Linear Discriminant Analysis vs Naive Bayes Calculator

Unknown Chemical Sample

Feature 1: pH

Feature 2: Absorbance

Feature 3: Conductivity

Class Labels and Priors

Class 1 Name

Class 2 Name

Prior for Class 1

Prior for Class 2

Class Means for Chemical Features

Class 1 Mean pH

Class 1 Mean Absorbance

Class 1 Mean Conductivity

Class 2 Mean pH

Class 2 Mean Absorbance

Class 2 Mean Conductivity

Shared Variances for LDA

Pooled Variance pH

Pooled Variance Absorbance

Pooled Variance Conductivity

Class Specific Variances for Naive Bayes

Class 1 Variance pH

Class 1 Variance Absorbance

Class 1 Variance Conductivity

Class 2 Variance pH

Class 2 Variance Absorbance

Class 2 Variance Conductivity

Example Data Table

Sample	Class	pH	Absorbance	Conductivity
S1	Batch A	6.20	0.61	760
S2	Batch A	6.55	0.67	790
S3	Batch B	7.30	0.84	960
S4	Batch B	7.55	0.91	1005
Unknown	To classify	6.80	0.72	850

Formula Used

LDA score: g_k(x) = ln(P(C_k)) + Σ[(x_jμ_kj / σ_j²) - (μ_kj² / 2σ_j²)]

Here, x is the unknown chemical sample. μ is the class mean for each feature. σ² is the pooled variance shared by both classes. The larger score gives the predicted class.

Naive Bayes score: ln(P(C_k)) + Σ[-0.5 ln(2πσ_kj²) - (x_j - μ_kj)² / 2σ_kj²]

Naive Bayes uses a separate variance for every class and feature. That makes it useful when different chemical categories show different spreads.

How to Use This Calculator

Enter the unknown sample values for pH, absorbance, and conductivity.
Name the two chemistry classes you want to compare.
Set priors for the classes. Use equal priors when unsure.
Enter class means from historical lab data.
Enter pooled variances for the LDA section.
Enter class-specific variances for the Naive Bayes section.
Click the compare button to see both method outputs.
Download the summary as CSV or PDF when needed.

About This Chemistry Classification Tool

This calculator helps chemistry teams compare two common classification approaches. It works well when you need a quick decision from measured lab features. Typical inputs include pH, absorbance, conductivity, concentration, or other analytical markers.

Linear discriminant analysis uses shared variance across classes. That means it expects the chemical groups to spread in a similar way. In practice, this assumption can work well for stable production batches. It is often easier to interpret because the rule stays linear.

Naive Bayes handles each class variance separately. It also treats every feature as conditionally independent. This can be useful when one chemical category is more variable than another. It may capture uneven lab behavior better than a shared variance model.

In chemistry, classification supports quality control and sample screening. It can also help compare raw materials, solvents, prepared solutions, or reaction outputs. You can use the tool to check whether an unknown sample looks closer to one reference group. Fast comparisons support earlier decisions before deeper testing.

The result section shows scores for both methods. Higher class scores indicate a stronger fit. The probability estimate gives a simple confidence view for the first class. A large score gap suggests clearer separation between the classes.

If LDA and Naive Bayes agree, your classification is more stable. If they disagree, your data may contain unequal spreads or overlapping signals. Review the feature means and variances carefully. Consider standardizing lab measurements before using any classifier.

This page is built for practical learning and fast comparisons. It does not replace full chemometric validation. Still, it offers a useful first pass for routine chemical data analysis. Use it with clean historical data for better results.

FAQs

1. What does this calculator compare?

It compares LDA and Gaussian Naive Bayes on the same chemical sample. Both methods score two classes using your feature values, class means, variances, and priors.

2. Why use chemistry features like pH and absorbance?

They are common measurable indicators in lab workflows. You can also replace them with concentration, density, retention time, or any numeric chemical descriptor.

3. When is LDA a better choice?

LDA is useful when both classes have similar spread patterns. It often performs well when production batches are controlled and the variance structure is relatively stable.

4. When is Naive Bayes a better choice?

Naive Bayes can help when classes have different variances. It is also handy for quick probabilistic screening with simple assumptions and limited modeling effort.

5. What do the prior values mean?

Priors represent expected class frequency before seeing the sample. If both classes are equally likely, enter 0.5 and 0.5.

6. Why can the two predictions differ?

The methods use different variance assumptions. LDA shares one variance structure, while Naive Bayes keeps separate class variances, so they may react differently to spread changes.

7. Can I use more than two classes?

This version is designed for two-class comparison. You can extend the logic in code by adding more class mean, variance, and score calculations.

8. Is this enough for final laboratory decisions?

No. It is a fast comparison tool. Final decisions should include validated methods, domain checks, calibration quality, and additional laboratory review.