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function
[]
=
CategoricalScatterplot(
X
,
varargin
)
%
function [] = categoricalscatterplot()
%
%
A replacement for the traditional box and whisker plots provided in
%
MATLAB (command boxplot). The categorical scatter plots additionally
%
shows the data points, which is useful the visualize the underlying
%
distribution (similar to violin plots).
%
%
Required Inputs:
%
X - Input Data - vector or a matrix (Group required if X is a vector)
%
%
Optional Inputs:
%
Group - Grouping variables - vector
%
'Color' - nx3 matrix for n groups or 1x3 vector for all groups
%
'Labels' - A cell string containing labels for all the groups
%
%
Plot parameters (to tweak style):
%
% Scatter parameters:
%
'binWidth': Sets the bin width that is used to stagger points along the
%
xaxis in the scatter plot. Smaller binwidths imply that the points will
%
be close to the central line. Larger values will make the points
%
distributed all over the box.
%
'binWidthRatio': Easier way of setting binwidth. It calulates the
%
binwidth automatically based on the value range of points (Y axis range).
%
'spreadWidth': Sets the extent of the point spread on the x axis.
%
'boxWidth': Sets the width of the boxes.
%
% Plotting styles:
%
'Marker': Marker type - char
%
'MarkerSize': Marker size - num
%
'FillMarker': Logical (true or false / 0 or 1)
%
'BoxColor': char ('r') or rgb vector ([0 0 1])
%
'BoxEdgeColor': char ('r') or rgb vector ([0 0 1])
%
'MedianColor': char ('r') or rgb vector ([0 0 1])
%
'WhiskerColor': char ('r') or rgb vector ([0 0 1])
%
'BoxAlpha': Transparency of the box. num (0 to 1)
%
'BoxLineStyle': char ('-')
%
'MedianLineStyle': char ('-')
%
'WhiskerLineStyle': char ('-')
%
'BoxLineWidth': num (2.0)
%
'MedianLineWidth': num (2.0)
%
'WhiskerLineWidth': num (2.0)
%
%
Dinesh Natesan (AbstractGeek)
%
Last Modified: 11th Dec 2016
%%
Parse Inputs
p
=
inputParser
;
%
Main arguments
addRequired(
p
,
'
X
'
, @(
X
) ismatrix(
X
));
addOptional(
p
,
'
Group
'
, [], @(
X
) isnumeric(
X
)
||
iscellstr(
X
));
addOptional(
p
,
'
Color
'
, [
0
0
0
], @(
x
) all(size(
x
)
==
size(
X
))
||
...
all([size(
X
,
1
),
3
]
==
size(
x
))
||
all(size(
x
)
==
[
1
,
3
]));
addOptional(
p
,
'
Labels
'
,
false
, @(
X
) iscellstr(
X
));
%
Scatter parameters
addParameter(
p
,
'
binWidth
'
,
false
, @(
x
) isnumeric(
x
));
addParameter(
p
,
'
binWidthRatio
'
,
0.05
, @(
x
) isnumeric(
x
));
addParameter(
p
,
'
spreadWidth
'
,
0.6
, @(
x
) isnumeric(
x
));
addParameter(
p
,
'
boxWidth
'
,
0.6
, @(
x
) isnumeric(
x
));
%
Plotting styles
addParameter(
p
,
'
Marker
'
,
'
o
'
, @(
X
) (ischar(
X
)
&&
length(
X
)==
1
));
addParameter(
p
,
'
MarkerSize
'
,
25
, @(
x
) isnumeric(
x
));
addParameter(
p
,
'
FillMarker
'
,
true
, @(
x
) islogical(
x
));
addParameter(
p
,
'
WhiskerLine
'
,
true
, @(
x
) islogical(
x
));
addParameter(
p
,
'
BoxColor
'
, [
0.31
,
0.31
,
0.31
], @(
X
) ...
all(size(
X
)
==
[
1
,
3
])
||
(ischar(
X
)
&&
length(
X
)==
1
));
addParameter(
p
,
'
BoxEdgeColor
'
,
'
none
'
, @(
X
) ...
all(size(
X
)
==
[
1
,
3
])
||
(ischar(
X
)
&&
(length(
X
)==
1
||
length(
X
)==
4
)));
addParameter(
p
,
'
MedianColor
'
,
'
r
'
, @(
X
) ...
all(size(
X
)
==
[
1
,
3
])
||
(ischar(
X
)
&&
length(
X
)==
1
));
addParameter(
p
,
'
WhiskerColor
'
, [
0
0
0
], @(
X
) ...
all(size(
X
)
==
[
1
,
3
])
||
(ischar(
X
)
&&
length(
X
)==
1
));
addParameter(
p
,
'
BoxAlpha
'
,
0.50
, @(
x
) isnumeric(
x
));
addParameter(
p
,
'
BoxLineStyle
'
,
'
-
'
, ...
