# US 2014/0156223 A1 · Quantitative analysis and visualization of spatial points > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 2014/0156223 A1 - Document ID: US20140156223A1 - Status: Published application - Kind: A1 - Application number: 14/176,186 - Filed: 2014-02-10 - Published: 2014-06-05 - Earliest claimed: 2011-08-09 - Assignees: Yale University - Inventors: Derek K. Toomre; Brian T. McNellis - Web page: https://patentgrep.com/patent/US20140156223A1 ## CPC - G06F 17/18: for evaluating statistical data {, e.g. average values, frequency distributions, probability functions, regression analysis (forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04)} - G06F 30/20: Design optimisation, verification or simulation (optimisation, verification or simulation of circuit designs G06F30/30) - G06V 20/695: {Preprocessing, e.g. image segmentation} - G06F 2111/08: Probabilistic or stochastic CAD - G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N) - G06V: IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING ## Abstract A method for analyzing spatial point patterns and visualizing the results is presented. The method includes simulating at least one point set within a region using a point process, dividing the region into a plurality of elements, determining scores for both real data and simulated data for each element by weighting the point sets within a domain of a predetermined kernel. The method further includes comparing scores for each element, computing confidence intervals for at least one confidence level having a predetermined statistical significance; and providing a visualization to identify clusters and exclusion zones. ## Claims ### Claim 1 A computer implemented method for analyzing spatial point patterns in a region comprising: receiving a point set; simulating at least one point set within the region using a point process; dividing the region into a plurality of elements; determining a first score for each element of the plurality of elements by weighting the point set within a domain of a predetermined kernel; and determining a second score for each element by weighting the at least one simulated point set within the domain of the predetermined kernel. ### Claim 2 (depends on 1) The computer implemented method of claim 1, wherein the predetermined kernel is one of: a continuous kernel; and a discrete kernel. ### Claim 3 (depends on 2) The computer implemented method of claim 2, wherein the domain of the kernel is isotropic having a radius greater than the radius of each of the plurality of elements. ### Claim 4 (depends on 3) The computer implemented method of claim 3, wherein weighting the point set comprises counting the number of points within the domain of the predetermined kernel centered on the element. ### Claim 5 (depends on 1) The computer implemented method of claim 1 further comprising comparing, for each element of the plurality of elements, the first score to the second score. ### Claim 6 (depends on 5) The computer implemented method of claim 5, wherein comparing the first score to the second score comprises one of: computing confidence intervals for at least one confidence level having a predetermined statistical significance; and computing p-values and comparing to a predetermined statistical significance. ### Claim 7 (depends on 6) The computer implemented method of claim 6 further comprising visualizing at least one of the plurality of elements having a higher score relative to the corresponding confidence intervals as belonging to a cluster and at least one of the plurality of elements having a lower score relative to the corresponding confidence intervals as belonging to an exclusion zone. ### Claim 8 (depends on 7) The computer implemented method of claim 7, wherein the plurality of elements correspond to a plurality of pixels to be visualized. ### Claim 9 (depends on 6) The computer implemented method of claim 6 further comprising: varying at least one parameter related to one of: the region division; the simulation; the first score determination; the second score determination; and repeating determining a first score, determining a second score, and comparing the first score to the second score to optimize the statistical significance in a visualization of one of: a cluster; and an exclusion zone. ### Claim 10 (depends on 1) The computer implemented method of claim 1, wherein the predetermined kernel has a domain comprising a Gaussian shape around a point within the element. ### Claim 11 (depends on 1) The computer implemented method of claim 1, wherein determining a first score for each element of the plurality of elements by weighting the point set within a domain of a predetermined kernel comprises using one of: a top hat weighting function; a bell-shaped Gaussian weighting function; a conical weighting function; and a parabolic weighting function. ### Claim 12 (depends on 1) The computer implemented method of claim 1, wherein the point process is a Poisson point process. ### Claim 13 (depends on 1) The computer implemented method of claim 1, wherein the point process simulating at least one point set within the region includes a distribution based on one of: a covariate dataset; a dataset having a non-uniform distribution; and a marked dataset. ### Claim 14 (depends on 1) The computer implemented method of claim 1, wherein each of the plurality of elements includes multiple dimensions. ### Claim 15 (depends on 1) The computer implemented method of claim 1, wherein simulating at least one point set comprises using random samples drawn from a predetermined distribution. ### Claim 16 (depends on 1) The computer implemented method of claim 1, wherein the point set comprises a distribution of exocytosis events in cells. ### Claim 17 (depends on 1) The computer implemented method of claim 1 further comprising testing the point set for a goodness-of-fit of a non-random distribution. ### Claim 18 A computer program product including a non-transitory computer-storage medium having instructions stored thereon for processing data information, such that the instructions, when carried out by a processing device, cause the processing device to perform operations of: receiving a point set; simulating at least one point set within the region using a point process; dividing the region into a plurality of elements; determining a first score for each element of the plurality of elements by weighting the point set within a domain of a predetermined kernel; determining a second score for each element by weighting the at least one simulated point set within the domain of the predetermined kernel; comparing, for each element, the first score to the second score; computing confidence intervals for at least one confidence level having a predetermined statistical significance; and visualizing at least one of the plurality of elements having a higher score relative to one of the confidence intervals as belonging to a cluster and at least one of the plurality of elements having a lower score relative to a different confidence interval as belonging to an exclusion zone. ### Claim 19 A system for analyzing spatial point patterns in a region comprising: a host processor coupled to memory, the memory storing instructions that when executed on the host processor cause the system to perform: receiving a point set; simulating at least one point set within the region using a point process; dividing the region into a plurality of elements; determining a first score for each element of the plurality of elements by weighting the point set within a domain of a predetermined kernel; determining a second score for each element by weighting the at least one simulated point set within the domain of the predetermined kernel; comparing, for each element, the first score to the second score; computing confidence intervals for at least one confidence level having a predetermined statistical significance; and visualizing at least one of the plurality of elements having a higher score relative to one of the confidence intervals as belonging to a cluster and at least one of the plurality of elements having a lower score relative to a different confidence interval as belonging to an exclusion zone.