DETAILED ACTION
This nonfinal office action is responsive to claims filed on December 18, 2023. Claims 1-20 are pending. Claims 1, 13, and 17 are independent.
Notice of Pre-AIA or AIA Status
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
Information Disclosure Statement
The information disclosure statement (IDS) submitted on March 18, 2024 is in compliance with the provisions of 37 CFR 1.97. Accordingly, the information disclosure statement is being considered by the examiner.
Claim Objections
Claims 6 and 8-10 are objected to because of the following informalities:
Claim 6 reads "the GMM distribution at least one of:" based off the description in paragraph 0038 of the instant specification, it should read “the GMM distribution is used for at least one of:”
Claim 10 reads “taking as an additional input to the analysis of the distance assignment of hypercubes analogous to the hypercubes to specific analogous constituent Gaussian distributions of the constructed analogous GMM distributions.” The wording is unclear, however, based off the description in paragraph 0043 of the instant specification, it should read “taking, as an additional input to the analysis of the distance, assignment of hypercubes
Appropriate correction is required.
Regarding claims 8 and 9:
A series of singular dependent claims is permissible in which a dependent claim refers to a preceding claim which, in turn, refers to another preceding claim.
A claim which depends from a dependent claim should not be separated by any claim which does not also depend from said dependent claim. It should be kept in mind that a dependent claim may refer to any preceding independent claim. In general, applicant's sequence will not be changed. See MPEP § 608.01(n).
Claim Rejections - 35 USC § 103
In the event the determination of the status of the application as subject to AIA 35 U.S.C. 102 and 103 (or as subject to pre-AIA 35 U.S.C. 102 and 103) is incorrect, any correction of the statutory basis (i.e., changing from AIA to pre-AIA ) for the rejection will not be considered a new ground of rejection if the prior art relied upon, and the rationale supporting the rejection, would be the same under either status.
The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action:
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made.
Claims 1-4, 6-7, 9, 11, and 13-20 are rejected under 35 U.S.C. 103 as being unpatentable over Eckart et al. (US20170249401), hereinafter Eckart, in view of Camuffo et al. (Recent Advancements in Learning Algorithms for Point Clouds: An Updated Overview), hereinafter Camuffo.
Camuffo was cited in applicant’s IDS dated March 18, 2024.
Regarding claim 1, Eckart teaches the method:
distributing the data set across a multi-dimensional grid … (Eckart, paragraph 0023: “At step 102, point cloud data is received. The point cloud data may include data for a plurality of N-dimensional points. In one embodiment, each point is a three-dimensional point specified by an x-coordinate, a y-coordinate, and a z-coordinate. The point cloud data may be stored in a data structure in a non-volatile memory. The point cloud data may be read into a volatile memory (e.g., SDRAM) and loaded into a processor for processing.” – The point cloud is analogous to a multi-dimensional grid.)
assigning a hypercube to each constituent Gaussian distribution of constituent Gaussian distributions of the GMM distribution as a subspace of the multi-dimensional grid to form a number of hypercubes; and (Eckart, paragraph 0024: “At step 104, a GMM hierarchy is defined that includes a number of mixels that represent a plurality of probabilistic occupancy maps. The GMM hierarchy may be implemented as a data structure, such as a tree, storing a plurality of mixels. A mixel, as used herein, refers to a mixture element that is one component of a probability density function (PDF) that represents a point cloud. Conceptually, mixels are similar to voxels, but with fuzzy, overlapping boundaries and probability densities that vary across a volume.” – The mixels are analogous to the hypercubes, while the GMM hierarchy teaches a number of Gaussian distributions of the GMM.)
reducing a data footprint of the data set through the GMM distribution based on assigning the hypercube to the each constituent Gaussian distribution of the constituent Gaussian distributions of the GMM distribution. (Eckart, paragraph 0022: “The following paragraphs detail a parametric representation for a 3D point cloud based on a Gaussian mixture model (GMM) that achieves high-fidelity with lossy compression.” – high-fidelity with lossy compression indicates reducing a data footprint by finding a parametric representation using the Gaussian distributions.)
Eckart does not explicitly teach:
the multi-dimensional grid having integer coordinates associated therewith
However, Camuffo teaches:
the multi-dimensional grid having integer coordinates associated therewith (Camuffo, page 22, paragraph 2: “The point cloud is first preprocessed by applying voxelization, and coordinates are downscaled, i.e., divided by a scale factor s > 1 and rounded to the closest integer. Then, the grid is partitioned into blocks of dimension W _W _W. In addition, in this case, since the whole PC is processed in blockwise order, the coding performance is high, even with a relatively small model.” – The point clouds are taught by Eckart above, Camuffo shows that the coordinates are rounded to the closest integer and are thus represented with integer coordinates.)