@(
X
) ischar(
X
)
&&
(length(
X
)==
1
||
length(
X
)==
2
));
addParameter(
p
,
'
MedianLineStyle
'
,
'
-
'
, ...
@(
X
) ischar(
X
)
&&
(length(
X
)==
1
||
length(
X
)==
2
));
addParameter(
p
,
'
WhiskerLineStyle
'
,
'
--
'
, ...
@(
X
) ischar(
X
)
&&
(length(
X
)==
1
||
length(
X
)==
2
));
addParameter(
p
,
'
BoxLineWidth
'
,
1.0
, @(
x
) isnumeric(
x
));
addParameter(
p
,
'
MedianLineWidth
'
,
1.0
, @(
x
) isnumeric(
x
));
addParameter(
p
,
'
WhiskerLineWidth
'
,
1.0
, @(
x
) isnumeric(
x
));
%
Alternate Y axis
addParameter(
p
,
'
YYaxis
'
,
false
, @(
X
) ismatrix(
X
)
||
iscellstr(
X
)
||
ischar(
X
));
%
Parse inputs and unpack structure
parse(
p
,
X
, varargin{
:
});
parsed
=
p
.Results;
Group
=
parsed
.Group;
%
Handle color input
if
all(size(
parsed
.Color)==[
1
,
3
])
if
isempty(
Group
)
Color
=
repmat({
parsed
.Color}, size(
X
,
1
), size(
X
,
2
));
else
Color
=
repmat(
parsed
.Color, length(
X
),
1
);
end
else
Color
=
parsed
.Color;
end
%
Handle fill input
if
all(size(
parsed
.FillMarker)
==
[
1
,
1
])
FillMarker
=
repmat(
parsed
.FillMarker,size(
X
,
1
),size(
X
,
2
));
else
FillMarker
=
parsed
.FillMarker;
end
if
(size(
X
,
2
)
==
1
)
||
(size(
X
,
1
)
==
1
)
%%
Convert the groups into a cell array
%
Ensure group exists
if
isempty(
Group
)
error(
'
Group input required if X input is a vector
'
);
end
if
ischar(
Group
)
Group
=
cellstr(
Group
);
end
%
Make it into column vectors
if
(size(
X
,
1
)
==
1
)
X
=
X
'
;
end
%
handle groups
[
group_names
,
~
,
group_ind
]
=
unique(
Group
);
groups
=
unique(
group_ind
);
%
Sort data into a cell array
data
=
cell(length(
groups
),
2
);
new_data
=
cell(length(
groups
),
2
);
plot_vars
=
cell(length(
groups
),
2
);
Xmax
=
-
999
;
Xmin
=
999
;
for
i
=
1
:
length(
groups
)
data{
i
,
1
}
=
X(
group_ind
==
groups(
i
));
data{
i
,
2
}
=
group_ind(
group_ind
==
groups(
i
));
plot_vars{
i
,
1
}
=
Color(
group_ind
==
groups(
i
),
:
);
plot_vars{
i
,
2
}
=
FillMarker(
group_ind
==
groups(
i
),
:
);
if
(
Xmin
>
floor(min(data{
i
,
1
})))
Xmin
=
floor(min(data{
i
,
1
}));
end
if
(
Xmax
<
ceil(max(data{
i
,
1
})))
Xmax
=
ceil(max(data{
i
,
1
}));
end
end
else
%%
Convert the matrix into cell array (after removing nans)
group_names
=
Group
;
groups
=
1
:
size(
X
,
2
);
%
Sort data into a cell array
data
=
cell(length(
groups
),
2
);
new_data
=
cell(length(
groups
),
2
);
plot_vars
=
cell(length(
groups
),
2
);
Xmax
=
-
999
;
Xmin
=
999
;
for
i
=
1
:
length(
groups
)
data{
i
,
1
}
=
X(~isnan(X(
:
,
i
)),
i
);
data{
i
