SVC_CLASSIFY

Support vector classification (SVC) fits separating hyperplanes that maximize the margin between classes. By using the “kernel trick,” SVC can efficiently fit curved decision boundaries in higher-dimensional spaces. The decision function for a sample x is:

f(x) = \sum_{i=1}^n \alpha_i y_i K(x_i, x) + b

where K(x_i, x) is the kernel function. For the common Radial Basis Function (RBF) kernel, it is defined as:

K(x, x') = \exp(-\gamma \|x - x'\|^2)

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 support-vector summary properties.

Excel Usage

=SVC_CLASSIFY(data, target, C, svc_kernel, degree, svc_gamma, 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.
C (float, optional, default: 1): Inverse regularization strength. Smaller values apply stronger regularization.
svc_kernel (str, optional, default: “rbf”): Kernel function used to build the separating boundary.
degree (int, optional, default: 3): Polynomial degree when the polynomial kernel is used.
svc_gamma (str, optional, default: “scale”): Gamma scaling mode for non-linear kernels.
tol (float, optional, default: 0.001): Convergence tolerance for the optimizer.
random_state (int, optional, default: null): Integer seed for operations that use randomness. Leave blank for the estimator default.

Returns (dict): Excel data type containing training accuracy, predictions, decision scores, and support-vector summary properties.

Example 1: Fit an RBF support vector classifier for two string-labeled groups

Inputs:

data		target	C	svc_kernel	degree	svc_gamma	tol	random_state
0	0	cold	1	rbf	3	scale	0.001	0
0	1	cold
1	0	cold
2	2	hot
2	3	hot
3	2	hot

Excel formula:

=SVC_CLASSIFY({0,0;0,1;1,0;2,2;2,3;3,2}, {"cold";"cold";"cold";"hot";"hot";"hot"}, 1, "rbf", 3, "scale", 0.001, 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":2},"classes":{"type":"Array","elements":[[{"type":"String","basicValue":"cold"}],[{"type":"String","basicValue":"hot"}]]},"predictions":{"type":"Array","elements":[[{"type":"String","basicValue":"cold"}],[{"type":"String","basicValue":"cold"}],[{"type":"String","basicValue":"cold"}],[{"type":"String","basicValue":"hot"}],[{"type":"String","basicValue":"hot"}],[{"type":"String","basicValue":"hot"}]]},"prediction_counts":{"type":"Array","elements":[[{"type":"String","basicValue":"class"},{"type":"String","basicValue":"count"}],[{"type":"String","basicValue":"cold"},{"type":"Double","basicValue":3}],[{"type":"String","basicValue":"hot"},{"type":"Double","basicValue":3}]]},"decision_scores":{"type":"Array","elements":[[{"type":"Double","basicValue":-0.999733}],[{"type":"Double","basicValue":-0.999851}],[{"type":"Double","basicValue":-0.999782}],[{"type":"Double","basicValue":0.999772}],[{"type":"Double","basicValue":0.999772}],[{"type":"Double","basicValue":0.999822}]]},"support_vector_count":{"type":"Double","basicValue":6},"support_counts":{"type":"Array","elements":[[{"type":"Double","basicValue":3}],[{"type":"Double","basicValue":3}]]},"support_indices":{"type":"Array","elements":[[{"type":"Double","basicValue":0}],[{"type":"Double","basicValue":1}],[{"type":"Double","basicValue":2}],[{"type":"Double","basicValue":3}],[{"type":"Double","basicValue":4}],[{"type":"Double","basicValue":5}]]}}}

Example 2: Fit a linear support vector classifier for one-dimensional numeric labels

Inputs:

data	target	C	svc_kernel	degree	svc_gamma	tol	random_state
0	0	1	linear	3	scale	0.001	0
0.2	0
0.4	0
1.2	1
1.4	1
1.6	1

Excel formula:

=SVC_CLASSIFY({0;0.2;0.4;1.2;1.4;1.6}, {0;0;0;1;1;1}, 1, "linear", 3, "scale", 0.001, 0)

Expected output:

Example 3: Fit a support vector classifier for three separated groups

Inputs:

data		target	C	svc_kernel	degree	svc_gamma	tol	random_state
0	0	left	1	rbf	3	scale	0.001	0
0.2	0.1	left
4	4	center
4.2	3.9	center
8	0	right
8.2	0.1	right

Excel formula:

