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Also known as: Financial Projections, Projected Financials
A transformation that maps data vectors onto a lower-dimensional subspace while preserving relevant structure.
DESCRIPTION
Projections estimate future financial results, such as revenue, expenses, cash flow, and capital needs. They can be model-driven (e.g., regression, time series) or assumption-driven (e.g., growth rates, price-volume). Projections support planning, fundraising, and risk assessment through scenarios and sensitivity analysis. In data pipelines, projections are versioned datasets linked to underlying drivers and assumptions for traceability. Clear distinction from budgets (targets) and forecasts (best estimates) avoids confusion. Transparency in methods and uncertainty ranges improves decision value.
ALTERNATIVE DEFINITIONS
Wikipedia
In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that P^2 = P.
Defines projection algebraically as idempotent linear operator.
Encyclopedia of Mathematics
A projection is a linear operator P satisfying P^2 = P, representing the mapping onto a subspace along another subspace.
Links algebraic definition with geometric subspace mapping.
StatLect
An orthogonal projection maps a vector to the closest point in a subspace with respect to the Euclidean distance.
Highlights distance-minimization property of orthogonal projections.
RELATED TERMS
Budget Scenario Planning What-if Analysis Time Series Forecasting Predictive Analytics Sensitivity Analysis Driver-based Planning Monte Carlo Simulation Actuals Principal Component Analysis Orthogonal Projection Linear Algebra Feature Extraction Singular Value Decomposition Manifold Learning t-SNE UMAP Embeddings
COMPETING TERMS
Forecasts Scenarios Feature Reduction
RELATIONS
- Narrower: Map Projection Random Projection
KNOWLEDGE AREAS
Domain & Business Context Data Science Data Products Data Warehousing & BI Mathematics AI
TARGET AUDIENCE
Data Analyst Data Scientist BI Specialist AI Product Manager Data Strategy Consultant Chief Data Officer AI Engineer Data Modeler
EXTERNAL SOURCES
- Wikipedia - Projection (linear algebra)
- MIT OpenCourseWare - Lecture on projections onto subspaces
- StatLect - Orthogonal projection tutorial
- Wikipedia - PCA as projection onto principal subspace
TOP QUESTIONS
What is Projection in data analysis?
It’s a transformation mapping data onto a subspace to reduce dimensionality or simplify structure, often used in PCA and SVD.
Category: Overview
What is an orthogonal Projection?
It maps a vector to the closest point in a subspace under Euclidean distance, minimizing squared error.
Category: Example
How does Projection differ from Feature Selection?
Projection creates new features by combining originals. Feature selection picks a subset of existing features without transformation.
Category: Comparison
Where is Projection used in machine learning?
In PCA, embeddings, and visualization to compress data, denoise, and reveal latent structure.
Category: Topic
What mistakes occur when using Projection?
Projecting onto too few dimensions, ignoring interpretability, and misapplying linear projections to nonlinear data.
Category: Mistakes
What risks arise from aggressive Projection?
Loss of critical information and degraded model performance. Validate reconstruction error and downstream metrics.
Category: Risks
How do you choose the projection dimension?
Use explained variance, scree plots, or cross-validation to balance compression and information retention.
Category: Requirements
Is t-SNE a Projection?
t-SNE is a nonlinear embedding that preserves local neighborhoods; it’s not a linear projection but serves a similar dimensionality reduction goal.
Category: Misunderstanding
What is a striking analogy for Projection?
Like casting a shadow: you reduce dimensions while preserving essential shape from a specific viewpoint.
Category: Example