{
  "id": 225086,
  "title": "Why common GB benchmarks train x- and y- coords separately?",
  "url": "/competitions/indoor-location-navigation/discussion/225086",
  "author_name": "Shuhao Cao",
  "post_date": "2021-03-10T19:36:14.424000",
  "votes": 4,
  "comment_count": 0,
  "views": 0,
  "content": "<p>I thought if we treat the coord as a vector function (\\boldsymbol{x} = [x,y]^{T} )<br>\n$$<br>\n\\frac{d \\boldsymbol{x}}{ dt} = A(t) \\boldsymbol{x} + \\boldsymbol{g}(\\boldsymbol{x}, t)<br>\n$$<br>\nEssentially we should have an autonomous system, with a nonlinear source affected by point of interest, like an external force etc.  Then, the (x)- and (y)- coordinates are highly correlated. A is a matrix that can be approximated by using triangulation.</p>\n<p>For people on top of the LB, do you train your model with ((x,y)) together? or adding a semi-supervised term to enforce the trajectory to be a piecewise linear function.</p>",
  "messages": [
    {
      "id": 1233929,
      "postDate": "2021-03-10T19:36:14.423Z",
      "content": "<p>I thought if we treat the coord as a vector function (\\boldsymbol{x} = [x,y]^{T} )<br>\n$$<br>\n\\frac{d \\boldsymbol{x}}{ dt} = A(t) \\boldsymbol{x} + \\boldsymbol{g}(\\boldsymbol{x}, t)<br>\n$$<br>\nEssentially we should have an autonomous system, with a nonlinear source affected by point of interest, like an external force etc.  Then, the (x)- and (y)- coordinates are highly correlated. A is a matrix that can be approximated by using triangulation.</p>\n<p>For people on top of the LB, do you train your model with ((x,y)) together? or adding a semi-supervised term to enforce the trajectory to be a piecewise linear function.</p>",
      "rawMarkdown": "I thought if we treat the coord as a vector function (\\boldsymbol{x} = [x,y]^{T} )\n$$\n\\frac{d \\boldsymbol{x}}{ dt} = A(t) \\boldsymbol{x} + \\boldsymbol{g}(\\boldsymbol{x}, t)\n$$\nEssentially we should have an autonomous system, with a nonlinear source affected by point of interest, like an external force etc.  Then, the (x)- and (y)- coordinates are highly correlated. A is a matrix that can be approximated by using triangulation.\n\nFor people on top of the LB, do you train your model with ((x,y)) together? or adding a semi-supervised term to enforce the trajectory to be a piecewise linear function.",
      "votes": 4
    }
  ],
  "comments": [],
  "raw_markdown_by_id": {
    "1233929": "I thought if we treat the coord as a vector function (\\boldsymbol{x} = [x,y]^{T} )\n$$\n\\frac{d \\boldsymbol{x}}{ dt} = A(t) \\boldsymbol{x} + \\boldsymbol{g}(\\boldsymbol{x}, t)\n$$\nEssentially we should have an autonomous system, with a nonlinear source affected by point of interest, like an external force etc.  Then, the (x)- and (y)- coordinates are highly correlated. A is a matrix that can be approximated by using triangulation.\n\nFor people on top of the LB, do you train your model with ((x,y)) together? or adding a semi-supervised term to enforce the trajectory to be a piecewise linear function."
  }
}