Github user derrickburns commented on a diff in the pull request:
https://github.com/apache/spark/pull/2634#discussion_r23430407
--- Diff:
mllib/src/main/scala/org/apache/spark/mllib/clustering/metrics/FastEuclideanOps.scala
---
@@ -0,0 +1,77 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.spark.mllib.clustering.metrics
+
+import breeze.linalg.{ DenseVector => BDV, SparseVector => BSV, Vector =>
BV }
+
+import org.apache.spark.mllib.base._
+import org.apache.spark.mllib.linalg.{ SparseVector, DenseVector, Vector }
+import org.apache.spark.mllib.base.{ Centroid, FPoint, PointOps, Infinity,
Zero }
+
+class FastEUPoint(raw: BV[Double], weight: Double) extends FPoint(raw,
weight) {
+ val norm = if (weight == Zero) Zero else raw.dot(raw) / (weight * weight)
--- End diff --
@mengxr
I spent some time thinking about clustering sparse data. I realized that
there may be a need to embed the sparse data into lower dimensional
spaces. Then, I realized that one of the Bregman divergences (i.e. the
generalized symmetrized Bregman divergence), also embeds data into a
different space before clustering. This led me to the conclusion that
embedding the data into a convenient space just prior to clustering is a
very useful generic feature. Adding it was trivial. See the README on my
GitHub project for details.
I implemented two generic embeddings: 1) a sparse to dense embedding that
maps points isomorphically and 2) random indexing
<https://www.sics.se/~mange/papers/RI_intro.pdf> that maps high dimensional
data into lower dimension in a way that preserves similarity per the
Johnson-Lindenstrauss
lemma <http://en.wikipedia.org/wiki/Johnson%E2%80%93Lindenstrauss_lemma>. I
also recoded the embedding that I did for a generalized symmetrized KL
divergence to use the new embedding design.
I think that with these improvements one can check the "clusterer supports
sparse data" feature box in a practical sense.
I am about to being performance testing of the randoming indexing embedding
on large volumes of high dimensional sparse data.
Please take a look at the new PointOps trait definition.
On Mon, Jan 19, 2015 at 5:36 PM, Derrick Burns <derrickrbu...@gmail.com>
wrote:
> For the squared Euclidean distance case, weights would naturally start at
> 1.0 for each input point, so that a cluster with 100 points would have
> weight 100.0.
>
> However, for the KL divergence where the points are derived from
> frequencies, the initial weight could be the sum of the frequencies. This
> puts the points on the simplex without having to perform the division.
>
> Sent from my iPhone
>
> On Jan 19, 2015, at 5:02 PM, Xiangrui Meng <notificati...@github.com>
> wrote:
>
> In
>
mllib/src/main/scala/org/apache/spark/mllib/clustering/metrics/FastEuclideanOps.scala
> <https://github.com/apache/spark/pull/2634#discussion-diff-23197316>:
>
> > + * distributed under the License is distributed on an "AS IS" BASIS,
> > + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
implied.
> > + * See the License for the specific language governing permissions and
> > + * limitations under the License.
> > + */
> > +
> > +package org.apache.spark.mllib.clustering.metrics
> > +
> > +import breeze.linalg.{ DenseVector => BDV, SparseVector => BSV, Vector
=> BV }
> > +
> > +import org.apache.spark.mllib.base._
> > +import org.apache.spark.mllib.linalg.{ SparseVector, DenseVector,
Vector }
> > +import org.apache.spark.mllib.base.{ Centroid, FPoint, PointOps,
Infinity, Zero }
> > +
> > +class FastEUPoint(raw: BV[Double], weight: Double) extends FPoint(raw,
weight) {
> > + val norm = if (weight == Zero) Zero else raw.dot(raw) / (weight *
weight)
>
> Could you elaborate more about the benefit of using homogeneous
> coordinates? It should be at least documented that what "weight" stands
for
> here. If a cluster have 100 points, do you assign its center with weight
> 100? If so, how to compute the distance between this center and an input
> point?
>
> â
> Reply to this email directly or view it on GitHub
> <https://github.com/apache/spark/pull/2634/files#r23197316>.
>
>
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