Download Spatial Analysis Clustering

Spatial Analysis
Clustering
Petteri Nurmi
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Henkilön nimi / Esityksen nimi
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28.3.2014
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Questions
• What kind of preprocessing steps are useful for GPS
measurements?
• What different classes of spatial clustering exist?
• What is the difference between partitioning
algorithms and density-based clustering?
• What is a place?
• How places can be detected?
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Spatial Analysis
• Process of inspecting geographical data with the aim
of extracting useful information
• Spatial data analysis process
• Preprocessing
‒ Cleaning the data, perform transformations (if needed)
• Analysis
‒ Exploratory: data is searched for models that describe it
well without clear hypothesis
‒ Confirmatory: hypotheses about data are tested empirically
• Post-processing
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Measurement Noise
• Location measurements are inherently noisy
• Reference point geometry
• Atmospheric effects
• Multipath effects
• Measurement errors (clock or reference point errors)
• See Lecture IV
• Preprocessing attempts to reduce the effect of noise
before data is being analyzed further
• Data cleaning: ensures good quality of measurements
• Check the validity of the data
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Preprocessing - GPS
• GPS requires at least 4 satellites for estimating
position (4 unknowns: 3D position + time offset)
• GPS uncertainty affected by range error and satellite
geometry
• Dilution of Precision gives an estimate of the influence
of satellite geometry
• Horizontal Dilution of Precision (HDOP) most important
for applications
• Cold/warm start can cause outliers in measurements
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Preprocessing – GPS Example
RAW GPS measurements
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Preprocessing – GPS Example
Points with satellites < 4 removed
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Preprocessing – GPS Example
Points with satellites < 4 and HDOP > 6.0
removed
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Preprocessing –
Removing Extreme Values
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Spatial Clustering
• Clustering refers to the process of grouping similar
objects into classes
• Points within same cluster more similar to each other
than to those in other clusters
• Spatial clustering refers to clustering that is applied
on data with a geographical component
• Identifying similar geographical areas, e.g., in terms of
crime rate or another statistic
• Merging of regions with similar weather patterns
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Spatial Clustering
• Four main categories of algorithms
• Partitioning methods (e.g., K-means, K-medoids)
• Hierarchical methods (e.g., BIRCH)
• Density-based methods (e.g., DBScan)
• Grid-based methods (e.g., CLIQUE)
• “Optimal” technique depends on various factors
• Application goal
• Trade-off between clustering quality and speed
• Characteristics and dimensionality of data
• Amount of noise in data
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Spatial Clustering Partitioning Algorithms
• Partition data into k clusters so that total deviation of
points from their cluster center is minimized
• Parameter k determines the number of clusters, given
usually beforehand
• Various ways to measure total deviation:
• Squared distance (K-Means)
• Posterior of data (Gaussian Mixture Models)
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Partitioning Algorithms –
K-Means
• One of the best-known clustering algorithms
• Iterative relocation algorithm, optimizes squared loss
• mi corresponds to the center of a cluster, Ci is the set of
points allocated to cluster i
• Basic structure:
• Initialization: generate k cluster centers according to some
criterion (e.g., random selection from data)
• During each iteration:
‒ Allocate each point to the cluster that is closest
‒ Revise cluster centers based on the points that are assigned
to the cluster
‒ Repeat until no change in values
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K-Means
• Algorithm guaranteed to find a local optimum of the
objective function (squared loss)
• Sensitive to the initial choice of cluster centers
• Clustering typically repeated multiple times with
different initial values and solution with smallest total
deviation used
• Initial values can be determined, e.g., using
• Random sampling
• Select fraction of data, perform clustering on that, use
resulting clusters as initial values
• Data spectroscopy: analyze spectral characteristics of
data values to determine a good initial guess
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K-Means Example
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Stopped after 2 iterations
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K-Means Example
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Partitioning Algorithms –
Probabilistic Clustering
• Generative: data assumed to be generated
according to some model
• Parameters of the model unknown and need to be
estimated from data
• Returns a probability distribution over the parameter
values
• Two possible assignments of points to cluster
• Hard: each point belongs exactly to one cluster
• Soft: allow multiple (or all) clusters to “contribute” to the
generation of the point
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Partitioning Algorithms –
Mixture Models
• Mixture Models provide a flexible and generic
approach to probabilistic clustering
• Data generated by k random variables, each variable Xi
characterized by probability density function fi(θi)
• For each point i, a hidden and unobservable variable ci
determines the cluster where i belongs to
• The clusters are called mixture components
• Probability of a point is a (convex) combination of the
mixture component densities
•
defines the weight or
contribution of a component
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Partitioning Algorithms –