,
2
}
=
i
*
ones(size(data{
i
,
1
}));
plot_vars{
i
,
1
}
=
cell2mat(Color(~isnan(X(
:
,
i
)),
i
));
plot_vars{
i
,
2
}
=
FillMarker(~isnan(X(
:
,
i
)),
i
);
if
(
Xmin
>
floor(min(data{
i
,
1
})))
Xmin
=
floor(min(data{
i
,
1
}));
end
if
(
Xmax
<
ceil(max(data{
i
,
1
})))
Xmax
=
ceil(max(data{
i
,
1
}));
end
end
end
%
Get binWidth ratio is only ratio is provided
if
(islogical(
parsed
.binWidth)
&&
~
parsed
.binWidth)
binWidth
=
parsed
.binWidthRatio
*
round(
Xmax
-
Xmin
);
else
binWidth
=
parsed
.binWidth;
end
%%
Discretize points in a group
for
i
=
1
:
length(
groups
)
Xtemp
=
data{
i
,
1
};
Ytemp
=
data{
i
,
2
};
[
counts
,
~
,
bins
]
=
histcounts(
Xtemp
,
'
BinWidth
'
,
binWidth
);
inds
=
find(
counts
~=
0
);
counts
=
counts(
inds
);
for
j
=
1
:
length(
inds
)
width
=
parsed
.spreadWidth
*
(
1
-
exp(-
0.1
*
(counts(
j
)-
1
)));
xpoints
=
linspace(-
width
/
2
,
width
/
2
, counts(
j
))
+
i
;
Ytemp(
bins
==
inds(
j
))
=
xpoints
;
end
new_data{
i
,
1
}
=
Xtemp
;
new_data{
i
,
2
}
=
Ytemp
;
end
%%
Plot the data beautifully
boxWidth
=
parsed
.boxWidth;
hold
on
;
for
i
=
1
:
length(
groups
)
if
parsed
.YYaxis
if
(any(ismember(
parsed
.YYaxis,groups(
i
))))
yyaxis
right
;
else
yyaxis
left
;
end
end
imp_quantiles
=
quantile(new_data{
i
,
1
}, [
0.25
,
0.5
,
0.75
]);
IQR
=
imp_quantiles(
3
)
-
imp_quantiles(
1
);
whisker
=
[imp_quantiles(
1
)
-
1.5
*
IQR
, ...
imp_quantiles(
3
)
+
1.5
*
IQR
];
%
Draw box
patch([
i
-
boxWidth
/
2
,
i
-
boxWidth
/
2
,
i
+
boxWidth
/
2
,
i
+
boxWidth
/
2
]
'
,...
[imp_quantiles(
3
), imp_quantiles(
1
), imp_quantiles(
1
), imp_quantiles(
3
)]
'
,...
parsed
.BoxColor,
'
FaceAlpha
'
,
parsed
.BoxAlpha,...
'
EdgeColor
'
,
parsed
.BoxEdgeColor, ...
'
LineStyle
'
,
parsed
.BoxLineStyle,
'
LineWidth
'
,
parsed
.BoxLineWidth);
%
Draw points
scatter(new_data{
i
,
2
}(plot_vars{
i
,
2
}), new_data{
i
,
1
}(plot_vars{
i
,
2
}),...
parsed
.MarkerSize, plot_vars{
i
,
1
}(plot_vars{
i
,
2
},
:
),
'
filled
'
);
scatter(new_data{
i
,
2
}(~plot_vars{
i
,
2
}), new_data{
i
,
1
}(~plot_vars{
i
,
2
}),...
parsed
.MarkerSize, plot_vars{
i
,
1
}(~plot_vars{
i
,
2
},
:
));
%
Draw median
plot([
i
-
boxWidth
/
2
,
i
+
boxWidth
/
2
], ...
[imp_quantiles(
2
), imp_quantiles(
2
)], ...
'
LineStyle
'
,
parsed
.MedianLineStyle, ...
'
Color
'
,
parsed
.MedianColor,...
'
LineWidth
'
,
parsed
.MedianLineWidth,...
'
Marker
'
,
'
none
'
);
%
Draw Q + 1.5 IQR
if
any(data{
i
,
1
}>whisker(
2
))
%
Outlier present
plot([
i
-
boxWidth
/
5
,
i
+
boxWidth
/
5
], ...
