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 comprises receiving data points, determining at least one size of a plurality of subsets based on a constraint of at least one computation device or an analysis server, transferring each of the subsets to different computation devices, each computation device selecting a group of data points to generate a first sub-subset of landmarks, add non-landmark data points that have the farthest distance to the closest landmark to create an expanded sub-subset of landmarks, create an analysis landmark set based on a combination of expanded sub-subsets of expanded landmarks from different computation devices, perform a similarity function on the analysis landmark set, generate a cover of the mathematical reference space to create overlapping subsets, cluster the mapped landmark points based on the overlapping subsets, create a plurality of nodes, each node being based on the clustering, each landmark point being a member of at least one node.

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 example method comprises receiving data points, determining at least one size of a plurality of subsets based on a constraint of at least one computation device or an analysis server, transferring each of the subsets to different computation devices, each computation device selecting a group of data points to generate a first sub-subset of landmarks, add non-landmark data points that have the farthest distance to the closest landmark to create an expanded sub-subset of landmarks, create an analysis landmark set based on a combination of expanded sub-subsets of expanded landmarks from different computation devices, perform a similarity function on the analysis landmark set, generate a cover of the mathematical reference space to create overlapping subsets, cluster the mapped landmark points based on the overlapping subsets, create a plurality of nodes, each node being based on the clustering, each landmark point being a member of at least one node.

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 for visualization of data analysis are provided. In various embodiments, a method comprises accessing a database, analyzing the database to identify clusters of data, generating an interactive visualization comprising a plurality of nodes and a plurality of edges wherein a first node of the plurality of nodes represents a cluster and an edge of the plurality of edges represents an intersection of nodes of the plurality of nodes, selecting and dragging the first node in response to a user action, and reorienting the interactive visualization in response to the user action of selecting and dragging the first node.

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: Exemplary systems and methods for visualization of data analysis are provided. In various embodiments, a method comprises accessing a database, analyzing the database to identify clusters of data, generating an interactive visualization comprising a plurality of nodes and a plurality of edges wherein a first node of the plurality of nodes represents a cluster and an edge of the plurality of edges represents an intersection of nodes of the plurality of nodes, selecting and dragging the first node in response to a user action, and reorienting the interactive visualization in response to the user action of selecting and dragging the first node.

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 receiving a data set, each data point in the data set being associated with an indication of time, and a distance function, determining overlapping intervals over a time period range, identifying subsets of data in each overlapping interval based on the indications of time, applying the distance function to each subset of data to identify groups, constructing a node for each group to create a plurality of nodes, determining if two nodes of the plurality of nodes in adjacent time periods are connected by scoring shared data point membership between the two nodes and comparing a score of the shared data point membership to a threshold, and displaying at least two nodes with an indication of time, the two nodes being connected by a line based on the comparison of the score and the threshold.

Abstract: An example method includes receiving a data set, each data point in the data set being associated with an indication of time, and a distance function, determining overlapping intervals over a time period range, identifying subsets of data in each overlapping interval based on the indications of time, applying the distance function to each subset of data to identify groups, constructing a node for each group to create a plurality of nodes, determining if two nodes of the plurality of nodes in adjacent time periods are connected by scoring shared data point membership between the two nodes and comparing a score of the shared data point membership to a threshold, and displaying at least two nodes with an indication of time, the two nodes being connected by a line based on the comparison of the score and the threshold.

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: A method comprises receiving a selection of data from a fact table and one or more dimension tables stored in a data warehouse, mapping data points from the selection of the data from the fact table and the one or more dimension tables to a reference space utilizing a lens function, generating a cover of the reference space using a resolution function, clustering the data points mapped to the reference space using the cover and a metric function to determine each node of a plurality of nodes of a graph, each node including at least one data point, determining a plurality of segments of the graph, each segment including at least one node, and generating a segment data structure identifying each segment as well as membership of each segment, the membership of each segment including at least one node from the plurality of nodes in the graph.

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 for visualization of data analysis are provided. In various embodiments, a method comprises accessing a database, analyzing the database to identify clusters of data, generating an interactive visualization comprising a plurality of nodes and a plurality of edges wherein a first node of the plurality of nodes represents a cluster and an edge of the plurality of edges represents an intersection of nodes of the plurality of nodes, selecting and dragging the first node in response to a user action, and reorienting the interactive visualization in response to the user action of selecting and dragging the first node.

Abstract: Autogrouping is described. An example method includes receiving a data set, building a first partition of subsets of the data set, computing a first subset score for each subset using a scoring function, generating a next partition including at least one subset that includes the elements of two or more subsets of the first partition, computing a second subset score for each subset of the next partition using the scoring function, defining a max score for each particular subset using a max score function, each max score being based on maximal subset scores of that particular subset and at least the subsets of the first partition related to that particular subset, selecting output subsets, selection of each of the output subsets being made using a maximum score of previously computed subset scores, and generating a report indicating an output partition, the output subsets being associated with the received data set.

Abstract: An example method comprises receiving historical information of episodes, constructing event sets from the historical information, categorizing each event with general labels and synthetic labels, learning an event metric on the events by using the general and synthetic labels to perform dimensionality reduction to associate a vector with each event and to determine an angle between every two vectors, determining an event set metric using distances between each pair of event sets, deriving a sequence metric on the episodes, the sequence metric obtaining a preferred match between two episodes, deriving a subsequence metric on the episodes, the subsequence metric is a function of the event set metric on subsequences of each episode, grouping episodes into subgroups based on distances, for at least one subgroup, generating a consensus sequence by finding a preferred sequence of events, and the episodes of the subgroup, and generating a report indicating the consensus sequence.

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: A method comprises receiving data points from a spreadsheet, mapping the data points to a reference space, generating a cover of the reference space, clustering the data points mapped to the reference space to determine each node of a graph, each node including at least one data point, generating a visualization depicting the nodes, the visualization including an edge between every two nodes that share at least one data point, generating a translation data structure indicating location of the data points in the spreadsheet as well as membership of each node, detecting a selection of at least one node, determining the location of data points in the spreadsheet corresponding to data points that are members of the selected node(s) using the translation data structure, and providing a first command to a spreadsheet application to provide a first visual identification of the first set of data points in the spreadsheet.