Linear Discriminant Analysis Calculator for Chemistry

Calculator Form

Class 1 label

Class 2 label

Feature names

Separate names with commas.

Prior probability for Class 1

Prior probability for Class 2

Regularization λ

Adds λ to diagonal terms for stability.

Reference Batch data

One sample per line. Use commas, spaces, or semicolons.

Test Batch data

Each row must match the same feature count.

Unknown sample

Optional single row for prediction.

Reset

Example Data Table

Chemistry sample set

Rows are samples. Columns are features. The same values are preloaded in the form for quick testing.

Sample	Class	Absorbance 450nm	Conductivity	Density
1	Reference Batch	0.82	12.4	1.018
2	Reference Batch	0.79	12.1	1.021
3	Reference Batch	0.85	12.7	1.017
4	Reference Batch	0.81	12.3	1.019
5	Reference Batch	0.84	12.6	1.020
6	Test Batch	0.61	10.8	0.998
7	Test Batch	0.58	10.5	1.001
8	Test Batch	0.64	11.0	0.997
9	Test Batch	0.60	10.7	0.999
10	Test Batch	0.63	10.9	1.000

Suggested unknown sample: 0.74, 11.7, 1.011

Formula Used

Class mean vectors

μ_k = (1 / n_k) Σ x_i

Pooled covariance matrix

Σ_p = [ (n₁ - 1)S₁ + (n₂ - 1)S₂ ] / (n₁ + n₂ - 2)

Regularized covariance

Σ_reg = Σ_p + λI

Weight vector and score

w = Σ_reg^-1(μ₁ - μ₂)

g(x) = w^Tx - 0.5μ₁^TΣ_reg^-1μ₁ + 0.5μ₂^TΣ_reg^-1μ₂ + ln(π₁/π₂)

In this calculator, a score of zero is the decision boundary. Positive values classify toward Class 1, while negative values classify toward Class 2.

How to Use This Calculator

Enter labels for the two chemistry classes you want to compare.
List feature names in order, such as absorbance, conductivity, density, peak area, or pH.
Paste one sample per line for each class. Keep the same number of values in every row.
Set prior probabilities and, if needed, add regularization to stabilize inversion.
Optionally enter one unknown sample, then submit to view scores, coefficients, covariance, prediction, and graph.

Frequently Asked Questions

1) What does this calculator do in chemistry?

It separates two chemical groups using measured variables such as absorbance, conductivity, density, retention time, or concentration. The calculator builds one discriminant axis, scores each sample, predicts an unknown, and reports coefficients, centroids, and pooled covariance.

2) How many variables can I enter?

You can enter any consistent number of variables, as long as every row contains the same count. More variables usually need more samples. If inversion becomes unstable, increase the regularization value slightly.

3) Why are at least two samples per class required?

LDA needs within-class variation to estimate covariance. With only one sample, the class spread cannot be measured properly, so the pooled covariance matrix and decision boundary become unreliable.

4) What does regularization change?

Regularization adds a small value to diagonal covariance terms. This reduces numerical instability when features are highly correlated, nearly duplicated, or when the sample size is small relative to the number of variables.

5) How do prior probabilities affect the result?

Priors shift the classification boundary toward the less likely class and favor the more likely class. Use them when one chemistry class is expected to occur more often before you inspect the measurements.

6) What does a positive discriminant score mean?

A positive score means the sample lies on the Class 1 side of the LDA boundary. A negative score means it lies on the Class 2 side. Larger magnitudes imply stronger separation from the boundary.

7) Can I use raw laboratory units directly?

Yes, but think carefully about scale. Very large-unit variables can dominate the model. If measurements span very different magnitudes, standardizing outside the calculator may improve interpretation and balance.

8) When should I avoid LDA?

Avoid LDA when class boundaries are strongly nonlinear, covariance structures differ greatly, outliers dominate the data, or the dataset is tiny compared with the number of variables. In those cases, another classifier may perform better.