=SVC_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, "rbf", 3, "scale", 0.001, 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":0.847182},{"type":"Double","basicValue":2.22222},{"type":"Double","basicValue":-0.178542}],[{"type":"Double","basicValue":0.851956},{"type":"Double","basicValue":2.22115},{"type":"Double","basicValue":-0.17988}],[{"type":"Double","basicValue":2.22194},{"type":"Double","basicValue":0.835983},{"type":"Double","basicValue":-0.168615}],[{"type":"Double","basicValue":2.22125},{"type":"Double","basicValue":-0.167408},{"type":"Double","basicValue":0.836299}],[{"type":"Double","basicValue":0.850081},{"type":"Double","basicValue":-0.17988},{"type":"Double","basicValue":2.22184}],[{"type":"Double","basicValue":0.848998},{"type":"Double","basicValue":-0.179853},{"type":"Double","basicValue":2.22222}]]},"support_vector_count":{"type":"Double","basicValue":6},"support_counts":{"type":"Array","elements":[[{"type":"Double","basicValue":2}],[{"type":"Double","basicValue":2}],[{"type":"Double","basicValue":2}]]},"support_indices":{"type":"Array","elements":[[{"type":"Double","basicValue":2}],[{"type":"Double","basicValue":3}],[{"type":"Double","basicValue":0}],[{"type":"Double","basicValue":1}],[{"type":"Double","basicValue":4}],[{"type":"Double","basicValue":5}]]}}}

Example 4: Flatten a single-row boolean target range for support vector classification

Inputs:

data	target						C	svc_kernel	degree	svc_gamma	tol	random_state
0	false	false	false	true	true	true	1	linear	3	scale	0.001	0
0.3
0.6
1.4
1.7
2

Excel formula:

=SVC_CLASSIFY({0;0.3;0.6;1.4;1.7;2}, {FALSE,FALSE,FALSE,TRUE,TRUE,TRUE}, 1, "linear", 3, "scale", 0.001, 0)

Expected output:

Python Code

import numpy as np
from sklearn.svm import SVC as SklearnSVC

def svc_classify(data, target, C=1, svc_kernel='rbf', degree=3, svc_gamma='scale', tol=0.001, random_state=None):
    """
    Fit a support vector classifier and return training predictions.

    See: https://scikit-learn.org/stable/modules/generated/sklearn.svm.SVC.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.
        C (float, optional): Inverse regularization strength. Smaller values apply stronger regularization. Default is 1.
        svc_kernel (str, optional): Kernel function used to build the separating boundary. Valid options: RBF, Linear, Polynomial, Sigmoid. Default is 'rbf'.
        degree (int, optional): Polynomial degree when the polynomial kernel is used. Default is 3.
        svc_gamma (str, optional): Gamma scaling mode for non-linear kernels. Valid options: Scale, Auto. Default is 'scale'.
        tol (float, optional): Convergence tolerance for the optimizer. Default is 0.001.
        random_state (int, optional): Integer seed for operations that use randomness. Leave blank for the estimator default. Default is None.

    Returns:
        dict: Excel data type containing training accuracy, predictions, decision scores, and support-vector summary properties.
    """
    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

        if float(C) <= 0:
            return "Error: C must be greater than 0"
        kernel_value = str(svc_kernel).strip().lower()
        if kernel_value not in {"rbf", "linear", "poly", "sigmoid"}:
            return "Error: svc_kernel must be 'rbf', 'linear', 'poly', or 'sigmoid'"
        if int(degree) < 1:
            return "Error: degree must be at least 1"
        gamma_value = str(svc_gamma).strip().lower()
        if gamma_value not in {"scale", "auto"}:
            return "Error: svc_gamma must be 'scale' or 'auto'"
        if float(tol) <= 0:
            return "Error: tol must be greater than 0"

        fitted = SklearnSVC(
            C=float(C),
            kernel=kernel_value,
            degree=int(degree),
            gamma=gamma_value,
            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)))},
                "support_vector_count": {"type": "Double", "basicValue": float(len(fitted.support_))},
                "support_counts": {"type": "Array", "elements": col(fitted.n_support_.tolist())},
                "support_indices": {"type": "Array", "elements": col(fitted.support_.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.

Inverse regularization strength. Smaller values apply stronger regularization.

svc_kernel

Kernel function used to build the separating boundary.

degree

Polynomial degree when the polynomial kernel is used.

svc_gamma

Gamma scaling mode for non-linear kernels.

tol

Convergence tolerance for the optimizer.

random_state

Integer seed for operations that use randomness. Leave blank for the estimator default.