# US 2023/0069079 A1 · Statistical K-means Clustering > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 2023/0069079 A1 - Document ID: US20230069079A1 - Status: Published application - Kind: A1 - Application number: 17/460,546 - Filed: 2021-08-30 - Published: 2023-03-02 - Earliest claimed: 2021-08-30 - Assignees: International Business Machines Corporation - Applicants: International Business Machines Corporation - Inventors: Rahul M. Rao; Naiju Karim Abdul; Anay K. Desai; Suriya T Skariah - Web page: https://patentgrep.com/patent/US20230069079A1 ## CPC - G06F 16/285: {Clustering or classification} - G06F 16/906: Clustering; Classification - G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N) ## Abstract In a computer-implemented method for improving a k-means clustering algorithm, a processor modifies a first data point of a data set to include a first distribution boundary. A processor calculates a first effective distance between the first distribution boundary and a first centroid of a cluster. A processor assigns the first data point to the first cluster. A processor recomputes the first centroid based on the first data point and the first distribution boundary. ## Claims ### Claim 1 A computer-implemented method for improving a k-means clustering algorithm, comprising: modifying, by one or more processors, a first data point of a data set to include a first distribution boundary, wherein the first distribution boundary comprises a space in which the first data point may exist without changing the representation of the first data point within the data set; calculating, by one or more processors, a first effective distance between the first distribution boundary and a first centroid of a cluster; assigning, by one or more processors, the first data point to the first cluster; recomputing, by one or more processors, the first centroid based on the first data point and the first distribution boundary. ### Claim 2 (depends on 1) The method of claim 1, comprising initializing the first centroid to a data point of the data set and computing a Euclidian distance between the first centroid and each data point. ### Claim 3 (depends on 1) The method of claim 1, wherein the first distribution boundary comprises a selection from the group consisting of: a spherical distribution boundary, a cluster capacity, and a gaussian distribution boundary. ### Claim 4 (depends on 1) The method of claim 1, wherein the effective distance comprises a shortest distance between the first centroid and the first distribution boundary. ### Claim 5 (depends on 1) The method of claim 1, wherein recomputing a location of the first centroid comprises averaging all other data points in the cluster with a recomputing point on the first distribution boundary. ### Claim 6 (depends on 1) The method of claim 1, comprising calculating a second effective distance between the first distribution boundary and a second centroid of a second cluster before assigning the first data point to the first cluster, wherein the first effective distance is shorter than the second effective distance. ### Claim 7 (depends on 1) The method of claim 1, wherein the first distribution boundary comprises a representation of a timing slack and a device-specific metric. ### Claim 8 (depends on 1) The method of claim 1, wherein the first distribution boundary comprises a representation of geographical preferences, wherein the geographical preferences comprise directional constraints based on physical blockages. ### Claim 9 A computer program product for improving a k-means clustering algorithm, comprising: one or more computer readable storage media, and program instructions collectively stored on the one or more computer readable storage media, the program instructions comprising: program instructions to modify a first data point of a data set to include a first distribution boundary, wherein the first distribution boundary comprises a space in which the first data point may exist without changing the representation of the first data point within the data set; program instructions to calculate a first effective distance between the first distribution boundary and a first centroid of a cluster; program instructions to assign the first data point to the first cluster; program instructions to recompute the first centroid based on the first data point and the first distribution boundary. ### Claim 10 (depends on 9) The computer program product of claim 9, comprising program instructions to initialize the first centroid to a data point of the data set and computing a Euclidian distance between the first centroid and each data point. ### Claim 11 (depends on 9) The computer program product of claim 9, wherein the first distribution boundary comprises a selection from the group consisting of: a spherical distribution boundary, a cluster capacity, and a gaussian distribution boundary. ### Claim 12 (depends on 9) The computer program product of claim 9, wherein the effective distance comprises a shortest distance between the first centroid and the first distribution boundary. ### Claim 13 (depends on 9) The computer program product of claim 9, wherein recomputing a location of the first centroid comprises averaging all other data points in the cluster with a recomputing point on the first distribution boundary. ### Claim 14 (depends on 9) The computer program product of claim 9, comprising program instructions to calculate a second effective distance between the first distribution boundary and a second centroid of a second cluster before assigning the first data point to the first cluster, wherein the first effective distance is shorter than the second effective distance. ### Claim 15 A computer system for improving a k-means clustering algorithm, comprising: one or more computer processors, one or more computer readable storage media, and program instructions collectively stored on the one or more computer readable storage media for execution by at least one of the one or more computer processors, the program instructions comprising: program instructions to modify a first data point of a data set to include a first distribution boundary, wherein the first distribution boundary comprises a space in which the first data point may exist without changing the representation of the first data point within the data set; program instructions to calculate a first effective distance between the first distribution boundary and a first centroid of a cluster; program instructions to assign the first data point to the first cluster; program instructions to recompute the first centroid based on the first data point and the first distribution boundary. ### Claim 16 (depends on 15) The computer system of claim 15, comprising program instructions to initialize the first centroid to a data point of the data set and computing a Euclidian distance between the first centroid and each data point. ### Claim 17 (depends on 15) The computer system of claim 15, wherein the first distribution boundary comprises a selection from the group consisting of: a spherical distribution boundary, a cluster capacity, and a gaussian distribution boundary. ### Claim 18 (depends on 15) The computer system of claim 15, wherein the effective distance comprises a shortest distance between the first centroid and the first distribution boundary. ### Claim 19 (depends on 15) The computer system of claim 15, wherein recomputing a location of the first centroid comprises averaging all other data points in the cluster with a recomputing point on the first distribution boundary. ### Claim 20 (depends on 15) The computer system of claim 15, comprising program instructions to calculate a second effective distance between the first distribution boundary and a second centroid of a second cluster before assigning the first data point to the first cluster, wherein the first effective distance is shorter than the second effective distance.