Gaussian Mixture Models
• Mixture model where mixture components are
assumed to have a Gaussian distribution
• Mean μi determines the center of the cluster
• Covariance matrix ∑i determines shape of the cluster
‒ Assuming Euclidean distances:
‒ Shape is circle if variance of all dimensions is equal
‒ Shape is an ellipse aligned with coordinate axes when
covariance matrix is diagonal
‒ Shape is a tilted ellipse when full covariance matrix used
• K-means can be understood as a Gaussian mixture
model where variance is equal
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Partitioning Algorithms –
Gaussian Mixture Models
• Cluster parameters can be determined using the
expectation maximization (EM) algorithm
• Iterative algorithm for finding optimal parameter values in
models with latent (i.e., unobservable) variables
• Consists of two steps (E and M) which are iterated until
solution converges
• Algorithm outline:
• Initialization: draw initial parameter values
• E-step: compute expectation of log-likelihood using current
estimates
• M-step: compute parameters that maximize the expected
log-likelihood computed in the E-step
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Partitioning Algorithms –
Infinite Mixture Models
• A generalization of mixture models where number of
mixture models is assumed infinite (but countable)
• Example: Chinese restaurant process
• Customers arrive to a restaurant with an infinite number
of circular tables, each having infinite capacity
• As new customer arrives (s)he selects the table to sit
‒ Either one of the partially occupied tables
‒ Or completely new table
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Partitioning Algorithms –
K-Medoids
• Partitioning algorithm that represents a cluster using
the most centrally located measurement
• Instead of updating all centers during an iteration,
typically updates only a single medoid
• How to determine the new medoid?
• How to evaluate effectiveness of clustering?
• Covered in more detail during Lecture VIII
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Density-Based Algorithms
• Class of algorithms that represent clusters as dense
regions of objects
• In contrast to partitioning algorithms, can derive clusters
of arbitrary shape
• Areas with low-density of objects are considered noise
• Basic concepts
• Epsilon neighborhood: collection of points that are
within distance Eps from a point
• Dense neighborhood: Epsilon neighborhood that
contains at least MinPts points
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Density-Based Algorithms –
Radius-Based Clustering
• Predecessor to density-based clustering
• Cluster all points with distance Eps of each other to the
same cluster
• MinPts or some other criterion can be used to prune the
resulting clusters
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Density-Based Algorithms –
DBScan
• A point that has at least MinPts within its Epsilon
neighborhood is called a core object
• Object can only belong to a cluster if it is within the
Epsilon neighborhood of at least one core object
• Core object o within Epsilon neighborhood of another
core object p must belong to the same cluster as p
• Non-core object belonging to the Epsilon neighborhood
of some core objects must belong to the same cluster
as one of these core objects
• Non-core objects which do not belong to the Epsilon
neighborhood of any core objects are noise
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Density-Based Algorithms –
DBScan
Non-core object
Core object
Outlier / noise
Core object
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Clusters A,B and C can be merged
since they share a core object
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Density-Based Algorithms –
DBScan
• Algorithm that recursively merges Epsilon
neighborhoods together to identify dense regions
• Let c be a core object, within the Epsilon neighborhood
of c considered as seed points
• Cluster expanded with (previously unallocated) points
that are within the Epsilon neighborhood of a seed point
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Density-Based Clustering –
Example
DBScan: MinPts = 20, Eps = 0.102
DBScan: MinPts = 20, Eps = 0.124
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Density-Based Algorithms –
DJCluster
• Variant of DBScan where cluster expansion
performed iteratively instead of recursively
• Better suited for large datasets
• Basic idea:
• Find Epsilon neighborhood of a point
• Assign all points within the neighborhood into cluster
• Check if cluster shares a core point with any of the
previous clusters
‒ If so, clusters can be merged
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Notion of Place
• Location systems tend to provide information in
coordinate form (absolute or relative)
• People refer to locations using semantic (or
symbolic) descriptions
• Descriptions for the same place can vary between
different people
• Place
• Representation of location that is consistent with the
way people communicate location information
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Notion of Place
Monastery
Petra, Jordan
Church
Royal
Tombs
Treasury
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Hotel
Ticket
Office
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Notion of Place
• Definitions for place originate from the field of
humanistic geography
• Roots in phenomenology and philosophy
‒ Especially philosophy of Martin Heidegger
• Places entities that relate physical locations with
human experiences and meanings
• Relph: places physical locations that are linked with
meanings and activities
• Tuan: places are spaces (i.e., physical locations) that
are embodied with meanings
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Notion of Place
• The meanings attributed to places vary:
• Activities: swimming hall, movie theater, gym
• Social: friend’s home, regular place to meet friends
• Generic: library, grocery store, train station
• Multiple meanings can be attributed to a place
• Relate to different activities (and times) at the place
• Places can be perceived as public or private
• Note: space can be public even if place is private!
