Abstract: A system may configure a sensing system implemented by an embedded device. The system may configure a sensing system to generate an image from a point cloud including data points in three dimensions. The data points may be associated with at least three values. The image may be generated by mapping first and second values of data points to first and second coordinates of pixels of the image and third values of data points to intensities of the pixels. The system may configure a sensing system to invoke a machine learning model to process the image. The machine learning model may be trained for image processing. In some implementations, the mapping may include quantizing the first and second values into ranges of the first and second coordinates and quantizing the third values into a range of the intensities.

Abstract: A system may configure a sensing system implemented by an embedded device. The system may configure a sensing system to generate an image from a point cloud including data points in three dimensions. The data points may be associated with at least three values. The image may be generated by mapping first and second values of data points to first and second coordinates of pixels of the image and third values of data points to intensities of the pixels. The system may configure a sensing system to invoke a machine learning model to process the image. The machine learning model may be trained for image processing. In some implementations, the mapping may include quantizing the first and second values into ranges of the first and second coordinates and quantizing the third values into a range of the intensities.

Abstract: A computing device to compute clusters using random subsets of variables is provided. Each data point of a plurality of data points is associated with a variable to define a plurality of variables. A subset of the plurality of variables is randomly selected. The subset does not include all of the plurality of variables. A number of clusters into which to segment the received data is determined. Cluster data that defines each cluster of the determined number of clusters is determined by executing a clustering algorithm with the received data using only the plurality of data points defined for each observation that are associated with the randomly selected subset of the plurality of variables. The determined cluster data is stored to cluster second data into the determined number of clusters. The second data is different from the received data.

Abstract: A computing device to select decorrelated variables using a graph based method is provided. A correlation value is computed between each pair of a plurality of variables to define a correlation matrix. A binary threshold value is compared to each correlation value to define a binary similarity matrix from the correlation matrix. An undirected graph comprising a subgraph that includes one or more connected nodes is defined based on the binary similarity matrix to store connectivity information for the plurality of variables. Each node of the subgraph is pairwise associated with a unique variable of the variables. (a) A least connected node is selected from the undirected graph based on the connectivity information. (b) The selected least connected node is removed from the undirected graph. (c) The connectivity information for the undirected graph is updated based on the removed node. (d) (a)-(c) are repeated until a stop criterion is satisfied.

Abstract: A computing device to compute composite clusters is provided. A first and a second plurality of centroid locations are computed by executing a clustering algorithm with a first portion of data and a first input parameter and a second portion of the data and a second input parameter, respectively. The first portion is different from the second portion or the first input parameter is different from the second input parameter. A plurality of composite centroid locations is computed using the computed first and second plurality of centroid locations to define a composite set of clusters. An observation is selected. A cluster of the composite set of clusters to which to assign the observation is determined using the plurality of composite centroid locations. The selecting and the determining is repeated with each observation of the plurality of observations as the observation to define cluster assignments for the plurality of observations.

Abstract: A method of determining a number of clusters for a dataset is provided. Centroid locations for a defined number of clusters are determined using a clustering algorithm. Boundaries for each of the defined clusters are defined. A reference distribution that includes a plurality of data points is created. The plurality of data points are within the defined boundary of at least one cluster of the defined clusters. Second centroid locations for the defined number of clusters are determined using the clustering algorithm and the reference distribution. A gap statistic for the defined number of clusters based on a comparison between a first residual sum of squares and a second residual sum of squares is computed. The processing is repeated for a next number of clusters to create. An estimated best number of clusters for the received data is determined by comparing the gap statistic computed for each iteration of the number of clusters.

Abstract: A method for generating interfacial surfaces within a first composite stream having a generally planar layer interface lies generally in an x-z plane of an x-y-z coordinate system. The method includes dividing the first composite stream into a plurality of branch streams along the x-axis such that the pair of discrete overlapping layers and the generally planar layer interface are distributed among at least two branch streams. Within each individual branch stream of the at least two branch streams, the width dimension of the branch stream is expanded along the x-axis and the thickness dimension of the branch stream is simultaneously contracted along the y-axis. The branch streams are recombined in an overlapping relationship, after each of the at least two branch streams is simultaneously expanded and contracted, to form a second composite stream having a greater number of discrete overlapping layers of polymeric material than the first composite stream.

Abstract: A computing device presents a cluster visualization based on a neural network computation. First centroid locations are computed for first clusters. Second centroid locations are computed for second clusters. Each centroid location includes a plurality of coordinate values where each coordinate value relates to a single variable of a plurality of variables. Distances are computed pairwise between each centroid location. An optimum pairing is selected based on a minimum distance of the computed pairwise distances where each pair is associated with a different cluster of a set of composite clusters. Noised centroid location data is created. A multi-layer neural network is trained with the noised centroid location data. A projected centroid location is determined in a multidimensional space for each centroid location as values of hidden units of a middle layer of the multi-layer neural network. A graph is presented for display that indicates the determined, projected centroid locations.

Abstract: A computing device to assign observations to clusters based on a statistical probability is provided. A first cluster assignment is defined by assigning the plurality of observations to a first set of clusters. A second cluster assignment is defined by assigning the plurality of observations to a second set of clusters. A set of composite clusters is defined based on the defined first set of clusters and the defined second set of clusters. For each observation, a statistical probability value for assigning an observation to each composite cluster of the defined set of composite clusters is computed based on the first and second cluster assignments and a composite cluster assignment is defined by assigning the observation to a cluster of the set of composite clusters based on the computed statistical probability value. The defined composite cluster assignment is stored.

