Extracting frequent words from a collection of texts is commonly performed in many subjects. However, as useful as it is to obtain a collection of commonly occurring words from texts, there is a need for more specific information to be obtained from texts in the form of most commonly occurring phrases. Despite this need, extracting frequent phrases is not commonly done due to inherent complications, the most significant being double-counting. Double-counting occurs when words or phrases are counted when they appear inside longer phrases that themselves are also counted, resulting in a selection of mostly meaningless phrases that are frequent only because they occur inside frequent super phrases. Several papers have been written on phrase mining that describe solutions to this issue; however, they either require a list of so-called quality phrases to be available to the extracting process, or they require human interaction to identify those quality phrases during the process. We present here a method that eliminates double-counting via a unique rectification process that does not require lists of quality phrases. In the context of a set of texts, we define a principal phrase as a phrase that does not cross punctuation marks, does not start with a stop word, with the exception of the stop words "not" and "no", does not end with a stop word, is frequent within those texts without being double counted, and is meaningful to the user. Our method identifies such principal phrases independently without human input, and enables their extraction from any texts within a reasonable amount of time.

We seek to semantically describe a set of images, capturing both the attributes of single images and the variations within the set. Our procedure is analogous to Principle Component Analysis, in which the role of projection vectors is replaced with generated phrases. First, a centroid phrase that has the largest average semantic similarity to the images in the set is generated, where both the computation of the similarity and the generation are based on pretrained vision-language models. Then, the phrase that generates the highest variation among the similarity scores is generated, using the same models. The next phrase maximizes the variance subject to being orthogonal, in the latent space, to the highest-variance phrase, and the process continues. Our experiments show that our method is able to convincingly capture the essence of image sets and describe the individual elements in a semantically meaningful way within the context of the entire set. Our code is available at: https://github.com/OdedH/textual-pca.