# US 10,771,088 B1 · Optimal multi-dimensional data compression by tensor-tensor decompositions tensor > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 10,771,088 B1 - Document ID: US10771088B1 - Status: Granted - Kind: B1 - Application number: 16/289,064 - Filed: 2019-02-28 - Published: 2020-09-03 - Granted: 2020-09-08 - Earliest claimed: 2019-02-28 - Assignees: International Business Machines Corporation; Tufts University; Tel Aviv-Yafo University - Applicants: International Business Machines Corporation; Tufts University; Tel Aviv-Yafo University - Inventors: Lior Horesh; Misha E Kilmer; Haim Avron; Elizabeth Newman - Web page: https://patentgrep.com/patent/US10771088B1 ## CPC - H03M 7/3062: {Compressive sampling or sensing} - H03M 7/3082: {Vector coding (for television signals, see H04N19/94)} - G06F 16/1744: {using compression, e.g. sparse files} - G06F 16/283: {Multi-dimensional databases or data warehouses, e.g. MOLAP or ROLAP} - G06F 17/16: Matrix or vector computation {, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization (matrix transposition G06F7/78)} - H03M 7/3059: {Digital compression and data reduction techniques where the original information is represented by a subset or similar information, e.g. lossy compression} - H03M 7/40: Conversion to or from variable length codes, e.g. Shannon-Fano code, Huffman code, Morse code - H03M 7/55: {Compression Theory, e.g. compression of random number, repeated compression} - H03M: CODING; DECODING; CODE CONVERSION IN GENERAL (using fluidic means F15C4/00; optical analogue/digital converters G02F7/00; coding, decoding or code conversion, specially adapted for particular applications, see the relevant subclasses, e.g. G01D, G01R, G06F, G06T, G09G, G10L, G11B, G11C, H04B, H04L, H04M, H04N; ciphering or deciphering for cryptography or other purposes involving the need for secrecy G09C) - G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N) ## Abstract A tensor decomposition method, system, and computer program product include compressing multi-dimensional data by truncated tensor-tensor decompositions. ## Claims ### Claim 1 A computer-implemented tensor decomposition method, the method comprising: compressing multi-dimensional data by truncated tensor-tensor decompositions, wherein the compressing is performed with respect to at least two orientations of the multi-dimensional data, wherein the compressing is performed via a double sweep by sweeping over the two orientations with a multi-sided process and combining a result of the sweeping, and wherein the result of the sweeping as the compressing is less dependent on orientation than a result of the compressing. ### Claim 2 (depends on 1) The method of claim 1, wherein the multi-dimensional data is represented in a native tensor structure. ### Claim 3 (depends on 2) The method of claim 2, further comprising, for a tensor degree n where n is an integer, performing up to n−1 truncated tensor-tensor singular value decompositions. ### Claim 4 (depends on 2) The method of claim 2, further comprising, for a tensor degree n where n is an integer, performing QR decompositions per tensor permutation. ### Claim 5 (depends on 4) The method of claim 4, wherein the QR decompositions are performed with a predefined tensor-tensor product procedure. ### Claim 6 (depends on 3) The method of claim 3, wherein the tensor-tensor singular value decompositions are performed with a predefined tensor-tensor product procedure. ### Claim 7 (depends on 5) The method of claim 5, wherein the tensor-tensor singular value decompositions are performed with a predefined tensor-tensor product procedure. ### Claim 8 (depends on 1) The method of claim 1, wherein compression properties of the compressing the multi-dimensional data are user-defined parameters. ### Claim 9 (depends on 8) The method of claim 8, wherein truncation of the decompositions is performed per the user-defined parameters. ### Claim 10 (depends on 2) The method of claim 2, further comprising outputting a compact approximated representation of an original input tensor from the native tensor structure per user-defined compression parameters. ### Claim 11 (depends on 1) The method of claim 1, embodied in a cloud-computing environment. ### Claim 12 A computer program product for tensor decomposition, the computer program product comprising a non-transitory computer-readable storage medium having program instructions embodied therewith, the program instructions executable by a computer to cause the computer to perform: compressing multi-dimensional data by truncated tensor-tensor decompositions, wherein the compressing is performed with respect to at least two orientations of the multi-dimensional data, wherein the compressing is performed via a double sweep by sweeping over the two orientations with a multi-sided process and combining a result of the sweeping, and wherein the result of the sweeping as the compressing is less dependent on orientation than a result of the compressing. ### Claim 13 (depends on 12) The computer program product of claim 12, wherein the multi-dimensional data is represented in a native tensor structure. ### Claim 14 (depends on 13) The computer program product of claim 13, further comprising, for a tensor degree n where n is an integer, performing up to n−1 truncated tensor-tensor singular value decompositions. ### Claim 15 (depends on 13) The computer program product of claim 13, further comprising, for a tensor degree n where n is an integer, performing QR decompositions per tensor permutation. ### Claim 16 (depends on 15) The computer program product of claim 15, wherein the QR decompositions are performed with a predefined tensor-tensor product procedure. ### Claim 17 (depends on 14) The computer program product of claim 14, wherein the tensor-tensor singular value decompositions are performed with a predefined tensor-tensor product procedure. ### Claim 18 (depends on 16) The computer program product of claim 16, wherein the tensor-tensor singular value decompositions are performed with a predefined tensor-tensor product procedure. ### Claim 19 A tensor decomposition system, the system comprising: a processor; and a memory, the memory storing instructions to cause the processor to perform: compressing multi-dimensional data by truncated tensor-tensor decompositions, wherein the compressing is performed with respect to at least two orientations of the multi-dimensional data, wherein the compressing is performed via a double sweep by sweeping over the two orientations with a multi-sided process and combining a result of the sweeping, and wherein the result of the sweeping as the compressing is less dependent on orientation than a result of the compressing. ### Claim 20 (depends on 19) The system of claim 19, embodied in a cloud-computing environment.