# US 2023/0267352 A1 · System, Method, and Computer Program Product for Time Series Based Machine Learning Model Reduction Strategy > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 2023/0267352 A1 - Document ID: US20230267352A1 - Status: Published application - Kind: A1 - Application number: 17/677,159 - Filed: 2022-02-22 - Published: 2023-08-24 - Earliest claimed: 2022-02-22 - Assignees: Visa International Service Association - Applicants: Visa International Service Association - Inventors: Runxin He; Qingguo Chen; Subir Roy; Yu Gu; Dan Wang - Web page: https://patentgrep.com/patent/US20230267352A1 ## CPC - G06N 7/01: Probabilistic graphical models, e.g. probabilistic networks - G06F 17/16: Matrix or vector computation {, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization (matrix transposition G06F7/78)} - G06N 20/00: Machine learning - G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS - G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N) ## Abstract Provided are systems for generating a machine learning model and a prediction based on encoded time series data using model reduction techniques that include a processor to receive a training dataset of a plurality of data instances, wherein each data instance includes a time series of data points, perform an encoding operation on the training dataset to provide an encoded dataset having a lower dimension space than a dimension space of the training dataset, generate one or more prediction models based on the encoded dataset, determine an output of the one or more prediction models in the lower dimension space based on an input provided to the one or more prediction models, and perform a decoding operation on the output to project the output from the lower dimension space to the dimension space of the training dataset. Methods and computer program products are also provided. ## Claims ### Claim 1 A system for generating a machine learning model based on encoded time series data using model reduction techniques, the system comprising: at least one processor programmed or configured to: receive a training dataset of a plurality of data instances, wherein each data instance comprises a time series of data points; perform an encoding operation on the training dataset to provide an encoded dataset having a lower dimension space than a dimension space of the training dataset; generate one or more prediction models based on the encoded dataset, wherein the one or more prediction models are configured to provide an output in the lower dimension space; determine an output of the one or more prediction models in the lower dimension space based on an input provided to the one or more prediction models; and perform a decoding operation on the output to project the output from the lower dimension space to the dimension space of the training dataset. ### Claim 2 (depends on 1) The system of claim 1, wherein, when generating the one or more prediction models based on the encoded dataset, the at least one processor is programmed or configured to: train the one or more prediction models in the lower dimension space based on the encoded dataset. ### Claim 3 (depends on 1) The system of claim 1, wherein, when performing the encoding operation on the training dataset to provide the encoded dataset, the at least one processor is further programmed or configured to: perform a factorization operation based on an optimization problem, wherein the optimization problem is the following: min F , X , W ∑ ( i , t ) ∈ Ω ( Y it - f i T ⁢ x t ) 2 + λ f ⁢ ℛ f ( F ) + ∑ r = 1 k λ x ⁢ 𝒯 AR ( x _ r | ℒ , 𝓌 _ r , η ) + λ w ⁢ ℛ w ( 𝒲 ) , wherein : 𝒯 AR ( x _ | ℒ , ω _ , η ) = 1 2 ⁢ ∑ t = m T ( x t - ∑ l ∈ ℒ ω l ⁢ x t - l ) 2 + η 2 ⁢  x _  2 , and wherein: xt=Σl∈W(l)xt-l+ϵt wherein Yit is the training dataset, i is an i-th observation target, t is a time stamp of each data point of the time series of data points, F is a projection matrix, fiT is a translation to an i-th row of the projection matrix F, X is the encoded dataset having a lower dimension space, xt is a data point of the time series of data points, k is a first dimension of the encoded dataset X, f(F) is a squared Frobenius norm of the projection matrix F, λf is a weight of the projection matrix F, W is an auto-regression model, w(W) is a squared Frobenius norm of the auto-regression model W, λw is a weight of the auto-regression model W, is a score of the auto-regression model W, λx is a weight of the score of the auto-regression model , is a second dimension of the encoded dataset X, w is a prediction model, η is a weight to a vector norm, l is an individual component of the second dimension , T is a total time of the of the time series of data points, and ϵt is an error value associated with xt. ### Claim 4 (depends on 3) The system of claim 3, wherein, when performing the factorization operation, the at least one processor is programmed or configured to: update the projection matrix F using a least square optimization problem; update the transferred low-dimensional space X using a graph-regularized alternating least squares (GRALS); and update the auto-regression model by solving the following: arg min ω _ λ x ⁢ 𝒯 AR ( x _ r | ℒ , ω _ , η ) + λ w ⁢  ω _  2 = arg min ω _ ∑ t = m T ( x t - ∑ l ∈ ℒ ω l ⁢ x t - l ) 2 + λ w λ x ⁢  ω _  2 . ### Claim 5 (depends on 3) The system of claim 3, wherein, when performing the decoding operation on the output to project the output from the lower dimension space to the dimension space of the training dataset, the at least one processor is programmed or configured to: project the output from the lower dimension space to the dimension space of the training dataset using an inverse of the projection matrix F. ### Claim 6 (depends on 1) The system of claim 1, wherein the lower dimension space has a first dimension and a second dimension, and wherein the dimension space of the training dataset has a first dimension and a second dimension, wherein the first dimension of the lower dimension space is less than the first dimension of the training dataset, and wherein the second dimension of the lower dimension space is equal to the second dimension of the training dataset. ### Claim 7 (depends on 6) The system of claim 6, wherein the one or more prediction models comprise a number of prediction models, and wherein the number of prediction models is equal to the first dimension of the lower dimension space. ### Claim 8 A method for generating a machine learning model based on encoded time series data using model reduction techniques, the method comprising: receiving, with at least one processor, a training dataset of a plurality of data instances, wherein each data instance comprises a time series of data points; performing, with the at least one processor, an encoding operation on the training dataset to provide an encoded dataset having a lower dimension space than a dimension space of the training dataset; generating, with the at least one processor, one or more prediction models based on the encoded dataset, wherein the one or more prediction models are configured to provide an output in the lower dimension space; determining, with the at least one processor, an output of the one or more prediction models in the lower dimension space based on an input provided to the one or more prediction models; and performing, with the at least one processor, a decoding operation on the output to project the output from the lower dimension space to the dimension space of the training dataset. ### Claim 9 (depends on 8) The method of claim 8, wherein generating the one or more prediction models based on the encoded dataset comprises: training the one or more prediction models in the lower dimension space based on the encoded dataset. ### Claim 10 (depends on 8) The method of claim 8, wherein performing the encoding operation on the training dataset to provide the encoded dataset comprises: performing a factorization operation based on an optimization problem, wherein the optimization problem is the following: min F , X , W ∑ ( i , t ) ∈ Ω ( Y it - f i T ⁢ x t ) 2 + λ f ⁢ ℛ f ( F ) + ∑ r = 1 k λ x ⁢ 𝒯 AR ( x _ r | ℒ , 𝓌 _ r , η ) + λ w ⁢ ℛ w ( 𝒲 ) , wherein : 𝒯 AR ( x _ | ℒ , ω _ , η ) = 1 2 ⁢ ∑ t = m T ( x t - ∑ l ∈ ℒ ω l ⁢ x t - l ) 2 + η 2 ⁢  x _  2 , and wherein: xt=W(l)xt-l+ϵt wherein Yit is the training dataset, i is an i-th observation target, t is a time stamp of each data point of the time series of data points, F is a projection matrix, fiT is a translation to an i-th row of the projection matrix F, X is the encoded dataset having a lower dimension space, xt is a data point of the time series of data points, k is a first dimension of the encoded dataset X, f(F) is a squared Frobenius norm of the projection matrix F, λf is a weight of the projection matrix F, W is an auto-regression model, w(W) is a squared Frobenius norm of the auto-regression model W, λW is a weight of the auto-regression model W, is a score of the auto-regression model W, λx is a weight of the score of the auto-regression model , is a second dimension of the encoded dataset X, w is a prediction model, η is a weight to a vector norm, l is an individual component of the second dimension , T is a total time of the of the time series of data points, and ϵt is an error value associated with xt. ### Claim 11 (depends on 10) The method of claim 10, wherein performing the factorization operation comprises: updating the projection matrix F using a least square optimization problem; updating the transferred low-dimensional space X using a graph-regularized alternating least squares (GRALS); and updating the auto-regression model by solving the following: arg min ω _ λ x ⁢ 𝒯 AR ( x _ r | ℒ , ω _ , η ) + λ w ⁢  ω _  2 = arg min ω _ ∑ t = m T ( x t - ∑ l ∈ ℒ ω l ⁢ x t - l ) 2 + λ w λ x ⁢  ω _  2 . ### Claim 12 (depends on 10) The method of claim 10, wherein performing the decoding operation on the output to project the output from the lower dimension space to the dimension space of the training dataset comprises: projecting the output from the lower dimension space to the dimension space of the training dataset using an inverse of the projection matrix F. ### Claim 13 (depends on 8) The method of claim 8, wherein the lower dimension space has a first dimension and a second dimension, and wherein the dimension space of the training dataset has a first dimension and a