# US 2015/0146973 A1 · Distributed similarity learning for high-dimensional image features > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 2015/0146973 A1 - Document ID: US20150146973A1 - Status: Published application - Kind: A1 - Application number: 14/091,972 - Filed: 2013-11-27 - Published: 2015-05-28 - Earliest claimed: 2013-11-27 - Assignees: Adobe Systems Incorporated - Applicants: Adobe Systems Incorporated - Inventors: Jianchao Yang; Zhaowen Wang; Zhe Lin; Jonathan Brandt - Web page: https://patentgrep.com/patent/US20150146973A1 ## CPC - G06N 20/10: using kernel methods, e.g. support vector machines [SVM] - G06F 18/21322: {Rendering the within-class scatter matrix non-singular} - G06F 18/2411: based on the proximity to a decision surface, e.g. support vector machines - G06V 10/764: using classification, e.g. of video objects - G06V 10/7715: {Feature extraction, e.g. by transforming the feature space, e.g. multi-dimensional scaling [MDS]; Mappings, e.g. subspace methods} - G06N 20/20: Ensemble learning - G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS - G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N) - G06V: IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING ## Abstract A system and method for distributed similarity learning for high-dimensional image features are described. A set of data features is accessed. Subspaces from a space formed by the set of data features are determined using a set of projection matrices. Each subspace has a dimension lower than a dimension of the set of data features. Similarity functions are computed for the subspaces. Each similarity function is based on the dimension of the corresponding subspace. A linear combination of the similarity functions is performed to determine a similarity function for the set of data features. ## Claims ### Claim 1 A method comprising: accessing a set of data features; determining a plurality of subspaces from a space formed by the set of data features using a set of projection matrices, each subspace having a dimension lower than a dimension of the set of data features; computing, using a processor of a machine, a plurality of similarity functions for the plurality of subspaces, each similarity function based on a dimension of a corresponding subspace; and performing a linear combination of the plurality of similarity functions to determine a similarity function for the set of data features. ### Claim 2 (depends on 1) The method of claim 1, further comprising: computing the plurality of similarity functions for the plurality of subspaces in parallel in a plurality of processors. ### Claim 3 (depends on 1) The method of claim 1, wherein determining the plurality of subspaces further comprises: determining a plurality of random subspaces from the space formed by the set of data features, each random subspace having a dimension substantially lower than the dimension of the set of data features; and computing the plurality of similarity functions for the plurality of random subspaces, each similarity function based on a dimension of a corresponding random subspace. ### Claim 4 (depends on 1) The method of claim 1, wherein the similarity function is based on a similarity matrix with the dimension of the set of data features, wherein each similarity function of the plurality of subspaces is based on a corresponding similarity matrix that is smaller than the similarity matrix of the similarity function. ### Claim 5 (depends on 1) The method of claim 1, further comprising: forming the set of projection matrices from the set of data features; using the set of projection matrices to project the set of data features to a set of substantially lower dimensional data features; for each projection matrix, generating a substantially lower dimensional similarity function in a corresponding subspace defined by the projection matrix; and performing a linear combination of the substantially lower dimensional similarity functions to compute the similarity matrix. ### Claim 6 (depends on 5) The method of claim 5, wherein the set of projection matrices is constructed by random matrices, random selection matrices, or principal component analysis, wherein the linear combination comprises a linear coefficient for each similarity function of the subspaces, the linear coefficient determined using a linear support vector machine. ### Claim 7 (depends on 1) The method of claim 1, further comprising: using the similarity function for the set of data features to determine a similarity between a first image and a second image, the set of data features from the first and second image; and providing a same tag to the first image and the second image based on the similarity between the image and the second image. ### Claim 8 A system comprising: a plurality of processors; a projection module configured to: access a set of data features; determine a plurality of subspaces from a space formed by the set of data features using a set of projection matrices, each subspace having a dimension lower than a dimension of the set of data features; and compute, using the plurality of processors, a plurality of similarity functions for the plurality of subspaces, each similarity function based on a dimension of a corresponding subspace, and a linear combination module configured to perform a linear combination of the plurality of similarity functions to determine a