<s>
t-distributed	B-Algorithm
stochastic	I-Algorithm
neighbor	I-Algorithm
embedding	I-Algorithm
(	O
t-SNE	B-Algorithm
)	O
is	O
a	O
statistical	O
method	O
for	O
visualizing	O
high-dimensional	O
data	O
by	O
giving	O
each	O
datapoint	O
a	O
location	O
in	O
a	O
two	O
or	O
three-dimensional	O
map	O
.	O
</s>
<s>
It	O
is	O
a	O
nonlinear	B-Algorithm
dimensionality	I-Algorithm
reduction	I-Algorithm
technique	O
for	O
embedding	O
high-dimensional	O
data	O
for	O
visualization	O
in	O
a	O
low-dimensional	O
space	O
of	O
two	O
or	O
three	O
dimensions	O
.	O
</s>
<s>
The	O
t-SNE	B-Algorithm
algorithm	O
comprises	O
two	O
main	O
stages	O
.	O
</s>
<s>
First	O
,	O
t-SNE	B-Algorithm
constructs	O
a	O
probability	O
distribution	O
over	O
pairs	O
of	O
high-dimensional	O
objects	O
in	O
such	O
a	O
way	O
that	O
similar	O
objects	O
are	O
assigned	O
a	O
higher	O
probability	O
while	O
dissimilar	O
points	O
are	O
assigned	O
a	O
lower	O
probability	O
.	O
</s>
<s>
Second	O
,	O
t-SNE	B-Algorithm
defines	O
a	O
similar	O
probability	O
distribution	O
over	O
the	O
points	O
in	O
the	O
low-dimensional	O
map	O
,	O
and	O
it	O
minimizes	O
the	O
Kullback	O
–	O
Leibler	O
divergence	O
(	O
KL	O
divergence	O
)	O
between	O
the	O
two	O
distributions	O
with	O
respect	O
to	O
the	O
locations	O
of	O
the	O
points	O
in	O
the	O
map	O
.	O
</s>
<s>
t-SNE	B-Algorithm
has	O
been	O
used	O
for	O
visualization	O
in	O
a	O
wide	O
range	O
of	O
applications	O
,	O
including	O
genomics	O
,	O
computer	O
security	O
research	O
,	O
natural	B-Language
language	I-Language
processing	I-Language
,	O
music	O
analysis	O
,	O
cancer	O
research	O
,	O
bioinformatics	O
,	O
geological	O
domain	O
interpretation	O
,	O
and	O
biomedical	O
signal	O
processing	O
.	O
</s>
<s>
While	O
t-SNE	B-Algorithm
plots	O
often	O
seem	O
to	O
display	O
clusters	B-Algorithm
,	O
the	O
visual	O
clusters	B-Algorithm
can	O
be	O
influenced	O
strongly	O
by	O
the	O
chosen	O
parameterization	O
and	O
therefore	O
a	O
good	O
understanding	O
of	O
the	O
parameters	O
for	O
t-SNE	B-Algorithm
is	O
necessary	O
.	O
</s>
<s>
Such	O
"	O
clusters	B-Algorithm
"	O
can	O
be	O
shown	O
to	O
even	O
appear	O
in	O
non-clustered	O
data	O
,	O
and	O
thus	O
may	O
be	O
false	O
findings	O
.	O
</s>
<s>
It	O
has	O
been	O
demonstrated	O
that	O
t-SNE	B-Algorithm
is	O
often	O
able	O
to	O
recover	O
well-separated	O
clusters	B-Algorithm
,	O
and	O
with	O
special	O
parameter	O
choices	O
,	O
approximates	O
a	O
simple	O
form	O
of	O
spectral	B-Algorithm
clustering	I-Algorithm
.	O
</s>
<s>
Given	O
a	O
set	O
of	O
high-dimensional	O
objects	O
,	O
t-SNE	B-Algorithm
first	O
computes	O
probabilities	O
that	O
are	O
proportional	O
to	O
the	O
similarity	O
of	O
objects	O
and	O
,	O
as	O
follows	O
.	O
</s>
<s>
Since	O
the	O
Gaussian	O
kernel	O
uses	O
the	O
Euclidean	O
distance	O
,	O
it	O
is	O
affected	O
by	O
the	O
curse	B-Algorithm
of	I-Algorithm
dimensionality	I-Algorithm
,	O
and	O
in	O
high	O
dimensional	O
data	O
when	O
distances	O
lose	O
the	O
ability	O
to	O
discriminate	O
,	O
the	O
become	O
too	O
similar	O
(	O
asymptotically	O
,	O
they	O
would	O
converge	O
to	O
a	O
constant	O
)	O
.	O
</s>
<s>
It	O
has	O
been	O
proposed	O
to	O
adjust	O
the	O
distances	O
with	O
a	O
power	O
transform	O
,	O
based	O
on	O
the	O
intrinsic	B-Algorithm
dimension	I-Algorithm
of	O
each	O
point	O
,	O
to	O
alleviate	O
this	O
.	O
</s>
<s>
t-SNE	B-Algorithm
aims	O
to	O
learn	O
a	O
-dimensional	O
map	O
(	O
with	O
and	O
typically	O
chosen	O
as	O
2	O
or	O
3	O
)	O
that	O
reflects	O
the	O
similarities	O
as	O
well	O
as	O
possible	O
.	O
</s>
<s>
The	O
minimization	O
of	O
the	O
Kullback	O
–	O
Leibler	O
divergence	O
with	O
respect	O
to	O
the	O
points	O
is	O
performed	O
using	O
gradient	B-Algorithm
descent	I-Algorithm
.	O
</s>
<s>
The	O
R	B-Language
package	O
implements	O
t-SNE	B-Algorithm
in	O
R	B-Language
.	O
</s>
<s>
scikit-learn	B-Application
,	O
a	O
popular	O
machine	O
learning	O
library	O
in	O
Python	O
implements	O
t-SNE	B-Algorithm
with	O
both	O
exact	O
solutions	O
and	O
the	O
Barnes-Hut	O
approximation	O
.	O
</s>
