Machine learning teaches computers to behave like humans by exposing them to historical data and allowing them to predict upcoming events. This section investigates fascinating machine learning approaches, such as Sparse PCA, t-SNE, and the weighted majority algorithm.

Sparse PCA

Sparse principal component analysis (sparse PCA) is a specialized technique used in statistical analysis, specifically for analyzing multivariate data sets. It enhances the traditional principal component analysis method (PCA) for dimensionality reduction by incorporating sparsity structures into the input variables.

PCA is frequently employed in data processing and dimensionality reduction. However, PCA is difficult to interpret because each principal component is a linear combination of all the original variables. Using the lasso (elastic net) to generate modified principal components with sparse loadings, the researchers offer a novel method termed sparse PCA. The researchers demonstrate that PCA can be framed as an optimization problem of the regression type; sparse loadings are then generated by applying the lasso (elastic net) constraint on the regression coefficients. In addition, the researchers present efficient techniques for fitting SPCA models to multivariate data and gene expression arrays.

Furthermore, the fact that the principal components of conventional PCA are often linear combinations of all input variables is a significant drawback. This issue is overcome by sparse PCA, which finds linear combinations including only a few input variables.

t-distributed stochastic neighbour embedding (t-SNE)

t-SNE is a statistical technique for displaying high-dimensional data by assigning each data point a location on a two- or three-dimensional map. Laurens van der Maaten proposed the t-distributed variation of Stochastic Neighbor Embedding, initially created by Sam Roweis and Geoffrey Hinton. It is a technique for embedding high-dimensional data for viewing in a low-dimensional space of two or three dimensions. Precisely, it models each high-dimensional object as a two- or three-dimensional point, so that related objects are likely to be modelled by neighbouring points and dissimilar objects by distant points.

The t-SNE algorithm consists of two distinct phases. Initially, t-SNE creates a probability distribution over pairs of high-dimensional objects in which comparable items are assigned a higher probability, and different points have a lower probability. Then, it minimizes the Kullback–Leibler divergence (KL divergence) between the two distributions to the positions of the map's points. While the original approach bases its similarity metric on the Euclidean distance between objects, we can modify this as necessary.

Weighted majority algorithm

In machine learning, the weighted majority algorithm (WMA) is a meta-learning algorithm used to generate a compound algorithm from a pool of prediction algorithms, which may include any learning algorithm, classifiers, or even human experts. The method assumes we have no prior knowledge regarding the accuracy of the algorithms in the pool, but there are sufficient grounds to predict that at least one will perform well. For example, assume the problem involves a binary decision. The collection of algorithms is given a favourable weight to produce the compound algorithm. The compound algorithm then collects the weighted votes of each algorithm in the pool and returns the forecast with the highest vote.

Furthermore, numerous variants of the weighted majority algorithm accommodate various circumstances, such as changeable targets, infinite pools, and random forecasts. However, the core mechanism stays the same, with the compound algorithm's final performance constrained by the specialist's performance (highest performing algorithm in the pool).