Camuffo is considered analogous to the claimed invention as it is in the same field of endeavor, machine learning. Therefore, it would have been obvious to one of ordinary skill in the art before the effective filing date to have modified Eckart, which already teaches a multi-dimensional grid for the data but does not explicitly teach that the grid has integer coordinates, to include the teachings of Camuffo which does teach that the grid has integer coordinates in order to "improve the effect of entropy coding and thus obtain better compression rates." (Camuffo, page 22, paragraph 3)
Regarding claim 2, Eckart and Camuffo teach the method of claim 1, as cited above.
Eckart further teaches:
representing correlation between intensities of occurrence of numeric values likely to be derived from a specific constituent Gaussian distribution of the constituent Gaussian distributions and specific integer coordinates thereof within the assigned hypercube based on at least one of: regarding the numeric values likely to be derived from the specific constituent Gaussian distribution as occurring in an entirety of the corresponding hypercube assigned thereto; (Eckart, paragraph 0106: “In one embodiment, as shown in FIG. 8B, the technique begins by defining a bounding box 810 that encloses all points in the point cloud 800. The GMM hierarchy is initialized with a number of nodes in a first level of the GMM hierarchy, each node in the first level including a mixel that represents a probabilistic occupancy map.” – The bounding box that encloses all points in the point cloud is analogous to the specific integer coordinates within the assigned hypercube, where the probabilistic occupancy map is the correlation between the occurrence of numeric values likely derived from the Gaussian distribution.)
assigning a set of the number of hypercubes forming a chain of consecutive subsets thereof to the same constituent Gaussian distribution of the constituent Gaussian distributions, but with different weights; and (Eckart, paragraph 0027: “Each mixel represents a Gaussian basis function which is one component of the PDF that represents the point cloud data. However, a particular mixel only represents a sub-population of the points in the point cloud. The child pixels of the particular mixel represent the sub-population of the points as different sub-populations of the sub-population of the points in the point cloud, and so on and so forth. Thus, each mixel simply defines a location and spatial extent (i.e., probability distribution) within a volume where there is a high probability of enclosing one or more points in the point cloud.” – The mixel representing a particular sub-population of the point cloud is analogous to the consecutive subsets of Gaussian distributions. Each mixel representing a Gaussian basis function indicates that they would have different weights.)
regarding the specific constituent Gaussian distribution as a multi-dimensional Gaussian distribution and the integer coordinates of the specific constituent Gaussian distribution as additional numeric dimensions. (Eckart, paragraph 0027: “Thus, each mixel simply defines a location and spatial extent (i.e., probability distribution) within a volume where there is a high probability of enclosing one or more points in the point cloud.” – The location and special extent within a volume is analogous to the additional numeric dimensions which Camuffo teaches as integer coordinates in claim 1 above.)
Regarding claim 3, Eckart and Camuffo teach the method of claim 1, as cited above.
Eckart further teaches:
including information related to at least one of: an intensity of and a lack of co-occurrence of numeric values likely to be derived from different constituent Gaussian distributions of the constituent Gaussian distributions at different integer coordinates of the integer coordinates within a same array of the collection of multi-dimensional numeric arrays of the data set; and (Eckart, paragraph 0089: “For example, the stopping criteria may be reached once all of the PDFs fit the various clusters such that the determinant of the covariance matrix for each PDF is below a particular threshold value.” – The covariance matrix being below a particular threshold value is analogous to a lack of co-occurrence of numeric values. Each PDF fitting the various clusters is analogous to the different constituent Gaussian distributions.)
representing the information related to the at least one of: the intensity of and the lack of co- occurrence of the numeric values using at least one of: a square matrix of co-occurrence relations between all pairs of the constituent Gaussian distributions; a set of frequent itemsets, each frequent itemset representing a subset of the constituent Gaussian distributions that occur together for a frequency above a threshold value thereof; and a set of co-occurrence relations between specific constituent Gaussian distributions of the constituent Gaussian distributions and a data column with a specified number of distinct integer values. (Eckart, paragraph 0090: “For example, a PDF may be defined that has a mean based on the centroid of the points assigned to that cluster and a covariance matrix calculated based on the difference between each point and the location of the centroid of the points assigned to that cluster. If the determinant of the covariance matrix for each PDF is below a threshold value, then the algorithm is stopped and the number of PDFs represents the point cloud.” – The covariance matrix is analogous to the square matrix of co-occurrence relations between all pairs of the constituent Gaussian distributions which is the set of co-occurrence relations between specific Gaussian distributions.)
Regarding claim 4, Eckart and Camuffo teach the method of claim 1, as cited above.
