float(len(classes))},
                "classes": {"type": "Array", "elements": col(classes)},
                "predictions": {"type": "Array", "elements": col(predictions)},
                "prediction_counts": {"type": "Array", "elements": count_table(predictions, classes)},
                "decision_scores": {"type": "Array", "elements": mat(score_rows(fitted.decision_function(data_np)))},
                "coefficients": {"type": "Array", "elements": mat(np.atleast_2d(fitted.coef_).tolist())},
                "intercepts": {"type": "Array", "elements": col(np.atleast_1d(fitted.intercept_).tolist())}
            }
        }
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

data *

2D array of numeric feature data with rows as samples and columns as features.

target *

Target labels as a single row, single column, or scalar when only one sample is present.

alpha

L2 regularization strength applied to the classifier.

ridge_solver

Linear algebra solver used to fit the classifier.

fit_intercept

Whether to include an intercept term in the linear decision function.

tol

Convergence tolerance for iterative solvers.

random_state

Integer seed for stochastic solvers. Leave blank for the estimator default.