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Hierarchical clustering
in Python & elsewhere
For @PyDataConf London, June 2015, by Frank Kelly
Data Scientist, Engineer @analyticsseo
@norhustla
Hierarchical Clustering
Theory Practice Visualisation
Origins & definitions
Methods & considerations
Hierachical theory
Metrics & performance
My use case
Python libraries
Example
Static
Interactive
Further ideas
All opinions expressed are my own
Who am I?
All opinions expressed are my own
Clustering is an unsupervised learning problem
"SLINK-Gaussian-data" by Chire - Own work. Licensed under CC BY-SA 3.0 via Wikimedia Commons - https://commons.wikimedia.org/wiki/File:SLINK-Gaussian-data.svg#/media/File:SLINK-Gaussian-data.svg
based on some notion of similarity.
whereby we aim to group subsets of entities with one another
Origins
1930s:
Anthropology&Psychology
http://dienekes.blogspot.co.uk/2013/12/europeans-neolithic-farmers-mesolithic.html
Diverse applications
Attribution: stack overflow, wikipedia, scikit-learn.org, http://www.poolparty.biz/
Two main purposes
Exploratory analysis – standalone tool
(Data mining)
As a component of a supervised learning pipeline (in which distinct classifiers or regression models are trained for each cluster).
(Machine Learning)
Clustering considerations
Partitioning criteria(single / multi level)
SeparationExclusive / non-exclusive
Clustering space(Full-space / sub-space)
Similarity measure(distance / connectivity)
Use case: search keywords
RD
P
P
P
KW
KW
KW
KW
KW
CP
CP
KW
KW
KW
The competition!
KW
KW
CP
CDYou
Opportunity!
CD = Competing domainsCP = Competitor’s pages
RD = Ranking domainP = Your pageKW = Keyword
….x 100,000 !!
Use case: search keywords
KW…so we have found 100,000 new
‘s – now what?
How do we summarise and present these to a client?
Clients’ questions…
• Do search categories in general align with my website structure?
• Which categories of opportunity keywords have the highest search volume, bring the most visitors, revenue etc.?
• Which keywords are not relevant?
Website-like structure
Requirements• Need: visual insights;
structure
• Allow targeting of problem in hand
• May develop into a semi- supervised solution
• High-dimensional and sparse data set
• Values correspond to word frequencies
• Recommended methods include: hierarchical clustering, Kmeans with an appropriate distance measure, topic modelling (LDA, LSI), co-clustering
Options for text clustering?
Hierarchical Clusteringbringing structure
2 types
Agglomerative
Divisive Deterministic algorithms!
Attribution: Wikipedia
Agglomerative
Start with many “singleton” clusters
…Merge 2 at a time
continuously…
Build a hierarchy
Divisive
Start with a huge “macro” cluster
…Iteratively split into 2
groups…
Build a hierarchy
Agglomerative method: Linkage types
• Single (similarity between most similar – based on nearestneighbour - two elements)
• Complete (similarity between most dissimilar two elements)
Attribution: https://www.coursera.org/course/clusteranalysis
Agglomerative method: Linkage types
Average link( avg. of similarity between all inter-cluster pairs )Computationally expensive (Na*Nb)
Trick: Centroid link (similaritybetween centroid of two clusters)
Attribution: https://www.coursera.org/course/clusteranalysis
Ward’s criterion
• Minimise a function: total in-cluster variance
• As defined by, e.g.:
• Once merged, then the SSE will increase (cluster becomes bigger) by:
https://en.wikipedia.org/wiki/Ward's_method
Divisive clustering • Top-down approach
• Criterion to split: Ward’s criterion
• Handling noise: Use a threshold to determine the termination criteria
Attribution: https://www.coursera.org/course/clusteranalysis
Similarity measures
This will certainly influence the shape of the clusters!
