Taxonomy Distribution Report

Overview

• Total Concepts: 300
• Number of Taxonomies: 15
• Average Concepts per Taxonomy: 20.0

Distribution Summary

Category	TaxonomyID	Count	Percentage	Status
Foundation Concepts	FOUND	27	9.0%	✅
Transformations	TRANS	27	9.0%	✅
Neural Networks	NEURAL	26	8.7%	✅
Matrix Operations	MATOP	23	7.7%	✅
Linear Systems	LINSYS	23	7.7%	✅
ML Foundations	MLBASE	20	6.7%	✅
Autonomous Systems	AUTON	20	6.7%	✅
Decompositions	DECOMP	19	6.3%	✅
Inner Products	INPROD	19	6.3%	✅
Generative AI	GENAI	19	6.3%	✅
Eigentheory	EIGEN	17	5.7%	✅
3D Geometry	GEOM3D	17	5.7%	✅
Image Processing	IMGPROC	16	5.3%	✅
Optimization	OPTIM	14	4.7%	✅
Determinants	DETERM	13	4.3%	✅

Visual Distribution

FOUND  ████  27 (  9.0%)
TRANS  ████  27 (  9.0%)
NEURAL ████  26 (  8.7%)
MATOP  ███  23 (  7.7%)
LINSYS ███  23 (  7.7%)
MLBASE ███  20 (  6.7%)
AUTON  ███  20 (  6.7%)
DECOMP ███  19 (  6.3%)
INPROD ███  19 (  6.3%)
GENAI  ███  19 (  6.3%)
EIGEN  ██  17 (  5.7%)
GEOM3D ██  17 (  5.7%)
IMGPROC ██  16 (  5.3%)
OPTIM  ██  14 (  4.7%)
DETERM ██  13 (  4.3%)

Balance Analysis

✅ No Over-Represented Categories

All categories are under the 30% threshold. Good balance!

Category Details

Foundation Concepts (FOUND)

Count: 27 concepts (9.0%)

Concepts:

• 1. Scalar
• 1. Vector
• 1. Vector Notation
• 1. 2D Vector
• 1. 3D Vector
• 1. N-Dimensional Vector
• 1. Vector Addition
• 1. Scalar Multiplication
• 1. Vector Subtraction
• 1. Dot Product
• 1. Cross Product
• 1. Vector Magnitude
• 1. Unit Vector
• 1. Vector Normalization
• 1. Euclidean Distance
• ...and 12 more

Transformations (TRANS)

Count: 27 concepts (9.0%)

Concepts:

• 1. Function
• 1. Linear Transformation
• 1. Transformation Matrix
• 1. Domain
• 1. Codomain
• 1. Image
• 1. Rotation Matrix
• 1. 2D Rotation
• 1. 3D Rotation
• 1. Scaling Matrix
• 1. Uniform Scaling
• 1. Non-Uniform Scaling
• 1. Shear Matrix
• 1. Reflection Matrix
• 1. Projection
• ...and 12 more

Neural Networks (NEURAL)

Count: 26 concepts (8.7%)

Concepts:

• 1. Perceptron
• 1. Neuron Model
• 1. Activation Function
• 1. ReLU
• 1. Sigmoid
• 1. Tanh
• 1. Softmax
• 1. Weight Matrix
• 1. Bias Vector
• 1. Forward Propagation
• 1. Backpropagation
• 1. Chain Rule Matrices
• 1. Loss Function
• 1. Cross-Entropy Loss
• 1. Neural Network Layer
• ...and 11 more

Matrix Operations (MATOP)

Count: 23 concepts (7.7%)

Concepts:

• 1. Matrix
• 1. Matrix Notation
• 1. Matrix Dimensions
• 1. Row Vector
• 1. Column Vector
• 1. Matrix Entry
• 1. Matrix Addition
• 1. Matrix Scalar Multiply
• 1. Matrix-Vector Product
• 1. Matrix Multiplication
• 1. Matrix Transpose
• 1. Symmetric Matrix
• 1. Identity Matrix
• 1. Diagonal Matrix
• 1. Triangular Matrix
• ...and 8 more

Linear Systems (LINSYS)

Count: 23 concepts (7.7%)

Concepts:

• 1. Linear Equation
• 1. System of Equations
• 1. Matrix Equation Form
• 1. Augmented Matrix
• 1. Gaussian Elimination
• 1. Row Operations
• 1. Row Swap
• 1. Row Scaling
• 1. Row Addition
• 1. Row Echelon Form
• 1. Reduced Row Echelon Form
• 1. Pivot Position
• 1. Pivot Column
• 1. Free Variable
• 1. Basic Variable
• ...and 8 more

ML Foundations (MLBASE)

Count: 20 concepts (6.7%)

Concepts:

• 1. Feature Vector
• 1. Feature Matrix
• 1. Data Matrix
• 1. Covariance Matrix
• 1. Correlation Matrix
• 1. Standardization
• 1. PCA
• 1. Principal Component
• 1. Variance Explained
• 1. Scree Plot
• 1. Dimensionality Reduction
• 1. Linear Regression
• 1. Design Matrix
• 1. Ridge Regression
• 1. Lasso Regression
• ...and 5 more

Autonomous Systems (AUTON)

Count: 20 concepts (6.7%)

Concepts:

