In this article, I am going to show you how to choose the number of principal components when using principal component analysis for dimensionality reduction.
In the first section, I am going to give you a short answer for those of you who are in a hurry and want to get something working. Later, I am going to provide a more extended explanation for those of you who are interested in understanding PCA.
Uniform Manifold Approximation and Projection (UMAP) is a dimension reduction technique that can be used for visualisation similarly to t-SNE, but also for general non-linear dimension reduction. The algorithm is founded on three assumptions about the data
The data is uniformly distributed on Riemannian manifold;
The Riemannian metric is locally constant (or can be approximated as such);
The manifold is locally connected.
From these assumptions it is possible to model the manifold with a fuzzy topological structure. The embedding is found by searching for a low dimensional projection of the data that has the closest possible equivalent fuzzy topological structure.
Latent Semantic Analysis (LSA) is a theory and method for extracting and representing the contextual-usage meaning of words by statistical computations applied to a large corpus of text.
LSA is an information retrieval technique which analyzes and identifies the pattern in unstructured collection of text and the relationship between them.
LSA itself is an unsupervised way of uncovering synonyms in a collection of documents.
To start, we take a look how Latent Semantic Analysis is used in Natural Language Processing to analyze relationships between a set of documents and the terms that they contain. Then we go steps further to analyze and classify sentiment. We will review Chi Squared for feature selection along the way.
In natural language understanding (NLU) tasks, there is a hierarchy of lenses through which we can extract meaning — from words to sentences to paragraphs to documents. At the document level, one of the most useful ways to understand text is by analyzing its topics. The process of learning, recognizing, and extracting these topics across a collection of documents is called topic modeling.
In this post, we will explore topic modeling through 4 of the most popular techniques today: LSA, pLSA, LDA, and the newer, deep learning-based lda2vec.