πŸ“–
Wiki
CNCFSkywardAIHuggingFaceLinkedInKaggleMedium
  • Home
    • πŸš€About
  • πŸ‘©β€πŸ’»πŸ‘©Freesoftware
    • πŸ‰The GNU Hurd
      • πŸ˜„The files extension
      • πŸ“½οΈTutorial for starting
      • 🚚Continue Working for the Hurd
      • πŸš΄β€β™‚οΈcgo
        • πŸ‘―β€β™€οΈStatically VS Dynamically binding
        • 🧌Different ways in binding
        • πŸ‘¨β€πŸ’»Segfault
      • πŸ›ƒRust FFI
    • πŸ§šπŸ»β€β™‚οΈProgramming
      • πŸ“–Introduction to programming
      • πŸ“–Mutable Value Semantics
      • πŸ“–Linked List
      • πŸ“–Rust
        • πŸ“–Keyword dyn
        • πŸ“–Tonic framework
        • πŸ“–Tokio
        • πŸ“–Rust read files
  • πŸ›€οΈAI techniques
    • πŸ—„οΈframework
      • 🧷pytorch
      • πŸ““Time components
      • πŸ““burn
    • 🍑Adaptation
      • 🎁LoRA
        • ℹ️Matrix Factorization
        • πŸ“€SVD
          • ✝️Distillation of SVD
          • 🦎Eigenvalues of a covariance matrix
            • 🧧Eigenvalues
            • πŸͺCovariance Matrix
        • πŸ›«Checkpoint
      • 🎨PEFT
    • πŸ™‹β€β™‚οΈTraining
      • πŸ›»Training with QLoRA
      • 🦌Deep Speed
    • 🧠Stable Diffusion
      • πŸ€‘Stable Diffusion model
      • πŸ“ΌStable Diffusion v1 vs v2
      • πŸ€Όβ€β™€οΈThe important parameters for stunning AI image
      • ⚾Diffusion in image
      • 🚬Classifier Free Guidance
      • ⚜️Denoising strength
      • πŸ‘·Stable Diffusion workflow
      • πŸ“™LoRA(Stable Diffusion)
      • πŸ—ΊοΈDepth maps
      • πŸ“‹CLIP
      • βš•οΈEmbeddings
      • πŸ• VAE
      • πŸ’₯Conditioning
      • 🍁Diffusion sampling/samplers
      • πŸ₯ Prompt
      • πŸ˜„ControlNet
        • πŸͺ‘Settings Explained
        • 🐳ControlNet with models
    • πŸ¦™Large Language Model
      • ☺️SMID
      • πŸ‘¨β€πŸŒΎARM NEON
      • 🍊Metal
      • 🏁BLAS
      • πŸ‰ggml
      • πŸ’»llama.cpp
      • 🎞️Measuring model quality
      • πŸ₯žType for NNC
      • πŸ₯žToken
      • πŸ€Όβ€β™‚οΈDoc Retrieval && QA with LLMs
      • Hallucination(AI)
    • 🐹diffusers
      • πŸ’ͺDeconstruct the Stable Diffusion pipeline
  • 🎹Implementing
    • πŸ‘¨β€πŸ’»diffusers
      • πŸ“–The Annotated Diffusion Model
  • 🧩Trending
    • πŸ“–Trending
      • πŸ“–Vector database
      • 🍎Programming Languages
        • πŸ“–Go & Rust manage their memories
        • πŸ“–Performance of Rust and Python
        • πŸ“–Rust ownership and borrowing
      • πŸ“–Neural Network
        • 🎹Sliding window/convolutional filter
      • Quantum Machine Learning
  • 🎾Courses Collection
    • πŸ“–Courses Collection
      • πŸ“šAcademic In IT
        • πŸ“Reflective Writing
      • πŸ“–UCB
        • πŸ“–CS 61A
          • πŸ“–Computer Science
          • πŸ“–Scheme
          • πŸ“–Python
          • πŸ“–Data Abstraction
          • πŸ“–Object-Oriented Programming
          • πŸ“–Interpreters
          • πŸ“–Streams
      • 🍎MIT Algorithm Courses
        • 0️MIT 18.01
          • 0️Limits and continuity
          • 1️Derivatives
          • 3️Integrals
        • 1️MIT 6.042J
          • πŸ”’Number Theory
          • πŸ“ŠGraph Theory
            • 🌴Graph and Trees
            • 🌲Shortest Paths and Minimum Spanning Trees
        • 2️MIT 6.006
          • Intro and asymptotic notation
          • Sorting and Trees
            • Sorting
            • Trees
          • Hashing
          • Graphs
          • Shortest Paths
          • Dynamic Programming
          • Advanced
        • 3️MIT 6.046J
          • Divide and conquer
          • Dynamic programming
          • Greedy algorithms
          • Graph algorithms
Powered by GitBook
On this page
  • Background Information
  • What was it done?
  • What do eigenvalues and eigenvectors represent?
  • The important properties of eigenvalues of a covariance matrix
  • Summary

Was this helpful?

Edit on GitHub
  1. AI techniques
  2. Adaptation
  3. LoRA
  4. SVD

Eigenvalues of a covariance matrix

The eigenvalues of a covariance matrix play a crucial role in understanding the structure and properties of the data represented by the matrix.

Background Information

In statistics, a covariance matrix is a square matrix that summarizes the pairwise covariances between variables in a dataset. If you have a dataset with n variables, the covariance matrix will be an n x n matrix. The element in the i-th row and j-th column represents the covariance between variables i and j.

What was it done?

Now, the eigenvalues of a covariance matrix provide information about the variability or spread of the data along the principal components. Principal components are the directions in which the data vary the most. The eigenvalues quantify the amount of variance explained by each principal component.

What do eigenvalues and eigenvectors represent?

When you calculate the eigenvalues of a covariance matrix, you are essentially finding the scaling factors for each eigenvector. The eigenvectors, on the other hand, represent the directions along which the data varies the most.

The important properties of eigenvalues of a covariance matrix

  1. Non-negative: Eigenvalues are always non-negative. They can be zero or positive but not negative.

  2. Magnitude: The magnitude of an eigenvalue represents the amount of variance explained by the corresponding eigenvector. Larger eigenvalues indicate that the corresponding eigenvectors capture more of the data's variance.

  3. Ordering: Eigenvalues are typically ordered in descending order, with the largest eigenvalue corresponding to the first principal component, the second largest eigenvalue corresponding to the second principal component, and so on. This ordering allows us to prioritize the principal components based on the amount of variance they explain.

  4. Total variance: The sum of all eigenvalues equals the total variance of the data. This property is known as the trace property, and it implies that the sum of the eigenvalues gives us a measure of the total variability in the dataset.

Summary

Eigenvalues and eigenvectors provide a way to transform the original variables into a new set of variables called principal components. The principal components can be used to reduce the dimensionality of the data, visualize the data in a lower-dimensional space, or identify the most important features or patterns in the dataset.

PreviousDistillation of SVDNextEigenvalues

Last updated 1 year ago

Was this helpful?

πŸ›€οΈ
🍑
🎁
πŸ“€
🦎