Eckart further teaches:
building a separate GMM representation of each integer coordinate of the integer coordinates of the multi-dimensional grid from the collection of multi-dimensional numeric arrays at the each integer coordinate to form a number of separate GMM representations in accordance with executing an EM algorithm using the processor communicatively coupled to the memory; (Eckart, paragraph 0119: “In one embodiment, the PPU 200 scans the point cloud 800 to determine a minimum and maximum value for each coordinate (e.g., x-coordinate, y-coordinate, and z-coordinate) for every point in the point cloud 800.” And paragraph 0087: “Thus, the entire data set in the point cloud 700 may be represented by a number of different Gaussian distributions, with each point belonging to a particular cluster or subset of points represented by one of the Gaussian distributions.” And paragraph 0109: “After the EM algorithm has been completed and the set of probabilistic occupancy maps are defined, a refinement step may be performed that analyzes each of the probabilistic occupancy maps to determine if any nodes of the tree should be segmented to add a number of child nodes at a higher level of detail in the GMM hierarchy.” – The entire data set of the point cloud represented by a number of different Gaussian distributions indicates a separate GMM for each coordinate, which Camuffo teaches as integer coordinates above. The EM algorithm is used to build the GMM hierarchy, e.g., the separate GMM representations.)
in accordance with executing a data clustering algorithm using the processor communicatively coupled to the memory, searching for adjacent integer coordinates of the integer coordinates that share at least one constituent Gaussian distribution in the separate GMM representations of the number of separate GMM representations associated therewith that are similar to one another based on a similarity parameter being below a threshold value thereof; and (Eckart, paragraph 0089: “The points may be assigned to the PDFs using recursive binary splits of the points using k-means clustering and then performing PCA (principal component analysis) independently on each cluster until a certain stopping criteria is reached. For example, the stopping criteria may be reached once all of the PDFs fit the various clusters such that the determinant of the covariance matrix for each PDF is below a particular threshold value.” – k-means clustering searches adjacent coordinates to build the clusters, where the PDFs fitting the clusters is analogous to the separate GMM representations based on similarity being below a threshold value, i.e. the determinant of the covariance matrix being below a threshold.)
forming, from areas of the adjacent integer coordinates, the hypercube in which the shared at least one constituent Gaussian distribution in the separate GMM representations are merged together to form the each constituent Gaussian distribution of the constituent Gaussian distributions of the GMM distribution. (Eckart, paragraph 0092: “The technique for representing the point cloud 800, described herein, is to represent the point cloud 800 as a set of anisotropic basis functions (e.g., Gaussian basis functions) stored as mixels in a tree data structure. The mixels are arranged in a hierarchy, with each mixel representing a sub-surface patch modeled by the point cloud 800. A sub-surface path refers to an overlapping, probabilistic occupancy map that represents at least a portion of the model. The mixels associated with child nodes, therefore, represent different, smaller components of the sub-surface patch represented by the mixel associated with a parent node of the child nodes. As the number of levels of the GMM hierarchy increases, the mixels at the highest levels of detail represent smaller and smaller sub-surface patches.” – The mixels being arranged in a hierarchy indicates the separate GMM representations. The further up in the GMM hierarchy, the larger the GMM distribution, where the child nodes are combined in the parent node and thus the separate child representations are merged into a parent representation.)
Regarding claim 6, Eckart and Camuffo teach the method of claim 1, as cited above.
Eckart further teaches:
the GMM distribution at least one of: replacing the data set and being available as an approximate model of the data set for an operation to be performed through the processor; and (Eckart, paragraph 0145: “Each probabilistic occupancy map θj in the GMM hierarchy is applied to the set of samples X to generate a set of points pi associated with the probabilistic occupancy map that are binned according to the set of voxels defined for the volume.” – generating samples of points in the GMM hierarchy is analogous to being available as an approximation model for the dataset.)
storing the GMM distribution as metadata in the memory in addition to the data set for availability thereof for the operation to be performed trough the processor. (Eckart, paragraph 0148: “The system 1200 includes a GMM engine 1210, a voxel engine 1220, and a mesh engine 1230. The GMM engine 1210 receives point cloud data 800 and generates a GMM hierarchy 1080 by implementing method 900. The voxel engine 1220 receives the GMM hierarchy 1080 and generates a sparse voxel list 1202 based on the importance sampling algorithm. The mesh engine 1230 receives the sparse voxel list 1202 and the GMM hierarchy 1080 and generates a mesh 1204 by implementing the modified marching cubes algorithm.”)
Regarding claim 7, Eckart and Camuffo teach the method of claim 1, as cited above.