• Numerical: Use a variation of the Manhattan distance (e.g. City block, Euclidean)
• Binary: Manhattan, Jaccard co-efficient, Hamming
• Text: Cosine similarity.
Cosine similarityRepresent a document by a bag of terms
Record the frequency of a particular term (word/ topic/ phrase)
If d1 and d2 are two term vectors,
…can thus calculate the similarity between them
Attribution: https://www.coursera.org/course/clusteranalysis
Gather word documents = keyword phrases
Aggregate search words with URL “words”
Text clustering: preparations
• Add features where possibleo I added URL words to my word set
• Stem wordso Choose the right stemmer – too severe can be bad
• Stop wordso NLTK tokenisero Scikit learn TF-IDF tokeniser
• Low frequency cut-offo 2 => words appearing less than twice in whole corpus
• High frequency cut-offo 0.5 => words that appear in more than 50% of documents
• N-gramso Single words, bi-grams, tri-grams
• Beware of foreign languageso Separate datasets if possible
Text preparation
Dimensionality• Get a sparse matrix
o Mostly zeros
• Reduce the number of dimensionso PCAo Spectral clustering
• The “curse” of dimensionality
Results: reduced
dimensions
Results: reduced
dimensions
The
dendrogra
m
Assess the quality of your clusters
• Internal: Purity, completeness & homogeneity
• External: Adjusted Rand index, Normalised Information index
Topic labelling
Hierarchical ClusteringBeyond Python (!?)
Life on the inside: Elasticsearch
• Why not perform pre-processing and clustering inside elasticsearch?
• Document store
• TF-IDF and other• Stop words• Language specific analysers
Elasticsearch - try it ! -
• https://www.elastic.co/
• NoSQL document store• Aggregations and stats• Fast, distributed• Quick to set up
Document storage in ES
Lingo 3G algorithm
• Lingo 3G: Hierarchical clustering off-the-shelf• Built-in part of speech (POS)• User-defined word/synonym/label dictionaries• Built-in stemmer / word inflection database• Multi-lingual support, advanced tuning• Commercial: costs attached
http://download.carrotsearch.com/lingo3g/manual/#section.es
http://project.carrot2.org/algorithms.html
Elasticsearch with clustering – Utopia?
Carrot2’s Lingo3G in action : http://search.carrot2.org/stable/search
Foamtree visualisation example
Visualisation of hierarchical structure possible for large datasets via “lazy loading”
http://get.carrotsearch.com/foamtree/demo/demos/large.html
Limitations of hierarchical clustering• Can’t undo what’s done (divisive method, work on
sub clusters, cannot re-merge). Even true for agglomerative (once merged will never split it again)
• Every split or merge must be refined• Methods may not scale well, checking all possible
pairs, complexity goes high
There are extensions: BIRCH, CURE and CHAMELEON
Thank you!A decent introductory course to clustering;https://www.coursera.org/course/clusteranalysis
Hierarchical (agglomerative) clustering in Python:http://scikit-learn.org/stable/modules/generated/sklearn.cluster.AgglomerativeClustering.html
Recent (ish) relevant Kaggle challenge: https://www.kaggle.com/c/lshtc
Visualisation: http://carrotsearch.com/foamtree-overview
Clustering elsewhere (Lingo, Lingo3G) with Carrot2:http://download.carrotsearch.com/
Elasticsearch: https://www.elastic.co/
Analytics SEO: http://www.analyticsseo.com/
Me: @norhustla / [email protected]
Attribution: http://wynway.com/
Extra slide: Why work inside the database?
1. Sharing data (management of)Support concurrent access by multiple readers and writers
2. Data Model Enforcement Make sure all applications see clean, organised data
3. Scale Work with datasets too large to fit in memory (over a certain size, need specialised algorithms to deal with the data -> bottleneck)The database organises and exposes algorithms for you conveniently
4. Flexibility Use the data in new, unanticipated ways -> anticipate a broad set of ways of accessing the data
