Calculator Settings
Paste labeled vectors, choose analysis settings, and generate an interactive projection.
Formula Used
Each method transforms vectors while preserving selected geometric information. The formulas below explain projection, similarity, scaling, and clustering.
Principal Component Projection
PCA centers vectors and computes the covariance matrix. Leading eigenvectors define axes containing the largest observed variance.
Cosine Similarity
Cosine similarity compares directions rather than absolute vector magnitudes. Values near one indicate strongly aligned embedding directions.
Distance Measures
Euclidean distance measures straight separation across all dimensions. Manhattan distance sums absolute coordinate differences across the vectors.
K-Means Assignment
Each projected point joins its nearest centroid. Centroids update until assignments stabilize or iterations finish.
How to Use This Calculator
Enter one labeled vector on every input line. Keep every vector length equal and use numeric coordinates.
Choose scaling, projection, clustering, and neighbor settings. Direct plotting requires two different valid dimension numbers.
Press the calculation button to create the chart. Review neighbors, ranges, variance, clusters, and visible semantic patterns.
Word-Embedding Visualization Guide
Understanding Embedding Scatter Plots
Word embeddings convert language into vectors containing semantic relationships. Similar words often occupy nearby regions within high dimensional space. Scatter projections reveal those relationships through two dimensional views.
Why Projection Matters
Embedding dimensions frequently exceed limits for direct visual inspection. Projection methods compress dimensions while preserving useful geometric patterns. Methods introduce tradeoffs between fidelity, speed, and interpretability.
Using Principal Component Analysis
Principal component analysis finds directions containing maximum variance. The first component captures the strongest variation across vectors. The second component captures remaining variation along an orthogonal direction.
Exploring Direct Dimensions
Direct dimension plotting shows two selected embedding coordinates unchanged. This approach helps inspect specific learned features or debugging targets. However, selected dimensions may hide broader semantic organization completely.
Applying Random Projection
Random projection maps vectors through seeded weighted combinations of dimensions. It offers fast comparisons and preserves distances approximately across points. Reusing the seed produces consistent layouts during repeated analysis.
Preparing Vector Data
Each input row starts with a label and numeric coordinates. Consistent vector lengths are required for reliable calculations and projections. Remove malformed rows before comparing neighborhoods or generating clusters.
Choosing Vector Scaling
L2 normalization emphasizes direction instead of raw vector magnitude differences. Centering subtracts feature means before projection and variance analysis. Standardization also divides each feature by its observed spread.
Interpreting Similarity
Cosine similarity compares vector direction and suits many language models. Euclidean distance measures straight line separation between embedding points. Manhattan distance sums coordinate differences and reduces squared deviation effects.
Reading Clusters Carefully
Clusters can suggest topics, categories, contexts, or dataset artifacts. Projected overlap does not always imply identical high dimensional meaning. Always verify visual patterns using distances from original embedding vectors.
Using Neighbor Results
Choose an anchor label to inspect its closest semantic neighbors. Neighbor tables expose similarity scores beyond the displayed projection alone. Unexpected neighbors may reveal ambiguity, bias, noise, or preprocessing mistakes.
Improving Visual Clarity
Labels help small datasets but clutter charts containing many points. Marker opacity reveals dense regions where several projected points overlap. Cluster coloring can separate groups without changing calculated coordinates.
Practical Model Analysis
Compare projections before making conclusions about embedding quality or structure. Stable patterns across methods provide stronger evidence than isolated layouts. Use domain knowledge to explain groups, boundaries, and unusual neighbors.
Common Limitations
Two dimensional plots cannot preserve every relationship from larger spaces. PCA favors linear variance and may miss curved semantic manifolds. Random projections support exploration but do not explain learned directions.
Responsible Interpretation
Embeddings may encode social biases found within their training data. Visual clusters require careful review before supporting important decisions. Document settings, sources, and assumptions for reproducible embedding analysis.
Frequently Asked Questions
What input format does the calculator accept?
Each line needs one label and at least two numbers. Separate values with commas, tabs, semicolons, or spaces. Every row must contain the same coordinate count.
Which projection method should I choose?
PCA suits structured linear exploration and variance review. Direct dimensions help inspect known coordinates. Random projection supports fast, repeatable comparisons across larger vectors.
Does the scatter plot preserve every semantic relationship?
No two dimensional projection preserves every original relationship. Always compare visible placement with neighbor scores. Multiple projections provide stronger evidence than one chart.
Why should vectors be normalized?
L2 normalization reduces magnitude effects and emphasizes vector direction. This choice often supports cosine based embedding analysis. Other scaling methods may suit different model outputs.
How are nearest neighbors calculated?
The calculator compares the anchor against original input vectors. Cosine ranks higher similarity first. Distance metrics rank smaller values first.
What does cluster coloring mean?
Cluster coloring applies k-means to the projected coordinates. Colors show calculated groups within that specific layout. They do not prove true linguistic categories.
Can I plot hundreds of words?
Yes, the parser accepts up to five hundred valid rows. Hide labels for crowded datasets. Smaller markers and lower opacity improve dense charts.
Why do random projections change?
Random weights create different two dimensional combinations. The seed controls those generated weights. Reusing one seed produces the same projection.
Can the chart reveal embedding bias?
The chart may expose suspicious groups or neighboring terms. Visual evidence requires deeper testing and contextual review. Careful interpretation keeps projected patterns useful and responsibly explained.