Eckart further teaches:
splitting the collection of multi-dimensional numeric arrays into smaller sets thereof; (Eckart, paragraph 0092: “The mixels are arranged in a hierarchy, with each mixel representing a sub-surface patch modeled by the point cloud 800.” – The mixels representing sub-surface patches of the point cloud is analogous to splitting the multi-dimensional numeric arrays into smaller sets.)
for each smaller set of the smaller sets, constructing GMM distributions analogous to the GMM distribution and storing a GMM distribution of the constructed analogous GMM distributions for the each smaller set separately in the memory; and (Eckart, paragraph 0092: “The mixels associated with child nodes, therefore, represent different, smaller components of the sub-surface patch represented by the mixel associated with a parent node of the child nodes. As the number of levels of the GMM hierarchy increases, the mixels at the highest levels of detail represent smaller and smaller sub-surface patches.” – The mixels associated with a child node which represents a level of the GMM hierarchy is analogous to the GMM distribution of the smaller set.)
optimizing the splitting of the collection of multi-dimensional numeric arrays into the smaller sets in accordance with maximizing an ability of the constructed analogous GMM distributions to approximate original local distributions of array values within the smaller sets. (Eckart, paragraph 0109: “If the total expectation is above the threshold value, then the node associated with that probabilistic occupancy map may be divided into a number of child nodes at a new level of the GMM hierarchy. The child nodes may include new mixels that may be seeded, during a subsequent iteration of the EM algorithm, according to a skewed version of the bounding box 810.” – Dividing the child nodes into new levels of the GMM hierarchy during iterations of the EM algorithm indicates that the splitting is optimized as the training will stop once the EM algorithm is complete, e.g., is optimized.)
Eckart does not explicitly teach:
the collection of multi-dimensional numeric arrays corresponding to a collection of multi-dimensional numeric values of a data column of an array type in a data table distributed over consecutive rows stored in the data table;
However, Camuffo further teaches:
the collection of multi-dimensional numeric arrays corresponding to a collection of multi-dimensional numeric values of a data column of an array type in a data table distributed over consecutive rows stored in the data table; (Camuffo, page 21, paragraph 4: “In order to address the sparsity problem, the whole grid is divided into smaller blocks with dimensions 8 X 8 X 8, and only those that contain some useful information are processed by the network.” – The smaller blocks being divided from the whole indicates that there is a collection of multi-dimensional numeric arrays where the data is divided into a tabular distribution with rows and columns, e.g. the 8x8x8 dimension of the blocks.)
Regarding claim 9, Eckart and Camuffo teach the method of claim 7, as cited above.
Eckart further teaches:
the collection of multi-dimensional numeric arrays being an output of a transformation of at least one complex object; (Eckart, paragraph 0128: “Based on an examination of Equation 16, each input xi can be interpreted as undergoing an affine transformation before being evaluated through a zero-mean Gaussian basis function with identity covariance.” And paragraph 0074: “The data assembly stage 610 receives the input data 601 that specifies vertex data for high-order surfaces, primitives, or the like.”)
the at least one complex object being at least one of: image data, video data, text data and time-series of sensor measurement data; (Eckart, paragraph 0073: “The graphics processing pipeline 600 is an abstract flow diagram of the processing steps implemented to generate 2D computer-generated images from 3D geometry data. As is well-known, pipeline architectures may perform long latency operations more efficiently by splitting up the operation into a plurality of stages, where the output of each stage is coupled to the input of the next successive stage. Thus, the graphics processing pipeline 600 receives input data 601 that is transmitted from one stage to the next stage of the graphics processing pipeline 600 to generate output data 602.” – Paragraph 0021 also mentions incoming data from sensors.)
the constructed analogous GMM distributions of specific smaller sets of the at least one complex object being stored in the memory one of: instead of the input data and together with the input data relevant to at least one of: the at least one complex object and the output of the transformation of the at least one complex object; (Eckart, paragraph 0128: “Thus, sampling the GMM hierarchy can be performed by simply sampling each probabilistic occupancy map over the range [0, 1] in three dimensions and then transforming the sampled values through a probit function (φ−1). The transformed samples may be the same for each probabilistic occupancy map of the GMM hierarchy. Once the collection of transformed samples has been defined, a probability estimate may be calculated by keeping track of a proportion of samples, per probabilistic occupancy map included in the GMM hierarchy, that are associated with each voxel and then multiplying the ratio by an appropriate mixing parameter for the probabilistic occupancy map, as shown in Equation 17” – The transformed samples being used to construct the GMM hierarchy and then collected by keeping track of them is analogous to the GMM distributions being stored together with the transformation.)