• 1. LIDAR Point Cloud
• 1. Camera Calibration
• 1. Sensor Fusion
• 1. Kalman Filter
• 1. State Vector
• 1. Measurement Vector
• 1. Prediction Step
• 1. Update Step
• 1. Kalman Gain
• 1. Extended Kalman Filter
• 1. State Estimation
• 1. SLAM
• 1. Localization
• 1. Mapping
• 1. Object Detection
• ...and 5 more

Decompositions (DECOMP)

Count: 19 concepts (6.3%)

Concepts:

• 1. Matrix Factorization
• 1. LU Decomposition
• 1. Partial Pivoting
• 1. QR Decomposition
• 1. Gram-Schmidt QR
• 1. Householder QR
• 1. Cholesky Decomposition
• 1. Positive Definite Matrix
• 1. SVD
• 1. Singular Value
• 1. Left Singular Vector
• 1. Right Singular Vector
• 1. Full SVD
• 1. Compact SVD
• 1. Truncated SVD
• ...and 4 more

Inner Products (INPROD)

Count: 19 concepts (6.3%)

Concepts:

• 1. Abstract Vector Space
• 1. Subspace
• 1. Vector Space Axioms
• 1. Inner Product
• 1. Inner Product Space
• 1. Norm from Inner Product
• 1. Cauchy-Schwarz Inequality
• 1. Orthogonality
• 1. Orthogonal Vectors
• 1. Orthonormal Set
• 1. Orthonormal Basis
• 1. Gram-Schmidt Process
• 1. Projection onto Subspace
• 1. Least Squares Problem
• 1. Normal Equations
• ...and 4 more

Generative AI (GENAI)

Count: 19 concepts (6.3%)

Concepts:

• 1. Embedding
• 1. Embedding Space
• 1. Word Embedding
• 1. Semantic Similarity
• 1. Cosine Similarity
• 1. Attention Mechanism
• 1. Self-Attention
• 1. Cross-Attention
• 1. Query Matrix
• 1. Key Matrix
• 1. Value Matrix
• 1. Attention Score
• 1. Attention Weights
• 1. Multi-Head Attention
• 1. Transformer Architecture
• ...and 4 more

Eigentheory (EIGEN)

Count: 17 concepts (5.7%)

Concepts:

• 1. Eigenvalue
• 1. Eigenvector
• 1. Eigen Equation
• 1. Characteristic Polynomial
• 1. Characteristic Equation
• 1. Eigenspace
• 1. Algebraic Multiplicity
• 1. Geometric Multiplicity
• 1. Diagonalization
• 1. Diagonal Form
• 1. Similar Matrices
• 1. Complex Eigenvalue
• 1. Spectral Theorem
• 1. Symmetric Eigenvalues
• 1. Power Iteration
• ...and 2 more

3D Geometry (GEOM3D)

Count: 17 concepts (5.7%)

Concepts:

• 1. 3D Coordinate System
• 1. Euler Angles
• 1. Gimbal Lock
• 1. Quaternion
• 1. Quaternion Rotation
• 1. Homogeneous Coordinates
• 1. Rigid Body Transform
• 1. SE3 Transform
• 1. Camera Matrix
• 1. Intrinsic Parameters
• 1. Extrinsic Parameters
• 1. Projection Matrix
• 1. Perspective Projection
• 1. Stereo Vision
• 1. Triangulation
• ...and 2 more

Image Processing (IMGPROC)

Count: 16 concepts (5.3%)

Concepts:

• 1. Image Matrix
• 1. Grayscale Image
• 1. RGB Image
• 1. Image Tensor
• 1. Image Convolution
• 1. Image Filter
• 1. Blur Filter
• 1. Sharpen Filter
• 1. Edge Detection
• 1. Sobel Operator
• 1. Fourier Transform
• 1. Frequency Domain
• 1. Image Compression
• 1. Color Space Transform
• 1. Feature Detection
• ...and 1 more

Optimization (OPTIM)

Count: 14 concepts (4.7%)

Concepts:

• 1. Hessian Matrix
• 1. Convexity
• 1. Convex Function
• 1. Newtons Method
• 1. Quasi-Newton Method
• 1. BFGS Algorithm
• 1. SGD
• 1. Mini-Batch SGD
• 1. Momentum
• 1. Adam Optimizer
• 1. RMSprop
• 1. Lagrange Multiplier
• 1. Constrained Optimization
• 1. KKT Conditions

Determinants (DETERM)

Count: 13 concepts (4.3%)

Concepts:

• 1. Determinant
• 1. 2x2 Determinant
• 1. 3x3 Determinant
• 1. Cofactor Expansion
• 1. Minor
• 1. Cofactor
• 1. Determinant Properties
• 1. Multiplicative Property
• 1. Transpose Determinant
• 1. Singular Matrix
• 1. Volume Scaling Factor
• 1. Signed Area
• 1. Cramers Rule

Recommendations

• ✅ Excellent balance: Categories are evenly distributed (spread: 4.7%)
• ✅ MISC category minimal: Good categorization specificity

Educational Use Recommendations

• Use taxonomy categories for color-coding in graph visualizations
• Design curriculum modules based on taxonomy groupings
• Create filtered views for focused learning paths
• Use categories for assessment organization
• Enable navigation by topic area in interactive tools

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Report generated by learning-graph-reports/taxonomy_distribution.py