def find_d_min(kv):
X = list(kv[1])
minimum = Vectors.norm(X[0] - X[1], 2) # lets start from somewhere
count = len(X)
for i in xrange(count):
for j in xrange(i + 1, count):
d = Vectors.norm(X[i] - X[j], 2)
if d < minimum:
minimum = d
return minimum
# COMMAND ----------
# MAGIC %md
# MAGIC ** Norm **
# MAGIC
# MAGIC We can calculate the norm of a vector using `Vectors.norm`. The norm calculation is:
# MAGIC
# MAGIC \\[ ||x|| _p = \bigg( \sum_i^n |x_i|^p \bigg)^{1/p} \\]
# MAGIC
# MAGIC
# MAGIC
# MAGIC Sometimes we'll want to normalize our features before training a model. Later on we'll use the `ml` library to perform this normalization using a transformer.
# COMMAND ----------
Vectors.norm(denseVector, 2)
# COMMAND ----------
# MAGIC %md
# MAGIC In Python, `DenseVector` operations are delegated to an underlying NumPy array so we can perform multiplication, addition, division, etc.
# COMMAND ----------
denseVector * denseVector
# COMMAND ----------
5 + denseVector
# COMMAND ----------
# COMMAND ----------
# MAGIC %md
# MAGIC ** Norm **
# MAGIC
# MAGIC We can calculate the norm of a vector using `Vectors.norm`. The norm calculation is:
# MAGIC
# MAGIC \\[ ||x|| _p = \bigg( \sum_i^n |x_i|^p \bigg)^{1/p} \\]
# MAGIC
# MAGIC
# MAGIC
# MAGIC Sometimes we'll want to normalize our features before training a model. Later on we'll use the `ml` library to perform this normalization using a transformer.
# COMMAND ----------
Vectors.norm(denseVector, 2)
# COMMAND ----------
# MAGIC %md
# MAGIC In Python, `DenseVector` operations are delegated to an underlying NumPy array so we can perform multiplication, addition, division, etc.
# COMMAND ----------
denseVector * denseVector
# COMMAND ----------
5 + denseVector
# COMMAND ----------