second dimension, wherein the first dimension of the lower dimension space is less than the first dimension of the training dataset, and wherein the second dimension of the lower dimension space is equal to the second dimension of the training dataset. ### Claim 14 (depends on 13) The method of claim 13, wherein the one or more prediction models comprise a number of prediction models, and wherein the number of prediction models is equal to the first dimension of the lower dimension space. ### Claim 15 A computer program product for generating a machine learning model based on encoded time series data using model reduction techniques, the computer program product comprising at least one non-transitory computer-readable medium including one or more instructions that, when executed by at least one processor, cause the at least one processor to: receive a training dataset of a plurality of data instances, wherein each data instance comprises a time series of data points; perform an encoding operation on the training dataset to provide an encoded dataset having a lower dimension space than a dimension space of the training dataset; generate one or more prediction models based on the encoded dataset, wherein the one or more prediction models are configured to provide an output in the lower dimension space; determine an output of the one or more prediction models in the lower dimension space based on an input provided to the one or more prediction models; and perform a decoding operation on the output to project the output from the lower dimension space to the dimension space of the training dataset. ### Claim 16 (depends on 15) The computer program product of claim 15, wherein the one or more instructions that cause the at least one processor to generate the one or more prediction models based on the encoded dataset cause the at least one processor to: train the one or more prediction models in the lower dimension space based on the encoded dataset. ### Claim 17 (depends on 15) The computer program product of claim 15, wherein the one or more instructions that cause the at least one processor to perform the encoding operation on the training dataset to provide the encoded dataset cause the at least one processor to: perform a factorization operation based on an optimization problem, wherein the optimization problem is the following: min F , X , W ∑ ( i , t ) ∈ Ω ( Y it - f i T ⁢ x t ) 2 + λ f ⁢ ℛ f ( F ) + ∑ r = 1 k λ x ⁢ 𝒯 AR ( x _ r | ℒ , 𝓌 _ r , η ) + λ w ⁢ ℛ w ( 𝒲 ) , wherein : 𝒯 AR ( x _ | ℒ , ω _ , η ) = 1 2 ⁢ ∑ t = m T ( x t - ∑ l ∈ ℒ ω l ⁢ x t - l ) 2 + η 2 ⁢  x _  2 , and wherein: xt=W(l)xt-l+ϵt wherein Yit is the training dataset, i is an i-th observation target, t is a time stamp of each data point of the time series of data points, F is a projection matrix, fiT is a translation to an i-th row of the projection matrix F, X is the encoded dataset having a lower dimension space, xt is a data point of the time series of data points, k is a first dimension of the encoded dataset X, f(F) is a squared Frobenius norm of the projection matrix F, λf is a weight of the projection matrix F, W is an auto-regression model, w(W) is a squared Frobenius norm of the auto-regression model W, λw is a weight of the auto-regression model W, is a score of the auto-regression model W, λx is a weight of the score of the auto-regression model , is a second dimension of the encoded dataset X, w is a prediction model, η is a weight to a vector norm, l is an individual component of the second dimension , T is a total time of the of the time series of data points, and ϵt is an error value associated with xt. ### Claim 18 (depends on 17) The computer program product of claim 17, wherein the one or more instructions that cause the at least one processor to perform the factorization operation cause the at least one processor to: update the projection matrix F using a least square optimization problem; update the transferred low-dimensional space X using a graph-regularized alternating least squares (GRALS); and update the auto-regression model by solving the following: arg min ω _ λ x ⁢ 𝒯 AR ( x _ r | ℒ , ω _ , η ) + λ w ⁢  ω _  2 = arg min ω _ ∑ t = m T ( x t - ∑ l ∈ ℒ ω l ⁢ x t - l ) 2 + λ w λ x ⁢  ω _  2 . ### Claim 19 (depends on 17) The computer program product of claim 17, wherein the one or more instructions that cause the at least one processor to perform the decoding operation on the output to project the output from the lower dimension space to the dimension space of the training dataset cause the at least one processor to: project the output from the lower dimension space to the dimension space of the training dataset using an inverse of the projection matrix F. ### Claim 20 (depends on 15) The computer program product of claim 15, wherein the lower dimension space has a first dimension and a second dimension, and wherein the dimension space of the training dataset has a first dimension and a second dimension, wherein the first dimension of the lower dimension space is less than the first dimension of the training dataset, and wherein the second dimension of the lower dimension space is equal to the second dimension of the training dataset.