Online Manifold Regularization by Dual Ascending Procedure

<table>Error rates of <svg height="12.2" id="M469" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 16.487499 12.2" width="16.487499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.912)"><path d="M433 423l8 39h39q84 0 134.5 -49t50.5 -128q0 -116 -76 -205q-77 -90 -168 -90q-74 0 -104 65q-56 -65 -144 -65q-73 0 -112 49t-39 127q0 68 36 135q36 68 94 108q77 53 173 53h32l-10 -39q-56 0 -112 -47q-45 -39 -71 -106.5t-26 -142.5q0 -39 17 -68t43 -29t51.5 24.5
t37.5 65.5q-10 44 -10 84q0 62 27 115q29 53 80 53q52 0 52 -71q0 -67 -74 -179q-2 -14 -2 -18q0 -34 19 -54t47 -20q33 0 62 44q29 43 45 99.5t16 103.5q0 146 -116 146z" id="x1D74E"></path></g>
<g transform="matrix(.012,-0,0,-.012,11.738,12)"><path d="M324 430l-26 -36l-112 -4l-55 -265q-13 -66 7 -66q13 0 44.5 20t50.5 40l17 -24q-38 -40 -85.5 -73.5t-87.5 -33.5q-50 0 -21 138l55 262h-80l-2 8l25 34h66l25 99l78 63l10 -9l-37 -153h128z" id="x1D461"></path></g>
</svg> on the whole two moons dataset. The error rate of <svg height="12.2" id="M470" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 16.487499 12.2" width="16.487499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.912)"><path d="M433 423l8 39h39q84 0 134.5 -49t50.5 -128q0 -116 -76 -205q-77 -90 -168 -90q-74 0 -104 65q-56 -65 -144 -65q-73 0 -112 49t-39 127q0 68 36 135q36 68 94 108q77 53 173 53h32l-10 -39q-56 0 -112 -47q-45 -39 -71 -106.5t-26 -142.5q0 -39 17 -68t43 -29t51.5 24.5
t37.5 65.5q-10 44 -10 84q0 62 27 115q29 53 80 53q52 0 52 -71q0 -67 -74 -179q-2 -14 -2 -18q0 -34 19 -54t47 -20q33 0 62 44q29 43 45 99.5t16 103.5q0 146 -116 146z" id="x1D74E"></path></g>
<g transform="matrix(.012,-0,0,-.012,11.738,12)"><path d="M324 430l-26 -36l-112 -4l-55 -265q-13 -66 7 -66q13 0 44.5 20t50.5 40l17 -24q-38 -40 -85.5 -73.5t-87.5 -33.5q-50 0 -21 138l55 262h-80l-2 8l25 34h66l25 99l78 63l10 -9l-37 -153h128z" id="x1D461"></path></g>
</svg> has a downward trend, but it is not always decreasing along the online MR process.</table>

Mathematical Problems in Engineering

Online Manifold Regularization by Dual Ascending Procedure

Figure 9