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r cards

Methods for dimensionality reduction

Principal component analysis (PCA)
Multidimensinal scaling (MDS)

r cards

Methods for Clustering

k-means
model based clustering
hierarchical clustering
comparing clustering results

r cards

Multi-dimensional scaling general idea

Multidimensional scaling (MDS) is a means of visualizing the level of similarity of individual cases of a dataset. MDS is used to translate "information about the pairwise 'distances' among a set of n objects or individuals" into a configuration of n points mapped into an abstract Cartesian space. [Wikipedia]

r cards

Multi-dimensional scaling more technically...

More technically, MDS refers to a set of related ordination techniques used in information visualization, in particular to display the information contained in a distance matrix. It is a form of non-linear dimensionality reduction. Given a distance matrix with the distances between each pair of objects in a set, and a chosen number of dimensions, N, an MDS algorithm places each object into N-dimensional space such that the between-object distances are preserved as well as possible. If N is one or two, then 2D scatter plots of the resulting points are possible. [Wikipedia]

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Gaussian mixture model in general

Gaussian mixture model = probabilistic model
assumes all the data points are generated from a mixture of a finite number of Gaussian distributions with unknown parameters. One can think of mixture models as generalizing k-means clustering to incorporate information about the covariance structure of the data as well as the centers of the latent Gaussians. [https://scikit-learn.org/stable/modules/mixture.html]

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Deterministic model

In mathematics, computer science and physics, a deterministic system is a system in which no randomness is involved in the development of future states of the system. A deterministic model will thus always produce the same output from a given starting condition or initial state.

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Stochastic model

A stochastic model is a tool for estimating probability distributions of potential outcomes by allowing for random variation in one or more inputs over time. The random variation is usually based on fluctuations observed in historical data for a selected period using standard time-series techniques.

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Gaussian noise definition

Gaussian noise is statistical noise having a probability density function (PDF) equal to that of the normal distribution, which is also known as the Gaussian distribution.[1][2] In other words, the values that the noise can take on are Gaussian-distributed.
[Wikipedia]

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PCA and low redundancy

Correlation indicates that there is redundancy in the data. Due to this redundancy, PCA can be used to reduce the original variables into a smaller number of new variables ( = principal components) explaining most of the variance in the original variables.

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Intuition of PCA

PCA can be thought of as fitting an n-dimensional ellipsoid to the data.

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The Goals of a simple linear model analysis are?

1. Prediction of future observations
2. Assessment of the effect of, or relationship between, explanatory variables on the response
3. A general description of data structure

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Intuition of the way how to find the best parameters for the linear regression model?

Maximizing the likelihood is actually equivalent to minimizing the residual sum of squares (RSS)

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