added weighted correlation as the interestingness metric for heatmap

* bug fix heatmap export plot code
* minor typo `default_display` in FAQ.rst

doc/source/guide/FAQ.rst

@@ -24,7 +24,7 @@ How do I access all of the current recommendations shown in my widget?
 
 How do I set the Lux widgets to show up on default? 
 """"""""""""""""""""""""""""""""""""""""""""""""""""""""
-  By default, we show the Pandas display and users can use the toggle button to switch to the Lux display. The `set_default_display` function allows users to change the setting so that the Lux widget is set as the default view for future operations on the specified dataframe: 
+  By default, we show the Pandas display and users can use the toggle button to switch to the Lux display. The `default_display` property allows users to change the setting so that the Lux widget is set as the default view for future operations on the specified dataframe: 
 
     .. code-block:: python
     

lux/executor/PandasExecutor.py

@@ -253,10 +253,11 @@ def execute_2D_binning(vis: Vis):
             result = result.rename(columns={x_attr.attribute:"z"})
             result = result[result["z"]!=0]
 
-            result.loc[:,"xBinStart"] = result["xBin"].apply(lambda x: x.left)
+            # convert type to facilitate weighted correlation interestingess calculation
+            result.loc[:,"xBinStart"] = result["xBin"].apply(lambda x: x.left).astype('float') 
             result.loc[:,"xBinEnd"] = result["xBin"].apply(lambda x: x.right)
 
-            result.loc[:,"yBinStart"] = result["yBin"].apply(lambda x: x.left)
+            result.loc[:,"yBinStart"] = result["yBin"].apply(lambda x: x.left).astype('float')
             result.loc[:,"yBinEnd"] = result["yBin"].apply(lambda x: x.right)
 
             vis._vis_data = result.drop(columns=["xBin","yBin"])

lux/interestingness/interestingness.py

@@ -67,7 +67,7 @@ def interestingness(vis:Vis ,ldf:LuxDataFrame) -> int:
 	# Scatter Plot
 	elif (n_dim == 0 and n_msr == 2):
 		if (vis.mark=="heatmap"):
-			return 0.3 #TODO: Need better interestingness metric for binned scatterplots (heatmaps)
+			return weighted_correlation(vis.data["xBinStart"],vis.data["yBinStart"],vis.data["z"])
 		if (v_size<2): return -1 
 		if (n_filter==1):
 			v_filter_size = get_filtered_size(filter_specs, vis.data)
@@ -132,6 +132,16 @@ def skewness(v):
 	from scipy.stats import skew
 	return skew(v)
 
+def weighted_avg(x, w):
+    return np.average(x,weights=w)
+
+def weighted_cov(x, y, w):
+    return np.sum(w * (x - weighted_avg(x, w)) * (y - weighted_avg(y, w))) / np.sum(w)
+
+def weighted_correlation(x, y, w):
+    # Based on https://en.wikipedia.org/wiki/Pearson_correlation_coefficient#Weighted_correlation_coefficient
+    return weighted_cov(x, y, w) / np.sqrt(weighted_cov(x, x, w) * weighted_cov(y, y, w))
+
 def deviation_from_overall(vis:Vis, ldf:LuxDataFrame, filter_specs:list, msr_attribute:str) -> int:
 	"""
 	Difference in bar chart/histogram shape from overall chart

lux/vislib/altair/Heatmap.py

@@ -43,10 +43,10 @@ def initialize_chart(self):
 		# self.code += f"visData = pd.DataFrame({str(self.data.to_dict(orient='records'))})\n"
 		self.code += f"visData = pd.DataFrame({str(self.data.to_dict())})\n"
 		self.code += f'''
-		chart = alt.Chart(self.data).mark_rect().encode(
-			x=alt.X('xBinStart', type='quantitative', axis=alt.Axis(title=x_attr.attribute), bin = alt.BinParams(binned=True)),
+		chart = alt.Chart(visData).mark_rect().encode(
+			x=alt.X('xBinStart', type='quantitative', axis=alt.Axis(title='{x_attr.attribute}'), bin = alt.BinParams(binned=True)),
 			x2=alt.X2('xBinEnd'),
-			y=alt.Y('yBinStart', type='quantitative', axis=alt.Axis(title=y_attr.attribute), bin = alt.BinParams(binned=True)),
+			y=alt.Y('yBinStart', type='quantitative', axis=alt.Axis(title='{y_attr.attribute}'), bin = alt.BinParams(binned=True)),
 			y2=alt.Y2('yBinEnd'),
 			#opacity = alt.Opacity('z',type='quantitative',scale=alt.Scale(type="log"))
 			color = alt.Color('z',type='quantitative', scale=alt.Scale(scheme='blues',type="log"),legend=None)