Abstract: A method comprises receiving a network of a plurality of nodes and a plurality of edges, each of the nodes of the plurality of nodes comprising members representative of at least one subset of initial data points, selecting a subset of the data points based on each node of the plurality of nodes, for each selected data point of the set of selected data points, determining a predetermined number of other data points that are closest in distance to that particular selected data point, grouping the selected data points into a plurality of groups based, at least in part, on the predetermined number of other data points of the set of selected data points that are closest in distance, each group of the plurality of groups including a different subset of data points, and providing a list of selected data points and the plurality of groups.

Abstract: An example method includes determining a point from a data set closest to a particular data point using a particular metric and scoring a particular data point based on whether the closest point shares a similar characteristic, selecting a subset of metrics based on the metric score to generate a subset of metrics, evaluating a metric-lens combination by calculating a metric-lens score based on entropy of shared characteristics across subspaces of a reference map generated by the metric-lens combination, selecting a metric-lens combination based on the metric-lens score, generating topological representations using the received data set, associating each node with at least one shared characteristic based on member data points of that particular node sharing the shared characteristic, scoring groups within each topological representation based on entropy, scoring topological representation based on the group scores, and providing a visualization of at least one topological representation based on the graph sco

Abstract: An exemplary method comprises receiving data points, selecting a first subset of the data points to generate an initial set of landmarks, each data point of the first subset defining a landmark point and for each non-landmark data point: calculating first data point distances between a respective non-landmark data point and each landmark point of the initial set of landmarks, identifying a first shortest data point distance from among the first data point distances between the respective non-landmark data point and each landmark point of the initial set of landmarks, and storing the first shortest data point distance as a first landmark distance for the respective non-landmark data point. The method further comprising identifying a non-landmark data point with a longest first landmark distance in comparison with other first landmark distances and adding the identified non-landmark data point associated as a first landmark point to the initial set of landmarks.

Abstract: An example method includes determining a point from a data set closest to a particular data point using a particular metric and scoring a particular data point based on whether the closest point shares a similar characteristic, selecting a subset of metrics based on the metric score to generate a subset of metrics, evaluating a metric-lens combination by calculating a metric-lens score based on entropy of shared characteristics across subspaces of a reference map generated by the metric-lens combination, selecting a metric-lens combination based on the metric-lens score, generating topological representations using the received data set, associating each node with at least one shared characteristic based on member data points of that particular node sharing the shared characteristic, scoring groups within each topological representation based on entropy, scoring topological representation based on the group scores, and providing a visualization of at least one topological representation based on the graph sco

Abstract: A method comprises receiving a network of a plurality of nodes and a plurality of edges, each of the nodes of the plurality of nodes comprising members representative of at least one subset of initial data points, selecting a subset of the data points based on each node of the plurality of nodes, for each selected data point of the set of selected data points, determining a predetermined number of other data points that are closest in distance to that particular selected data point, grouping the selected data points into a plurality of groups based, at least in part, on the predetermined number of other data points of the set of selected data points that are closest in distance, each group of the plurality of groups including a different subset of data points, and providing a list of selected data points and the plurality of groups.

Abstract: An example method includes determining a point from a data set closest to a particular data point using a particular metric and scoring a particular data point based on whether the closest point shares a similar characteristic, selecting a subset of metrics based on the metric score to generate a subset of metrics, evaluating a metric-lens combination by calculating a metric-lens score based on entropy of shared characteristics across subspaces of a reference map generated by the metric-lens combination, selecting a metric-lens combination based on the metric-lens score, generating topological representations using the received data set, associating each node with at least one shared characteristic based on member data points of that particular node sharing the shared characteristic, scoring groups within each topological representation based on entropy, scoring topological representation based on the group scores, and providing a visualization of at least one topological representation based on the graph sco

Abstract: A method comprises receiving a network of a plurality of nodes and a plurality of edges, each of the nodes of the plurality of nodes comprising members representative of at least one subset of initial data points, selecting a subset of the data points based on each node of the plurality of nodes, for each selected data point of the set of selected data points, determining a predetermined number of other data points that are closest in distance to that particular selected data point, grouping the selected data points into a plurality of groups based, at least in part, on the predetermined number of other data points of the set of selected data points that are closest in distance, each group of the plurality of groups including a different subset of data points, and providing a list of selected data points and the plurality of groups.

