11. A computer-implemented method comprising: applying, via a first computing process, natural language processing to extract candidate topics from a data sample comprising a plurality of posts retrieved from one or more social media streams via a social engine, the data sample including text with assigned part-of-speech (POS) tags, wherein the first computing process utilizes a first rule comprising: identifying a sequence of a plurality of the assigned POS tags, wherein each POS tag of the sequence is selected from a group consisting of at least one of a proper noun tag, a plural proper noun tag, or a cardinal number tag; defining topic boundaries based on the identified sequence; and extracting a portion of the text corresponding to the topic boundaries as one of the candidate topics; determining, via a second computing process, an Accumulated Term Frequency (ATF) for each candidate topic of the candidate topics, the ATF counting an occurrence of the candidate topic once for each post in which the candidate topic appears; determining, via a third computing process, an inverse document frequency (IDF) for each of the candidate topics in the data sample; determining, via a fourth computing process, a relevance score that quantifies relative importance of the candidate topics using the ATF and the IDF to determine trending topics; and transmitting, via a fifth computing process, the trending topics for display on a user device; wherein each of the computing processes is performed by one or more computing devices.
11. A computer-implemented method comprising: applying, via a first computing process, natural language processing to extract candidate topics from a data sample comprising a plurality of posts retrieved from one or more social media streams via a social engine, the data sample including text with assigned part-of-speech (POS) tags, wherein the first computing process utilizes a first rule comprising: identifying a sequence of a plurality of the assigned POS tags, wherein each POS tag of the sequence is selected from a group consisting of at least one of a proper noun tag, a plural proper noun tag, or a cardinal number tag; defining topic boundaries based on the identified sequence; and extracting a portion of the text corresponding to the topic boundaries as one of the candidate topics; determining, via a second computing process, an Accumulated Term Frequency (ATF) for each candidate topic of the candidate topics, the ATF counting an occurrence of the candidate topic once for each post in which the candidate topic appears; determining, via a third computing process, an inverse document frequency (IDF) for each of the candidate topics in the data sample; determining, via a fourth computing process, a relevance score that quantifies relative importance of the candidate topics using the ATF and the IDF to determine trending topics; and transmitting, via a fifth computing process, the trending topics for display on a user device; wherein each of the computing processes is performed by one or more computing devices. 16. The computer-implemented method of claim 11 , wherein the one or more social media streams are sampled in accordance with a user selection of a data source, a time constraint, desired demographics, a product, a service, a feature, an organization, a person, or a location.