Sparse Principal Component Analysis (PCA)

Dimensionality Reduction

• Sparse Principal Component Analysis (Sparse PCA) is a variant of traditional Principal Component Analysis (PCA) that introduces sparsity constraints on the principal components.
• Sparse PCA provides a more interpretable set of principal components, performs feature selection and dimensionality reduction simultaneously, and is more efficient than regular PCA in handling high-dimensional data.
• Factor Analysis (FA) is a statistical technique used for dimensionality reduction and exploring the underlying structure in a dataset, assuming that observed variables are influenced by latent factors.

Clustering

• Two-steps clustering is a clustering algorithm used to group data points into clusters based on their similarities, particularly useful for dealing with large datasets or data sets containing both categorical and continuous variables.
• Bi-clustering, also known as block clustering or co-clustering, is a data mining technique that allows simultaneous clustering of both rows and columns of a matrix, particularly useful for identifying groups of data items that exhibit consistent patterns across both rows and columns.
• Latent clustering, also known as Latent Class Cluster Analysis (LCCA), is a powerful technique that can uncover hidden structures in data by identifying latent subgroups or classes.
• K-means clustering is a popular and powerful unsupervised machine learning algorithm that can be used to group data points into distinct clusters based on their similarities.

Time Series Analysis

• Stochastic approach is a type of time series analysis that involves modeling the future behavior of a time series as uncertain and can be modeled using probability distributions.
• Time series decomposition is a technique used to break down a time series into its underlying component, typically trend, seasonality, and residual components.
• Linear trend model is a deterministic approach used to identify and model trends in time series, assuming that the time series follows a straight line trend over time.
• Exponential growth or decay models are powerful tools for analyzing and forecasting a wide range of real-world processes that exhibit proportional rates of change over time.

Time Series Models

• ARIMA (Autoregression Integrated Moving Average) is a stochastic approach used to model time series data, combining autoregression and moving average.
• GARCH model (Generalized Autoregression Conditional Heteroskedasticity) is used to capture and predict changing volition in time series data.
• VAR (Vector Auto Regression) is a multivariate time series model used to capture the linear interdependencies among multiple time series.
• VECM (Vector Error Correction Model) is a multivariate time series model used to analyze and forecast the long-term and short-term dynamics of co-integrated variables.