Abstract: A computing device to assign observations to clusters based on a statistical probability is provided. A first cluster assignment is defined by assigning the plurality of observations to a first set of clusters. A second cluster assignment is defined by assigning the plurality of observations to a second set of clusters. A set of composite clusters is defined based on the defined first set of clusters and the defined second set of clusters. For each observation, a statistical probability value for assigning an observation to each composite cluster of the defined set of composite clusters is computed based on the first and second cluster assignments and a composite cluster assignment is defined by assigning the observation to a cluster of the set of composite clusters based on the computed statistical probability value. The defined composite cluster assignment is stored.

Abstract: A computing device to select decorrelated variables using a graph based method is provided. A correlation value is computed between each pair of a plurality of variables to define a correlation matrix. A binary threshold value is compared to each correlation value to define a binary similarity matrix from the correlation matrix. An undirected graph comprising a subgraph that includes one or more connected nodes is defined based on the binary similarity matrix to store connectivity information for the plurality of variables. Each node of the subgraph is pairwise associated with a unique variable of the variables. (a) A least connected node is selected from the undirected graph based on the connectivity information. (b) The selected least connected node is removed from the undirected graph. (c) The connectivity information for the undirected graph is updated based on the removed node. (d) (a)-(c) are repeated until a stop criterion is satisfied.

Abstract: A computing device presents a cluster visualization based on a neural network computation. First centroid locations are computed for first clusters. Second centroid locations are computed for second clusters. Each centroid location includes a plurality of coordinate values where each coordinate value relates to a single variable of a plurality of variables. Distances are computed pairwise between each centroid location. An optimum pairing is selected based on a minimum distance of the computed pairwise distances where each pair is associated with a different cluster of a set of composite clusters. Noised centroid location data is created. A multi-layer neural network is trained with the noised centroid location data. A projected centroid location is determined in a multidimensional space for each centroid location as values of hidden units of a middle layer of the multi-layer neural network. A graph is presented for display that indicates the determined, projected centroid locations.

Abstract: A computing device to compute clusters using random subsets of variables is provided. Each data point of a plurality of data points is associated with a variable to define a plurality of variables. A subset of the plurality of variables is randomly selected. The subset does not include all of the plurality of variables. A number of clusters into which to segment the received data is determined. Cluster data that defines each cluster of the determined number of clusters is determined by executing a clustering algorithm with the received data using only the plurality of data points defined for each observation that are associated with the randomly selected subset of the plurality of variables. The determined cluster data is stored to cluster second data into the determined number of clusters. The second data is different from the received data.

Abstract: A computing device to compute composite clusters is provided. A first and a second plurality of centroid locations are computed by executing a clustering algorithm with a first portion of data and a first input parameter and a second portion of the data and a second input parameter, respectively. The first portion is different from the second portion or the first input parameter is different from the second input parameter. A plurality of composite centroid locations is computed using the computed first and second plurality of centroid locations to define a composite set of clusters. An observation is selected. A cluster of the composite set of clusters to which to assign the observation is determined using the plurality of composite centroid locations. The selecting and the determining is repeated with each observation of the plurality of observations as the observation to define cluster assignments for the plurality of observations.

Abstract: A computing device to automatically cluster a dataset is provided. Data that includes a plurality of observations with a plurality of data points defined for each observation is received. Each data point of the plurality of data points is associated with a variable to define a plurality of variables. A number of clusters into which to segment the received data is repeatedly selected by repeatedly executing a clustering algorithm with the received data. A plurality of sets of clusters is defined based on the repeated execution of the clustering algorithm that resulted in the selected number of clusters. A plurality of composite clusters is defined based on the defined plurality of sets of clusters. The plurality of observations is assigned to the defined plurality of composite clusters using the plurality of data points defined for each observation.

Abstract: A computing device to automatically cluster a dataset is provided. Data that includes a plurality of observations with a plurality of data points defined for each observation is received. Each data point of the plurality of data points is associated with a variable to define a plurality of variables. A number of clusters into which to segment the received data is repeatedly selected by repeatedly executing a clustering algorithm with the received data. A plurality of sets of clusters is defined based on the repeated execution of the clustering algorithm that resulted in the selected number of clusters. A plurality of composite clusters is defined based on the defined plurality of sets of clusters. The plurality of observations is assigned to the defined plurality of composite clusters using the plurality of data points defined for each observation.

Abstract: A method of determining a number of clusters for a dataset is provided. Centroid locations for a defined number of clusters are determined using a clustering algorithm. Boundaries for each of the defined clusters are defined. A reference distribution that includes a plurality of data points is created. The plurality of data points are within the defined boundary of at least one cluster of the defined clusters. Second centroid locations for the defined number of clusters are determined using the clustering algorithm and the reference distribution. A gap statistic for the defined number of clusters based on a comparison between a first residual sum of squares and a second residual sum of squares is computed. The processing is repeated for a next number of clusters to create. An estimated best number of clusters for the received data is determined by comparing the gap statistic computed for each iteration of the number of clusters.

Abstract: A method for generating interfacial surfaces within a first composite stream having a generally planar layer interface lies generally in an x-z plane of an x-y-z coordinate system. The method includes dividing the first composite stream into a plurality of branch streams along the x-axis such that the pair of discrete overlapping layers and the generally planar layer interface are distributed among at least two branch streams. Within each individual branch stream of the at least two branch streams, the width dimension of the branch stream is expanded along the x-axis and the thickness dimension of the branch stream is simultaneously contracted along the y-axis. The branch streams are recombined in an overlapping relationship, after each of the at least two branch streams is simultaneously expanded and contracted, to form a second composite stream having a greater number of discrete overlapping layers of polymeric material than the first composite stream.

Abstract: A method for producing 3-(2,2,2-trimethylhydrazinium)propionate dihydrate by saponification of salts of 3-(2,2,2-trimethylhydrazinium)propionate esters with subsequent purification step using saturation with carbon dioxide or sulphur dioxide in alcoholic solution.