Representation
Geometric Models: Represent data and relationships using geometric constructs like
points, vectors, lines, and surfaces in high-dimensional spaces.
Probabilistic Models: Represent uncertainty and variability using probabilities,
capturing the likelihood of different outcomes and relationships between variables.
Logic Models: Represent relationships and rules using formal logic, with statements
that can be true or false based on logical reasoning.
2. Core Concepts
Geometric Models:
o Vectors and Matrices: Data points represented as vectors.
o Transformations: Operations such as rotation, translation, and scaling.
o Distances and Angles: Measures of similarity or difference.
Probabilistic Models:
o Probability Distributions: Describe the likelihood of different outcomes.
o Random Variables: Variables with probabilistic behaviors.
o Bayesian Inference: Updating beliefs based on new data.
Logic Models:
o Propositions: Basic statements that can be true or false.
o Predicates: Functions that return true or false values.
o Inference Rules: Logical operations to derive new truths from existing ones.
3. Applications
Geometric Models:
o Computer Graphics: Rendering and visualization.
o Machine Learning: Feature representation and dimensionality reduction.
o Robotics: Navigation and spatial reasoning.
Geometric Models: Represent data and relationships using geometric constructs like
points, vectors, lines, and surfaces in high-dimensional spaces.
Probabilistic Models: Represent uncertainty and variability using probabilities,
capturing the likelihood of different outcomes and relationships between variables.
Logic Models: Represent relationships and rules using formal logic, with statements
that can be true or false based on logical reasoning.
2. Core Concepts
Geometric Models:
o Vectors and Matrices: Data points represented as vectors.
o Transformations: Operations such as rotation, translation, and scaling.
o Distances and Angles: Measures of similarity or difference.
Probabilistic Models:
o Probability Distributions: Describe the likelihood of different outcomes.
o Random Variables: Variables with probabilistic behaviors.
o Bayesian Inference: Updating beliefs based on new data.
Logic Models:
o Propositions: Basic statements that can be true or false.
o Predicates: Functions that return true or false values.
o Inference Rules: Logical operations to derive new truths from existing ones.
3. Applications
Geometric Models:
o Computer Graphics: Rendering and visualization.
o Machine Learning: Feature representation and dimensionality reduction.
o Robotics: Navigation and spatial reasoning.