similarity function for the set of data features. ### Claim 9 (depends on 8) The system of claim 8, wherein the projection module is configured to compute the plurality of similarity functions for the plurality of subspaces in parallel using the plurality of processors. ### Claim 10 (depends on 8) The system of claim 8, wherein the projection module is configured to: determine a plurality of random subspaces from the space formed by the set of data features, each random subspace having a dimension substantially lower than the dimension of the set of data features; and compute the plurality of similarity functions for the plurality of random subspaces, each similarity function based on a dimension of a corresponding random subspace. ### Claim 11 (depends on 8) The system of claim 8, wherein the similarity function is based on a similarity matrix with the dimension of the set of data features, wherein each similarity function of the plurality of subspaces is based on a corresponding similarity matrix that is smaller than the similarity matrix of the similarity function. ### Claim 12 (depends on 8) The system of claim 8, wherein the projection module is configured to: form the set of projection matrices from the set of data features; use the set of projection matrices to project the set of data features to a set of substantially lower dimensional data features; for each projection matrix, generate a substantially lower dimensional similarity function in a corresponding subspace defined by the projection matrix; and perform a linear combination of the substantially lower dimensional similarity functions to compute the similarity matrix. ### Claim 13 (depends on 12) The system of claim 12, wherein the set of projection matrices is constructed using by random matrices, random selection matrices, or principal component analysis, wherein the linear combination comprises a linear coefficient for each similarity function of the subspaces, the linear coefficient determined using a linear support vector machine. ### Claim 14 (depends on 8) The system of claim 8, wherein at least one of the plurality of the processors is configured to use the similarity function for the set of data features to determine a similarity between a first image and a second image, the set of data features from the first and second image, and to provide a same tag to the first image and the second image based on the similarity between the image and the second image. ### Claim 15 A non-transitory machine-readable storage medium storing instructions which, when executed by at least one processor, performs operations comprising: accessing a set of data features; determining a plurality of subspaces from a space formed by the set of data features using a set of projection matrices, each subspace having a dimension lower than a dimension of the set of data features; computing, using a processor of a machine, a plurality of similarity functions for the plurality of subspaces, each similarity function based on a dimension of a corresponding subspace; and performing a linear combination of the plurality of similarity functions to determine a similarity function for the set of data features. ### Claim 16 (depends on 15) The storage medium of claim 15, wherein the operations further comprises: computing the plurality of similarity functions for the plurality of subspaces independently in parallel in a plurality of processors. ### Claim 17 (depends on 15) The storage medium of claim 15, wherein the operations further comprises: determining a plurality of random subspaces from the space formed by the set of data features, each random subspace having a dimension substantially lower than the dimension of the set of data features; and computing the plurality of similarity functions for the plurality of random subspaces, each similarity function based on a dimension of a corresponding random subspace. ### Claim 18 (depends on 15) The storage medium of claim 15, wherein the similarity function is based on a similarity matrix with the dimension of the set of data features, wherein each similarity function of the plurality of subspaces is based on a corresponding similarity matrix that is smaller than the similarity matrix of the similarity function. ### Claim 19 (depends on 15) The storage medium of claim 15, wherein the operations further comprises: forming the set of projection matrices from the set of data features; using the set of projection matrices to project the set of data features to a set of substantially lower dimensional data features; for each projection matrix, generating a substantially lower dimensional similarity function in a corresponding subspace defined by the projection matrix; and performing a linear combination of the substantially lower dimensional similarity functions to compute the similarity matrix, wherein the set of projection matrices is constructed using by random matrices, random selection matrices, or principal component analysis. ### Claim 20 (depends on 15) The storage medium of claim 15, wherein the operations further comprises: using the similarity function for the set of data features to determine a similarity between a first image and a second image, the set of data features from the first and second image; and providing a same tag to the first image and the second image based on the similarity between the image and the second image.