A simple way for Nearest to operate on multilevel data

Questions
1

I need some help with simplification of a function. [Nearest can be very handy, but does not have level specification. My problem is simple. I have the following data consisting of integers and binary vectors:

dat = Table[{RandomInteger[100], RandomInteger[1, 15]}, {10}];
dat // Column

Out[] = 
{{21, {0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1}},
{15, {1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0}},
{55, {0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0}},
{79, {1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1}},
{55, {1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1}}}

I also have a test vector:

tst = RandomInteger[1, 15]
Out[] = {1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0}

I need to find a vector in my data nearest to test and return it and its corresponding integer. If several solutions exist I take the first one. I came up with this

f[dat_, tst_] := First[Extract[dat, Position[#, First[Nearest[#, tst]]] &[dat[[All, 2]]]]]
f[dat, tst]
Out[] = {15, {1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0}}

Which works but feels rather convoluted. Can anyone suggest an alternative solution?](Nearest—Wolfram Documentation)

2

Nearest is eactly what you want.

In[43]:= f =
Nearest [#[[2]] -> # & /@ {{21, {0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0,
1, 1, 1}}, {15, {1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0,
0}}, {55, {0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0,
0}}, {79, {1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1,
1}}, {55, {1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1}}}]

In[46]:= f[{1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0}, 1][[1]]

Out[46]= {15, {1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0}}
3

You can have Nearest give you the index of the data that matches the test.

In[59]:= dat = Table[{RandomInteger[100], RandomInteger[1, 15]}, {10}];

In[64]:= test = RandomInteger[1, 15]

In[69]:= nf = Nearest[dat[[All, 2]] -> Automatic] ;

In[68]:= dat[[nf[test]]]

Out[68]= {{61, {1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0}}}
4

Thank you, Paritosh and Jeremy, - this is exactly what I needed!