# US 12,602,584 B2 · Method and apparatus for learning equivariant and invariant representation for rotation of image based on graph convolutional network > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 12,602,584 B2 - Document ID: US12602584B2 - Status: Granted - Kind: B2 - Application number: 17/973,408 - Filed: 2022-10-25 - Published: 2023-11-16 - Granted: 2026-04-14 - Earliest claimed: 2022-05-10 - Assignees: Korea Advanced Institute of Science and Technology - Applicants: Korea Advanced Institute of Science and Technology - Inventors: Hyun Myung; Sungwon Hwang - Web page: https://patentgrep.com/patent/US12602584B2 ## CPC - G06N 3/0464: Convolutional networks [CNN, ConvNet] - G06N 3/08: Learning methods - G06N 3/084: Backpropagation, e.g. using gradient descent - G06V 10/82: using neural networks - G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS - G06V: IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING ## Abstract Disclosed are a method and apparatus for learning equivariant and invariant representations for rotation of an image based on a graph convolutional network. The method of learning an equivariant and invariant representation for rotation of an image based on a graph convolutional network performed by a computer device includes learning an equivariant representation for rotation of an image by using a self-weighted nearest neighbors graph convolutional network (SWN-GCN); and finally obtaining the equivariant representation for the rotation of the image obtained from the self-weighted nearest neighbors graph convolutional network as an invariant representation of the rotation of the image by using permutation invariance of global average pooling (GAP). ## Claims ### Claim 1 A method of learning an equivariant and invariant representation for rotation of an image based on a graph convolutional network performed by a computer device, the method comprising: learning the equivariant representation for rotation of the image by using a self-weighted nearest neighbors graph convolutional network (SWN-GCN); and finally obtaining the equivariant representation for the rotation of the image obtained from the self-weighted nearest neighbors graph convolutional network as the invariant representation of the rotation of the image by using permutation invariance of global average pooling (GAP). ### Claim 2 (depends on 1) The method of claim 1, wherein the self-weighted nearest neighbors graph convolutional network (SWN-GCN) learns the equivariant representation of the rotation of the image based on a scheme of applying the graph convolutional network to a graphed image. ### Claim 3 (depends on 1) The method of claim 1, wherein the learning of the equivariant representation includes: representing an image as a graph having a vertex by using the self-weighted nearest neighbors graph convolutional network (SWN-GCN); obtaining an adjacency matrix representing adjacency between two vertices; and constructing a unit layer of an equivariant network by using unit propagation of the self-weighted nearest neighbors graph convolutional network (SWN-GCN) when a propagation set of the vertex is given. ### Claim 4 (depends on 3) The method of claim 3, wherein the unit propagation of the self-weighted nearest neighbors graph convolutional network (SWN-GCN) includes a self-weighted message passing network (SMP) and a shared-weight graph propagation network (SGP). ### Claim 5 (depends on 1) The method of claim 1, wherein the final obtaining of the equivariant representation includes: representing a set of equivariant vertices for rotation of the image in an invariant representation by using the global average pooling (GAP). ### Claim 6 (depends on 1) The method of claim 1, wherein the final obtaining of the equivariant representation includes: performing final classification with a fully connected layer non-linearized with ReLU. ### Claim 7 (depends on 1) The method of claim 1, wherein the equivariant and invariant representation for the rotation of the image is obtained by utilizing a structural feature of the self-weighted nearest neighbors graph convolutional network (SWN-GCN) without data augmentation. ### Claim 8 An apparatus for learning an equivariant and invariant representation for rotation of an image based on a graph convolutional network, the apparatus comprising: a rotation equipvarient representation unit configured to learn the equivariant representation for the rotation of the image by using a self-weighted nearest neighbors graph convolutional network (SWN-GCN); and a rotation invariant representation unit configured to finally obtain the equivariant representation for the rotation of the image obtained from the self-weighted nearest neighbors graph convolutional network as the invariant representation of the rotation of the image by using permutation invariance of global average pooling (GAP). ### Claim 9 (depends on 8) The apparatus of claim 8, wherein the self-weighted nearest neighbors graph convolutional network (SWN-GCN) learns the equivariant representation of the rotation of the image based on a scheme of applying the graph convolutional network to a graphed image. ### Claim 10 (depends on 8) The apparatus of claim 8, wherein the rotation equipvarient representation unit is configured to represent an image as a graph having a vertex by using the self-weighted nearest neighbors graph convolutional network (SWN-GCN), obtain an adjacency matrix representing adjacency between two vertices, and construct a unit layer of an equivariant network by using unit propagation of the self-weighted nearest neighbors graph convolutional network (SWN-GCN) when a propagation set of the vertex is given. ### Claim 11 (depends on 10) The apparatus of claim 10, wherein the unit propagation of the self-weighted nearest neighbors graph convolutional network (SWN-GCN) includes a self-weighted message passing network (SMP) and a shared-weight graph propagation network (SGP). ### Claim 12 (depends on 8) The apparatus of claim 8, wherein the rotation invariant representation unit is configured to: represent a set of equivariant vertices for the rotation of the image in the invariant representation by using the global average pooling (GAP). ### Claim 13 (depends on 8) The apparatus of claim 8, wherein the rotation invariant representation unit is configured to: perform final classification with a fully connected layer non-linearized with ReLU. ### Claim 14 (depends on 8) The apparatus of claim 8, wherein the equivariant and invariant representation for the rotation of the image is obtained by utilizing a structural feature of the self-weighted nearest neighbors graph convolutional network (SWN-GCN) without data augmentation.