Abstract: Exemplary systems and methods to improve capture of relationships within information are provided. In various embodiments, a system comprises a landmark module configured to choose a set of landmarks from data in a finite metric space, the set of landmarks being a subset of points in the finite metric space, a nearest neighbor module configured to compute, for each landmark, a predetermined number of nearest neighbor landmarks in the set of landmarks, a graph construction module configured to identify at least one pair of landmarks that are nearest neighbors to each other, an edge generator module configured to add an edge between the at least one pair of landmarks, and a non-landmark projection module configured to project non-landmark points based on the landmarks and one or more edges thereby enabling at least one shape to indicate relationships in the data.

Abstract: An exemplary method comprises receiving data points, selecting a first subset of the data points to generate an initial set of landmarks, each data point of the first subset defining a landmark point and for each non-landmark data point: calculating first data point distances between a respective non-landmark data point and each landmark point of the initial set of landmarks, identifying a first shortest data point distance from among the first data point distances between the respective non-landmark data point and each landmark point of the initial set of landmarks, and storing the first shortest data point distance as a first landmark distance for the respective non-landmark data point. The method further comprising identifying a non-landmark data point with a longest first landmark distance in comparison with other first landmark distances and adding the identified non-landmark data point associated as a first landmark point to the initial set of landmarks.

Abstract: An exemplary method comprises receiving data points, selecting a first subset of the data points to generate an initial set of landmarks, each data point of the first subset defining a landmark point and for each non-landmark data point: calculating first data point distances between a respective non-landmark data point and each landmark point of the initial set of landmarks, identifying a first shortest data point distance from among the first data point distances between the respective non-landmark data point and each landmark point of the initial set of landmarks, and storing the first shortest data point distance as a first landmark distance for the respective non-landmark data point. The method further comprising identifying a non-landmark data point with a longest first landmark distance in comparison with other first landmark distances and adding the identified non-landmark data point associated as a first landmark point to the initial set of landmarks.

Abstract: An exemplary method may comprise receiving a matrix for a set of documents, each cell of the matrix including a frequency value indicating a number of instances of a corresponding text segment in a corresponding document, receiving an indication of a relationship between two text segments, each of the two text segments associated with a first column and a second column, respectively, of the matrix, adjusting, for each document, a frequency value of the second column based on the frequency value of the first column, projecting each frequency value into a reference space to generate a set of projection values, identifying a plurality of subsets of the reference space, clustering, for each subset of the plurality of subsets, at least some documents that correspond to projection values, and generating a graph of nodes, each of the nodes identifying one or more of the documents corresponding to each cluster.

Abstract: An example method includes receiving text from a plurality of documents, segmenting text received text of the plurality of documents, calculating a frequency statistic for each segment of each document, determining segments of potential interest of each document based on calculated frequency statistic, calculating distances between each document of the plurality of documents based on a text metric, and storing segments of potential interest of each document and the distances in a search database. The method may further include receiving a search query and performing a search of information contained in the search database, partitioning documents of search results using the distances, for each partition, determining labels of segments of potential interest for documents of that particular partition, the labels being determined based on a plurality of frequency statistics, and providing determined labels of segments of potential interest for documents of each partition.

Abstract: An example method includes determining a point from a data set closest to a particular data point using a particular metric and scoring a particular data point based on whether the closest point shares a similar characteristic, selecting a subset of metrics based on the metric score to generate a subset of metrics, evaluating a metric-lens combination by calculating a metric-lens score based on entropy of shared characteristics across subspaces of a reference map generated by the metric-lens combination, selecting a metric-lens combination based on the metric-lens score, generating topological representations using the received data set, associating each node with at least one shared characteristic based on member data points of that particular node sharing the shared characteristic, scoring groups within each topological representation based on entropy, scoring topological representation based on the group scores, and providing a visualization of at least one topological representation based on the graph sco

Abstract: An exemplary method comprises receiving data points, selecting a first subset of the data points to generate an initial set of landmarks, each data point of the first subset defining a landmark point and for each non-landmark data point: calculating first data point distances between a respective non-landmark data point and each landmark point of the initial set of landmarks, identifying a first shortest data point distance from among the first data point distances between the respective non-landmark data point and each landmark point of the initial set of landmarks, and storing the first shortest data point distance as a first landmark distance for the respective non-landmark data point. The method further comprising identifying a non-landmark data point with a longest first landmark distance in comparison with other first landmark distances and adding the identified non-landmark data point associated as a first landmark point to the initial set of landmarks.