• Depends on the activity, time of day etc.
• Influences preferences regarding location disclosure
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Why place matters?
• Personalized information delivery
• E.g., associate notes/to-do lists with places
• Select advertisements or other information to provide
‒ E.g., provide train or bus schedules
‒ Depends on stability of information and familiarity of place
• Awareness cue
• Places often a cue of activity and availability
‒ Automated status messages, e.g., in phone contact list
• Support user studies
• Differentiating meaningful situations in analysis phase
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Detecting places
• Locations correlate strongly with activities
• “What are you doing?” often answered with
location during mobile phone calls
• People assign activity-related labels to places
• Places correlate with time
• Humans spend the majority of time in a few places
• Probability of labeling a place increases with time
‒ But traffic stops (traffic jams, traffic lights) seldom
labeled
èPlaces can be detected from location traces
• Activity information can help (if available)
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Place Identification
• Place Identification = the process of
detecting places from data
• A data analysis step with four steps
•
•
•
•
Preparation: clean data, transform data
Preprocessing: making data ready for analysis
Analysis: performing the actual analysis
Post-processing: refining the results
• Additionally a labeling step
• Assign semantics with the detected places
• Can take place before or after analysis
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Labeling
• Common choice is to prompt the user to
label a place after it has been detected
• Alternative to label first and learn the places
automatically based on the labels
• Some labels can be assigned automatically
• Geographic databases can be used to mine
information about the type of building
• Time information can be used to identify home and
workplace
• Different modalities: text, photo, photo + text
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Detecting Places –
Overview
• Most place detection algorithms operate on
coordinate data
• Pruning: remove measurements that are unlikely to be
meaningful
• Clustering: apply spatial clustering on the data
• Post-processing: determine which clusters are likely to
correspond to meaningful places
‒ Spatial criteria: matching against Geo-databases,
considering size of clusters etc.
‒ Temporal criteria: requiring a minimum stay duration
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Detecting Places –
Velocity Pruning
• Measurements where the user is moving are unlikely
to correspond to significant places
• Velocity can be used to prune measurements and
clustering applied on remaining data
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Place Detection –
Further Topics
• Coordinate algorithms unable to separate between
different places within the same indoor space
• Radio fingerprinting based place detection uses stability
of signal environment to detect places
• Current state-of-the-art in mobile phone based place
detection
• Performance decreases in areas with limited signal
environment
• Hybrid algorithms
• Combine coordinate-based techniques with radio
fingerprinting based place detection
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Fingerprint-based Place
Detection
• Basic idea is to compare similarity of fingerprint
information over time
• If radio environment sufficiently similar, over a time
window t, the user is assumed to be a in a place
• Many possible ways to measure similarity of RF
environments
• Rank Correlation (NearMe)
• Extended Tanimoto (SensLoc)
• Normalized Euclidean distance
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Fingerprint-based Place
Detection - Example
Mac
address:
1
2
A. -82 -74
B. -84 -79
C. -40 -40
• Consider the data on the left:
• ExtTanimoto(A,B) = (-82 * -84 + -74 * -79) / (82^2 +
74^2 + 84^2 + 79^2 - (-82 * -84 + -74 * -79)) = 0.9977
• ExtTanimoto(A,C) = 0.68
• A and B from same location with high probability, C
likely from a different location
• If we get successive similar measurements for, e.g.,
5 minutes or 10 minutes, we are assumed to be in a
place