[whisker(
2
), whisker(
2
)], ...
'
LineStyle
'
,
'
-
'
, ...
'
Color
'
,
parsed
.WhiskerColor,...
'
LineWidth
'
,
parsed
.WhiskerLineWidth,...
'
Marker
'
,
'
none
'
);
if
parsed
.WhiskerLine
%
Draw top whiskers
plot([
i
,
i
], [whisker(
2
), imp_quantiles(
3
)],...
'
LineStyle
'
,
parsed
.WhiskerLineStyle, ...
'
Color
'
,
parsed
.WhiskerColor,...
'
LineWidth
'
,
parsed
.WhiskerLineWidth,...
'
Marker
'
,
'
none
'
);
end
else
%
No outliers
temp
=
sortrows([whisker(
2
)
-
data{
i
,
1
}, (
1
:
length(data{
i
,
1
}))
'
],
1
);
closest_point
=
temp(find(temp(
:
,
1
)
>=
0
,
1
,
'
first
'
),
2
);
plot([
i
-
boxWidth
/
5
,
i
+
boxWidth
/
5
], ...
[new_data{
i
,
1
}(
closest_point
), new_data{
i
,
1
}(
closest_point
)], ...
'
LineStyle
'
,
'
-
'
, ...
'
Color
'
,
parsed
.WhiskerColor,...
'
LineWidth
'
,
parsed
.WhiskerLineWidth,...
'
Marker
'
,
'
none
'
);
if
parsed
.WhiskerLine
%
Draw top whiskers
plot([
i
,
i
], [new_data{
i
,
1
}(
closest_point
), imp_quantiles(
3
)],...
'
LineStyle
'
,
parsed
.WhiskerLineStyle, ...
'
Color
'
,
parsed
.WhiskerColor,...
'
LineWidth
'
,
parsed
.WhiskerLineWidth,...
'
Marker
'
,
'
none
'
);
end
end
%
Draw Q - 1.5 IQR
if
any(data{
i
,
1
}<whisker(
1
))
%
Outlier present
plot([
i
-
boxWidth
/
5
,
i
+
boxWidth
/
5
], ...
[whisker(
1
), whisker(
1
)], ...
'
LineStyle
'
,
'
-
'
, ...
'
Color
'
,
parsed
.WhiskerColor,...
'
LineWidth
'
,
parsed
.WhiskerLineWidth,...
'
Marker
'
,
'
none
'
);
if
parsed
.WhiskerLine
%
Draw top whiskers
plot([
i
,
i
], [whisker(
1
), imp_quantiles(
3
)],...
'
LineStyle
'
,
parsed
.WhiskerLineStyle, ...
'
Color
'
,
parsed
.WhiskerColor,...
'
LineWidth
'
,
parsed
.WhiskerLineWidth,...
'
Marker
'
,
'
none
'
);
end
else
%
No outliers
temp
=
sortrows([data{
i
,
1
}
-
whisker(
1
), (
1
:
length(data{
i
,
1
}))
'
],
1
);
closest_point
=
temp(find(temp(
:
,
1
)
>=
0
,
1
,
'
first
'
),
2
);
plot([
i
-
boxWidth
/
5
,
i
+
boxWidth
/
5
], ...
[new_data{
i
,
1
}(
closest_point
), new_data{
i
,
1
}(
closest_point
)], ...
'
LineStyle
'
,
'
-
'
, ...
'
Color
'
,
parsed
.WhiskerColor,...
'
LineWidth
'
,
parsed
.WhiskerLineWidth,...
'
Marker
'
,
'
none
'
);
if
parsed
.WhiskerLine
%
Draw bottom whiskers
plot([
i
,
i
], [new_data{
i
,
1
}(
closest_point
), imp_quantiles(
1
)],...
'
LineStyle
'
,
parsed
.WhiskerLineStyle, ...
'
Color
'
,
parsed
.WhiskerColor,...
'
LineWidth
'
,
parsed
.WhiskerLineWidth,...
'
Marker
'
,
'
none
'
);
end
end
end
ax
=
gca
;
ax.XTick
=
1
:
length(
groups
);
if
(islogical(
parsed
.Labels)
&&
~
parsed
.Labels)
ax.XTickLabel
=
group_names
;
else
ax.XTickLabel
=
parsed
.Labels;
end
end
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