generating at least one data sample comprising artificial multi-dimensional numeric arrays based on the constructed analogous GMM distributions for an operation to be performed using the processor communicatively coupled to the memory; (Eckart, paragraph 0144: “At step 1104, a set of voxels is defined for a particular volume. The set of voxels may be determined based on a desired voxel resolution. The particular volume may be determined based on a viewing frustum associated with the model. The viewing frustum may define a position and an orientation of the camera relative to the model defined by the point cloud represented by the GMM hierarchy” – The set of voxels being defined is analogous to generating the data sample, these voxels are coming from the point cloud representation which is analogous to the multi-dimensional numeric arrays.)
the operation to be performed using the processor communicatively coupled to the memory relating to at least one of: learning at least one Machine Learning (ML) model and data clustering; (Eckart, paragraph 0022: “The following paragraphs detail a parametric representation for a 3D point cloud based on a Gaussian mixture model (GMM) that achieves high-fidelity with lossy compression. Once the hierarchical representation of the point cloud has been created, a novel approach to the Marching Cubes algorithm may be employed in order to extract a polygonal mesh (i.e., a triangle mesh) from the compressed, hierarchical representation of the point cloud.” – The Marching Cubes algorithm used to extract a polygonal mesh is analogous to the machine learning model being learned.)
generating the at least one data sample based on selecting the smaller sets by finding the constructed analogous GMM distributions that are representative of the constructed analogous GMM distributions of all the smaller sets; and (Eckart, paragraph 0128: “Once the collection of transformed samples has been defined, a probability estimate may be calculated by keeping track of a proportion of samples, per probabilistic occupancy map included in the GMM hierarchy, that are associated with each voxel and then multiplying the ratio by an appropriate mixing parameter for the probabilistic occupancy map, as shown in Equation 17”)
generating the artificial multi-dimensional numeric arrays at least one of: based on the constructed analogous GMM distributions of the selected smaller sets and selecting an actual numeric array belonging to the selected smaller sets. (Eckart, paragraph 0128: “ A relatively low number of samples can be used to sample each probabilistic occupancy map to get sufficient results (e.g., 32 samples per probabilistic occupancy map) with low variance.” – The samples being used to sample each probabilistic occupancy map is analogous to the smaller sets based on the constructed analogous GMM distributions.)
Regarding claim 11, Eckart and Camuffo teach the method of claim 9, as cited above.
Eckart further teaches:
the operation to be performed using the processing communicatively to the memory involving finding a subset of the at least one complex object that are most similar to another complex object specified as an input thereto in accordance with: (Eckart, paragraph 0089: “The points may be assigned to the PDFs using recursive binary splits of the points using k-means clustering and then performing PCA (principal component analysis) independently on each cluster until a certain stopping criteria is reached.” – The k-means clustering of the points indicates that there is a subset most similar to another specified from the input, as the clustering is clustering similar objects.)
transforming the another complex object into a corresponding one of: a numeric array and a multiple numeric array representation thereof; and (Eckart, paragraph 0128: “Based on an examination of Equation 16, each input xi can be interpreted as undergoing an affine transformation before being evaluated through a zero-mean Gaussian basis function with identity covariance.” And paragraph 0074: “The data assembly stage 610 receives the input data 601 that specifies vertex data for high-order surfaces, primitives, or the like.”)
analyzing the corresponding one of: the numeric array and the multiple numeric array representation against the constructed analogous GMM distributions of the specific smaller sets of the at least one complex object to determine the smaller sets that deliver a highest probability of contents thereof comprising objects similar to the at least one complex object. (Eckart, paragraph 0128: “Once the collection of transformed samples has been defined, a probability estimate may be calculated by keeping track of a proportion of samples, per probabilistic occupancy map included in the GMM hierarchy, that are associated with each voxel and then multiplying the ratio by an appropriate mixing parameter for the probabilistic occupancy map, as shown in Equation 17.” – The probability estimate represents the probability. Thus, the probabilistic occupancy map analyzes the array to determine the highest probability of content comprising similar objects.)
Regarding claim 13, claim 13 has all the same limitations as claim 1 which are taught by Eckart and Camuffo – see claim 1 above.
Eckart additionally teaches:
a memory; and (Eckart, paragraph 0154: “Computer programs, or computer control logic algorithms, may be stored in the main memory 1304 and/or the secondary storage 1310. Such computer programs, when executed, enable the system 1300 to perform various functions. The memory 1304, the storage 1310, and/or any other storage are possible examples of computer-readable media.”)
a processor communicatively coupled to the memory, the processor executing instructions to: (Eckart, paragraph 0155: “In one embodiment, the architecture and/or functionality of the various previous figures may be implemented in the context of the central processor 1301, the graphics processor 1306, an integrated circuit (not shown) that is capable of at least a portion of the capabilities of both the central processor 1301 and the graphics processor 1306, a chipset (i.e., a group of integrated circuits designed to work and sold as a unit for performing related functions, etc.), and/or any other integrated circuit for that matter.”)