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Case Study: Zero Interaction
Authentication (ZIA)
B
• Fingerprint similarity generic tool that has many
other applications, as an example we consider ZIA
• Assume device B unlocks automatically whenever
device A is in close proximity (zero user interaction)
• Car locks
• “Token”-based authentication for laptops / terminals
A
• Susceptible to relay attacks where another device
pretends to be A
• If A and B compare their WiFi environments, the
similarity of these environments can be used to
resist against relay attacks
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Summary
• Spatial analysis refers to the process of inspecting
geographical data
• Preprocessing: cleaning and preparing data for analysis
• Analysis: exploratory or confirmatory
• Post-processing: validating, pruning results
• Spatial clustering
• Grouping of similar (spatial) objects together
• Partitioning algorithms: divide data “optimally” to
clusters
• Density-based algorithms: identify dense spatial regions
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Summary
• Place
• Representation of location that is consistent with the
way people communicate location information
• Semantic / symbolic
• Place detection
• Process of identifying places from location
measurements
• On coordinate data, can be solved using spatial
clustering and temporal + spatial pruning
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Literature
•
Ester, M.; Kriegel, H.-P.; Sander, J. & Xu, X., A Density-Based Algorithm for
Discovering Clusters in Large Spatial Databases with Noise, Proceedings of the
International Conference on Knowledge Discovery and Data Mining (KDD), AAAI,
1996, 226 - 231
•
Sander, J.; Ester, M.; Kriegel, H.-P. & Xu, X., Density-Based Clustering in Spatial
Databases: The Algorithm GDBSCAN and Its Applications, Data Mining and
Knowledge Discovery, 1998, 2, 169-194
•
Zhou, C.; Frankowski, D.; Ludford, P.; Shekhar, S. & Terveen, L., Discovering
Personally Meaningful Places: An Interactive Clustering Approach, ACM
Transactions on Information Systems, 2007, 25, 12
•
Ashbrook, D. & Starner, T., Learning significant locations and predicting user
movement with GPS, Proceedings of the 6th International Symposium on Wearable
Computers (ISWC), IEEE, 2002, 101- 108
•
Kang, J.; Welbourne, W.; Stewart, B. & Borriello, G., Extracting places from traces
of locations, Proceedings of the 2nd ACM international workshop on Wireless
mobile applications and services on WLAN hotspots (WMASH), ACM Press, 2004,
110 - 118
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Literature
•
Liao, L.; Fox, D. & Kautz, H., Extracting Places and Activities from GPS Traces
Using Hierarchical Conditional Random Fields, International Journal of Robotics
Research, 2007, 26, 119-134
•
Marmasse, N. & Schmandt, C., A user-centered location model, Personal and
Ubiquitous Computing, 2002, 6, 318 - 321
•
Nurmi, P. & Bhattacharya, S., Identifying Meaningful Places: The Nonparametric
Way, Proceedings of the 6th International Conference on Pervasive Computing
(Pervasive), Springer, 2008, 5013, 111-127
•
Tuan, Y.-F., Space and Place: The Perspective of Experience, University of
Minnesota Press, 2001
•
Relph, E., Place and Placelessness, Pion Books, 1976
•
Han, J.; Kambar, M. & Tung, A. K. H., Spatial Clustering Methods in Data Mining: A
Survey, Geographic Data Mining and Knowledge Discovery, Taylor & Francis, 2001
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Literature
•
Kim, D. H.; Kim, Y.; Estrin, D. & Srivastava, M. B. SensLoc: sensing everyday
places and paths using less energy, Proceedings of the 8th ACM Conference on
Embedded Networked Sensor Systems (SenSys), ACM, 2010, 43-56
•
Hightower, J.; Consolvo, S.; LaMarca, A.; Smith, I. & Hughes, J.
Learning and Recognizing the Places We Go, Proceedings of the 7th International
Conference on Ubiquitous Computing (UBICOMP), Springer-Verlag, 2005, 3660,
159-176
•
Truong, H. T. T.; Gao, X.; Shrestha, B.; Saxena, N.; Asokan, N. & Nurmi, P.
Comparing and Fusing Different Sensor Modalities for Relay Attack Resistance in
Zero-Interaction Authentication, Proceedings of the 12th International Conference
on Pervasive Computing and Communications (PerCom), 2014
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