An association rule is a rule-based method for finding relationships between variables in a given dataset. These methods are frequently used for market basket analysis, allowing companies to better understand relationships between different products. Understanding consumption habits of customers enables businesses to develop better cross-selling strategies and recommendation engines. Examples of this can be seen in Amazon’s “Customers Who Bought This Item Also Bought” or Spotify’s "Discover Weekly" playlist. While there are a few different algorithms used to generate association rules, such as Apriori, Eclat, and FP-Growth, the Apriori algorithm is most widely used.

Apriori algorithms have been popularized through market basket analyses, leading to different recommendation engines for music platforms and online retailers. They are used within transactional datasets to identify frequent itemsets, or collections of items, to identify the likelihood of consuming a product given the consumption of another product. For example, if I play Black Sabbath’s radio on Spotify, starting with their song “Orchid”, one of the other songs on this channel will likely be a Led Zeppelin song, such as “Over the Hills and Far Away.” This is based on my prior listening habits as well as the ones of others. Apriori algorithms use a hash tree to count itemsets, navigating through the dataset in a breadth-first manner.

While more data generally yields more accurate results, it can also impact the performance of machine learning algorithms (e.g. overfitting) and it can also make it difficult to visualize datasets. Dimensionality reduction is a technique used when the number of features, or dimensions, in a given dataset is too high. It reduces the number of data inputs to a manageable size while also preserving the integrity of the dataset as much as possible. It is commonly used in the preprocessing data stage, and there are a few different dimensionality reduction methods that can be used, such as:

Principal component analysis (PCA) is a type of dimensionality reduction algorithm which is used to reduce redundancies and to compress datasets through feature extraction. This method uses a linear transformation to create a new data representation, yielding a set of "principal components." The first principal component is the direction which maximizes the variance of the dataset. While the second principal component also finds the maximum variance in the data, it is completely uncorrelated to the first principal component, yielding a direction that is perpendicular, or orthogonal, to the first component. This process repeats based on the number of dimensions, where a next principal component is the direction orthogonal to the prior components with the most variance.

Singular value decomposition (SVD) is another dimensionality reduction approach which factorizes a matrix, A, into three, low-rank matrices. SVD is denoted by the formula, A = USVT, where U and V are orthogonal matrices. S is a diagonal matrix, and S values are considered singular values of matrix A. Similar to PCA, it is commonly used to reduce noise and compress data, such as image files.

Autoencoders leverage neural networks to compress data and then recreate a new representation of the original data’s input. Looking at the image below, you can see that the hidden layer specifically acts as a bottleneck to compress the input layer prior to reconstructing within the output layer. The stage from the input layer to the hidden layer is referred to as “encoding” while the stage from the hidden layer to the output layer is known as “decoding.”