Regarding claim 14, Eckart and Camuffo teach the data processing device of claim 13, as cited above.
Claim 14 additionally has the same limitations of claim 2 which are taught by Eckart and Camuffo – see claim 2 above.
Regarding claim 15, Eckart and Camuffo teach the data processing device of claim 13, as cited above.
Claim 15 additionally has the same limitations of claim 3 which are taught by Eckart and Camuffo – see claim 3 above.
Regarding claim 16, Eckart and Camuffo teach the data processing device of claim 13, as cited above.
Claim 16 additionally has the same limitations of claim 4 which are taught by Eckart and Camuffo – see claim 4 above.
Regarding claim 17, claim 17 has the same limitations of claim 1 which are taught by Eckart and Camuffo – see claim 1 above.
Eckart additionally teaches:
a memory; and (Eckart, paragraph 0154: “Computer programs, or computer control logic algorithms, may be stored in the main memory 1304 and/or the secondary storage 1310. Such computer programs, when executed, enable the system 1300 to perform various functions. The memory 1304, the storage 1310, and/or any other storage are possible examples of computer-readable media.”)
a processor communicatively coupled to the memory, the processor executing instructions to: (Eckart, paragraph 0155: “In one embodiment, the architecture and/or functionality of the various previous figures may be implemented in the context of the central processor 1301, the graphics processor 1306, an integrated circuit (not shown) that is capable of at least a portion of the capabilities of both the central processor 1301 and the graphics processor 1306, a chipset (i.e., a group of integrated circuits designed to work and sold as a unit for performing related functions, etc.), and/or any other integrated circuit for that matter.”)
utilize the GMM distribution: to approximate the data set, and one of: along with and instead of the data set for a computational operation using a Machine Learning (ML) algorithm also executing on the processor. (Eckart, paragraph 0145: “Each probabilistic occupancy map θj in the GMM hierarchy is applied to the set of samples X to generate a set of points pi associated with the probabilistic occupancy map that are binned according to the set of voxels defined for the volume.” – generating samples of points in the GMM hierarchy is analogous to being available as an approximation model for the dataset.)
Regarding claim 18, Eckart and Camuffo teach the data processing device of claim 17, as cited above.
Claim 18 additionally has the same limitations of claim 2 which are taught by Eckart and Camuffo – see claim 2 above.
Regarding claim 19, Eckart and Camuffo teach the data processing device of claim 13, as cited above.
Claim 19 additionally has the same limitations of claim 3 which are taught by Eckart and Camuffo – see claim 3 above.
Regarding claim 20, Eckart and Camuffo teach the data processing device of claim 13, as cited above.
Claim 20 additionally has the same limitations of claim 4 which are taught by Eckart and Camuffo – see claim 4 above.
Claim 5 is rejected under 35 U.S.C. 103 as being unpatentable over Eckart in view of Camuffo in view of Cao (Practice on Classification using Gaussian Mixture Model), hereinafter Cao.
Regarding claim 5, Eckart and Camuffo teach the method of claim 1, as cited above.
Eckart and Camuffo do not explicitly teach:
specifying a first number of the constituent Gaussian distributions of the GMM distribution as an input parameter to a construction of the GMM distribution; and
working with a second number of the constituent Gaussian distributions of the GMM distribution that is less than the first number of the constituent Gaussian distributions in accordance with the GMM distribution inadequately approximating the data set.
However, Cao teaches:
specifying a first number of the constituent Gaussian distributions of the GMM distribution as an input parameter to a construction of the GMM distribution; and (Cao, page 4, column 2, paragraph 3: “First, compute the GMM model given the number of components k and the model covers all of the training data;” – The components is analogous to the number of Gaussian distributions, Thus, computing the GMM model given the number of components k indicates that a number of constituent Gaussian distributions is specified as an input parameter.)
working with a second number of the constituent Gaussian distributions of the GMM distribution that is less than the first number of the constituent Gaussian distributions in accordance with the GMM distribution inadequately approximating the data set. (Cao, page 4, column 1, pseudo code, last 3 lines and column 2, paragraph 4: “This reveals that the jth component is most likely to generate the examples in the class c.” – The components give
θ
c
which is used to find the best output, e.g., the component that has the best accuracy is used for the final output. Table 2 on page 5 shows that this would occur with the GMM with lower components which is analogous to working with a second number of Gaussian distributi9ons that is less than the first number.)
