Calculator Inputs
Formulas Used
Sum normalization
pi = (xi + ε) / Σ(xj + ε)
Softmax scaling
pi = exp(xi/T) / Σ exp(xj/T)
Power scaling
pi = (xiα + ε) / Σ(xjα + ε)
Shannon entropy
H = −Σ pi ln(pi)
Normalized entropy
Hn = H / ln(K)
Concentration and perplexity
HHI = Σpi2, Perplexity = exp(H)
How to Use This Calculator
- Enter one topic label and value on every line.
- Select normalization matching your model output format.
- Adjust temperature, power, smoothing, or grouping controls.
- Choose the chart style, ordering, labels, and precision.
- Press Calculate Distribution to generate metrics and visualization.
- Review entropy, concentration, dominance, and cumulative topic mass.
- Export the chart or table for reporting workflows.
Understanding Topic Distribution Charts
Distribution Foundations
Topic distribution charts summarize how strongly themes appear within modeled text. Each bar or slice represents one estimated topic probability. Together, these values explain the model’s thematic emphasis.
Normalized distributions make outputs comparable across documents, batches, and experiments. Raw scores often use different ranges or model-specific scales. Normalization converts them into proportions with a shared total.
Dominance and Uncertainty
Dominance describes how strongly the largest topic controls the distribution. A high dominant share suggests narrow thematic focus. A low share usually indicates broader topic mixing.
Entropy measures uncertainty across the complete set of topics. Higher entropy indicates more even probability allocation. Lower entropy highlights concentrated or specialized model behavior.
Comparable Diversity
Normalized entropy adjusts entropy for the number of active topics. This makes different topic counts easier to compare. Values near one indicate strongly balanced topic weights.
Perplexity transforms entropy into an effective topic count. It estimates how many equally likely topics match observed uncertainty. Larger values represent richer thematic diversity.
Concentration and Filtering
The concentration index squares every normalized topic probability. Large probabilities therefore influence the index more heavily. Higher concentration reveals distributions driven by fewer topics.
Threshold controls can remove tiny values from visual attention. Small topics may otherwise crowd labels and legends. Grouping them as Other preserves their combined contribution.
Reducing Visual Noise
Top-topic limits simplify charts with many discovered themes. The calculator keeps leading topics based on selected ordering. Remaining probabilities can be grouped without losing total mass.
Percentage labels support quick communication with nontechnical audiences. Exact values still matter during model review. Display both when precision and accessibility matter.
Scaling Controls
Softmax scaling is useful when inputs are unrestricted model scores. Temperature controls how sharply softmax separates competing topics. Lower temperatures emphasize winners, while higher temperatures flatten differences.
Power scaling offers another controlled contrast adjustment. Exponents above one increase separation between strong and weak topics. Exponents below one create a gentler, more balanced distribution.
Selecting Charts
Chart selection should match the question being investigated. Bars support precise comparisons across many topics. Pie and donut charts communicate broad composition quickly.
Radar charts reveal shape patterns across repeated evaluations. They work best with a limited topic count. Excess categories can make radial comparisons difficult.
Coverage and Interpretation
Cumulative shares help identify compact topic coverage. Analysts can inspect how quickly leading topics explain mass. This supports trimming, reporting, and downstream routing.
Reliable interpretation requires consistent labels, preprocessing, and model settings. Compare charts only when their inputs share equivalent meaning. Reliable inputs produce clearer charts and stronger model decisions.
Frequently Asked Questions
1. What values can I enter?
Enter probabilities, counts, weights, logits, or positive model scores. Select the matching normalization method before calculating. Softmax supports negative logits, while other scaling methods require nonnegative values.
2. Which separator should each row use?
Use a comma, colon, equals sign, or tab. Place the topic label first and its value second. Every topic should appear on a separate line.
3. When should softmax scaling be selected?
Choose softmax when inputs are logits or unrestricted model scores. Temperature below one sharpens differences between topics. Temperature above one creates a flatter distribution.
4. What does normalized entropy show?
Normalized entropy measures balance while considering topic count. Values near zero indicate strong concentration. Values near one indicate probabilities distributed more evenly.
5. Why use a grouping threshold?
A threshold combines very small topics into one category. This reduces clutter without discarding their combined mass. It is useful for presentations and crowded topic models.
6. What does the concentration index mean?
The concentration index sums squared topic probabilities. Larger values indicate stronger dominance by fewer topics. Its reciprocal estimates the effective number of topics.
7. Can duplicate topic labels be entered?
Yes. Duplicate labels are combined before normalization. Their values are added, producing one final topic entry.
8. Which chart type supports precise comparison?
Bar charts usually provide the clearest numerical comparison. Horizontal bars help when labels are long. Pie charts are better for broad composition summaries.
9. How should different documents be compared?
Use consistent topic labels, preprocessing, and normalization settings. Keep chart ordering stable across every comparison. Reliable inputs produce clearer charts and stronger model decisions.