Abstract: An example method includes determining a point from a data set closest to a particular data point using a particular metric and scoring a particular data point based on whether the closest point shares a similar characteristic, selecting a subset of metrics based on the metric score to generate a subset of metrics, evaluating a metric-lens combination by calculating a metric-lens score based on entropy of shared characteristics across subspaces of a reference map generated by the metric-lens combination, selecting a metric-lens combination based on the metric-lens score, generating topological representations using the received data set, associating each node with at least one shared characteristic based on member data points of that particular node sharing the shared characteristic, scoring groups within each topological representation based on entropy, scoring topological representation based on the group scores, and providing a visualization of at least one topological representation based on the graph sco

Abstract: A method comprises receiving a network of a plurality of nodes and a plurality of edges, each of the nodes of the plurality of nodes comprising members representative of at least one subset of initial data points, selecting a subset of the data points based on each node of the plurality of nodes, for each selected data point of the set of selected data points, determining a predetermined number of other data points that are closest in distance to that particular selected data point, grouping the selected data points into a plurality of groups based, at least in part, on the predetermined number of other data points of the set of selected data points that are closest in distance, each group of the plurality of groups including a different subset of data points, and providing a list of selected data points and the plurality of groups.

Abstract: An exemplary method may comprise receiving a matrix for a set of documents, each cell of the matrix including a frequency value indicating a number of instances of a corresponding text segment in a corresponding document, receiving an indication of a relationship between two text segments, each of the two text segments associated with a first column and a second column, respectively, of the matrix, adjusting, for each document, a frequency value of the second column based on the frequency value of the first column, projecting each frequency value into a reference space to generate a set of projection values, identifying a plurality of subsets of the reference space, clustering, for each subset of the plurality of subsets, at least some documents that correspond to projection values, and generating a graph of nodes, each of the nodes identifying one or more of the documents corresponding to each cluster.

Abstract: Exemplary systems and methods to improve capture of relationships within information are provided. In various embodiments, a system comprises a landmark module configured to choose a set of landmarks from data in a finite metric space, the set of landmarks being a subset of points in the finite metric space, a nearest neighbor module configured to compute, for each landmark, a predetermined number of nearest neighbor landmarks in the set of landmarks, a graph construction module configured to identify at least one pair of landmarks that are nearest neighbors to each other, an edge generator module configured to add an edge between the at least one pair of landmarks, and a non-landmark projection module configured to project non-landmark points based on the landmarks and one or more edges thereby enabling at least one shape to indicate relationships in the data.

Abstract: An exemplary method may comprise receiving a matrix for a set of documents, each cell of the matrix including a frequency value indicating a number of instances of a corresponding text segment in a corresponding document, receiving an indication of a relationship between two text segments, each of the two text segments associated with a first column and a second column, respectively, of the matrix, adjusting, for each document, a frequency value of the second column based on the frequency value of the first column, projecting each frequency value into a reference space to generate a set of projection values, identifying a plurality of subsets of the reference space, clustering, for each subset of the plurality of subsets, at least some documents that correspond to projection values, and generating a graph of nodes, each of the nodes identifying one or more of the documents corresponding to each cluster.

Abstract: Exemplary systems and methods to improve capture of relationships within information are provided. In various embodiments, a system comprises a landmark module configured to choose a set of landmarks from data in a finite metric space, the set of landmarks being a subset of points in the finite metric space, a nearest neighbor module configured to compute, for each landmark, a predetermined number of nearest neighbor landmarks in the set of landmarks, a graph construction module configured to identify at least one pair of landmarks that are nearest neighbors to each other, an edge generator module configured to add an edge between the at least one pair of landmarks, and a non-landmark projection module configured to project non-landmark points based on the landmarks and one or more edges thereby enabling at least one shape to indicate relationships in the data.