Cao is considered analogous to the claimed invention as it is in the same field of endeavor, machine learning. Therefore, it would have been obvious to one of ordinary skill in the art before the effective filing date to have modified Eckart and Camuffo, which already teaches a GMM distribution with a number of constituent Gaussian distributions but does not explicitly teach specifying the number of constituent Gaussian distributions and refining that number based on the approximation, to include the teachings of Cao which does teach specifying the number of constituent Gaussian distributions and refining that number based on the approximation as “the accuracy is quite correlated with the selection of k, and with different settings, the optimal selection of k may be different.” (Cao, page 6, column 1, paragraph 3)
Claim 8 is rejected under 35 U.S.C. 103 as being unpatentable over Eckart in view of Camuffo in view of Kahn et al. (DVAEGMM: Dual Variational Autoencoder With Gaussian Mixture Model for Anomaly Detection on Attributed Networks), hereinafter Kahn.
Regarding claim 8, Eckart and Camuffo teach the method of claim 1, as cited above.
Eckart further teaches:
the collection of multi-dimensional numeric arrays being an output of a transformation of at least one complex object; (Eckart, paragraph 0128: “Based on an examination of Equation 16, each input xi can be interpreted as undergoing an affine transformation before being evaluated through a zero-mean Gaussian basis function with identity covariance.” And paragraph 0074: “The data assembly stage 610 receives the input data 601 that specifies vertex data for high-order surfaces, primitives, or the like.”)
the at least one complex object being at least one of: image data, video data, text data and time- series of sensor measurement data; (Eckart, paragraph 0073: “The graphics processing pipeline 600 is an abstract flow diagram of the processing steps implemented to generate 2D computer-generated images from 3D geometry data. As is well-known, pipeline architectures may perform long latency operations more efficiently by splitting up the operation into a plurality of stages, where the output of each stage is coupled to the input of the next successive stage. Thus, the graphics processing pipeline 600 receives input data 601 that is transmitted from one stage to the next stage of the graphics processing pipeline 600 to generate output data 602.” – Paragraph 0021 also mentions incoming data from sensors.)
generating at least one data sample comprising artificial multi-dimensional numeric arrays based on the GMM distribution for an operation to be performed using the processor communicatively coupled to the memory. (Eckart, paragraph 0144: “At step 1104, a set of voxels is defined for a particular volume. The set of voxels may be determined based on a desired voxel resolution. The particular volume may be determined based on a viewing frustum associated with the model. The viewing frustum may define a position and an orientation of the camera relative to the model defined by the point cloud represented by the GMM hierarchy” – The set of voxels being defined is analogous to generating the data sample, these voxels are coming from the point cloud representation which is analogous to the multi-dimensional numeric arrays.)
Eckart and Camuffo do not explicitly teach:
the transformation of the at least one complex object being at least one of: a tensor decomposition and an internal layer of an autoencoder;
However, Kahn teaches:
the transformation of the at least one complex object being at least one of: a tensor decomposition and an internal layer of an autoencoder; and (Kahn, page 91165, column 2, last paragraph: “Two non-linear feature transform layers are employed in the encoder of the attribute variational autoencoder to learn a non-linear feature mapping of the node attributes, rather than relying on the structure information, as is the case with the structure autoencoder” and page 91166, column 1, paragraph 2: “Following the attribute encoder, a feature fusion module is also built to fuse the learnt node embeddings ZS from structure space and ZA from attribute space into a fused embedding ZF, which is accepted as input by the GMM to capture the relationship between structure and attribute.” – the feature transformation layers of the variational autoencoder is analogous to the transformation being an internal layer of an autoencoder.)
Kahn is considered analogous to the claimed invention as it is in the same field of endeavor, machine learning. Therefore, it would have been obvious to one of ordinary skill in the art before the effective filing date to have modified Eckart and Camuffo, which already teaches The input data to the GMM distribution being a transformation of a complex object but does not explicitly teach the transformation is an internal layer of an autoencoder, to include the teachings of Kahn which does teach the transformation is an internal layer of an autoencoder in order to "enforce the learnt latent embedding to match a prior distribution while simultaneously minimizing the reconstruction errors of the topological structure and node attributes." (Kahn, page 91161, column 2, paragraph 7)
Claims 10 and 12 are rejected under 35 U.S.C. 103 as being unpatentable over Eckart in view of Camuffo in view of Kolouri et al. (Sliced Wasserstein Distance for Learning Gaussian Mixture Models), hereinafter Kolouri.
Regarding claim 10, Eckart and Camuffo teach the method of claim 9, as cited above.
Eckart further teaches:
choosing the constructed analogous GMM distributions that are representative of the constructed analogous GMM distributions of all the smaller sets based on an analysis of a distance between the constructed analogous GMM distributions; (Eckart, paragraph 0128: “In other words, the PDF of the Gaussian distribution represents a measurement of a probability that any random point will be a represented by a particular Gaussian distribution, where the probability is a maximum at a location specified by the mean (μ) associated with the Gaussian distribution and the probability decreases the further the distance, along a particular direction, of the point from the location specified by the mean.”)
taking as an additional input to the analysis of the distance assignment of hypercubes analogous to the hypercubes to specific analogous constituent Gaussian distributions of the constructed analogous GMM distributions. (Eckart, paragraph 0090: “For example, a PDF may be defined that has a mean based on the centroid of the points assigned to that cluster and a covariance matrix calculated based on the difference between each point and the location of the centroid of the points assigned to that cluster. If the determinant of the covariance matrix for each PDF is below a threshold value, then the algorithm is stopped and the number of PDFs represents the point cloud. However, if the determinant of the covariance matrix for each PDF is above the threshold value, then each of the clusters is split into two separate sub-clusters using the k-means clustering algorithm and the process is recursively repeated.” – The PDF being defined by the mean and centroid points of the cluster indicates that the analysis of the distance assignments is used as an input to construct the GMM distributions.)
Eckart and Camuffo do not explicitly teach:
the analysis of the distance being based on at least one of: a Wasserstein distance and a Kullback-Leibler (KL) divergence;
However, Kolouri teaches:
the analysis of the distance being based on at least one of: a Wasserstein distance and a Kullback-Leibler (KL) divergence; and (Kolouri, page 5, column 2, paragraph 2: “Figure 2 demonstrates the high-level idea behind slicing high-dimensional PDFs
I
x
and
I
y
and minimizing the p-Wasserstein distance between these slices over GMM components.” – The high-dimensional PDFs are analogous to the PDFs as taught by Eckart above.)
Kolouri is considered analogous to the claimed invention as it is in the same field of endeavor, machine learning. Therefore, it would have been obvious to one of ordinary skill in the art before the effective filing date to have modified Eckart and Camuffo, which already teaches using a distance measure to construct GMM distributions but does not explicitly teach the distance measure is a Wasserstein distance, to include the teachings of Kolouri which does teach the distance measure is a Wasserstein distance as it is “more well-behaved and therefore more suitable for stochastic gradient descent scheme to obtain the optimal GMM parameters.” (Kolouri, abstract)
Regarding claim 12, Eckart and Camuffo teach the method of claim 9, as cited above.
Eckart further teaches:
the operation to be performed using the processor communicatively coupled to the memory taking as input thereto two data tables; (Eckart, paragraph 0036: “In one embodiment, each of the voxels in the sparse voxel list may be processed in parallel.” – Processing the voxels in parallel indicates the input being two data tables.)
finding pairs of array data column types belonging to the two data tables whose constructed analogous GMM distributions are closest to one another; and (Eckart, paragraph 0036: “For example, in a first step, all eight probability values for the eight vertices of a voxel may be calculated in parallel by sampling the GMM hierarchy using the corresponding locations for each vertex. Furthermore, probability values for multiple voxels in the sparse voxel list may be calculated substantially simultaneously. In a second step, the set of probability values for each voxel may be compared to an iso-value and a determination made as to whether the voxel encloses, at least in part, an iso-surface. Again, the second step may also be performed in parallel for multiple voxels.” – The probabilities being calculated and compared to determine if the voxel encloses an iso-surface indicates that the voxels can be paired as being close to one another.)
Eckart and Camuffo do not explicitly teach:
measuring closeness of the constructed analogous GMM distributions based on at least one of: a Wasserstein distance and a KL divergence.
However, Kolouri teaches:
measuring closeness of the constructed analogous GMM distributions based on at least one of: a Wasserstein distance and a KL divergence. (Kolouri, page 5, column 2, paragraph 2: “Figure 2 demonstrates the high-level idea behind slicing high-dimensional PDFs
I
x
and
I
y
and minimizing the p-Wasserstein distance between these slices over GMM components.” – The high-dimensional PDFs are analogous to the PDFs as taught by Eckart above.)
Kolouri is considered analogous to the claimed invention as it is in the same field of endeavor, machine learning. Therefore, it would have been obvious to one of ordinary skill in the art before the effective filing date to have modified Eckart and Camuffo, which already teaches measuring closeness of the GMM distributions but does not explicitly teach that the measuring is done based on a Wasserstein distance, to include the teachings of Kolouri which does teach that the measuring is done based on a Wasserstein distance as it is “more well-behaved and therefore more suitable for stochastic gradient descent scheme to obtain the optimal GMM parameters.” (Kolouri, abstract)
Conclusion
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure.
Delon and Desolneux (A Wasserstein-type Distance in the Space of Gaussian Mixture Models)
Achlioptas et al. (Learning Representations and Generative Models for 3D Point Clouds)
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/J.C.M./ Examiner, Art Unit 2144 /TAMARA T KYLE/Supervisory Patent Examiner, Art Unit 2144
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