Segmentacion - Departamento de...
Transcript of Segmentacion - Departamento de...
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Segmentacion
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Segmentacion
• Tecnica no supervisada que intenta particionar (segmentar) a los individuos (casos) de modo tal que los grupos formados sean heterogeneos entre si y homogeneos en si (dentro de los grupos).
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Objetivos
• Obtener una representación “compacta” de los datos, para: – Generar una clasificación – Describir los datos – Definir “prototipos” de interes. – Resumir la infprmación. – Achicar el tamaño del problema.
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Sin Clusterización
X1
X2
Prototipo (centro) erroneo
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Con Clusterización
X1
X2 Prototipo 1 Prototipo 2
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Ejemplo: 4 clusters o 9 clusters ?
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Complejidad del problema
Para K=3 y N=30 P(N,K)= 2 * 1014
Cantidad de objetos
Cantidad de clusters
Cantidad de segmentaciones posibles
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Espacios Métricos
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Ejemplo de Espacio Métrico
M
x
y
z
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Métricas • Datos continuos: Distancia Euclidea
• Datos categóricos: Distancia Manhattan
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Distancia Chi Cuadrado
Distancia
Proporción promedio marginal de la variable j
Las J proporciones de la observación X
Las J proporciones de la observación Y
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Dos tipos de segmentacion
• Metodos jerarquicos – Ascendentes o Aglomerativos – Decendentes o de Difusión
• Metodos no jerarquicos o de particion – K medias – PAM
• Métodos mixtos
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Ejemplo Distancias
Sitio o localización
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Definiciones Objetos
Dimensión del
espacio Cantidad de grupos
Partición
Disjuntos
Totalidad
No hay grupos vacios
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Métodos Jerarquicos
• Producen un “continuo” de particiones jerarquicas facilmente visualizable mediante un dendograma.
• Dependen de dos nociones de similaridad : – Entre objetos. – Entre clusters.
• No necesitan definir una cantidad de grupos “a priori”.
hclust
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Métodos Jerárquicos (HC)
Descendente Ascendente
Cluster 1 Cluster 2
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Jerarquia de particiones Objetos
Particiones
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Método Ascendente
INICIO
1 IND. = 1 CLUST.
MATRIZ DIST.
UNIR 2 CLUSTERS
1 CLUSTER ?
SI
NO
CORTAR EL DENDOGRAMA
FIN
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Matriz de Distancias C1 … Cl Ci Cj … Cn
C1 0 … Cl 0 D(Cl,Ci) D(Cl,Cj)
Ci D(Cl,Ci)
0 D(Ci,Cj)
Cj D(Cl,Ci)
… D(Cl,Cj)
D(Ci,Cj)
0 … D(Cl,Cn)
… Cn 0
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Recalculo de la Matriz de Distancias
C1 … Cl Ci,j … Cn
C1 0 … Cl 0 D(Cl,Ci,j) Ci,j D(Cl,Ci,j)
D(Cl,Ci,j)
0 D(Cn,Ci,j)
… Cn 0
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Distancia entre clusters: Single linkage
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Distancia entre clusters: Complete Linkage
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Distancia entre clusters: Centroid
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Distancia entre clusters: Average
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Otras distancias entre clusters
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Desventajas de HC
• Costoso en grandes bases de datos. • Es lento.
Ventajas de HC • Sugiere el número de clusters. • Establece una jerarquía de clusters. • El dendograma permite la visualización
del proceso.
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Métodos de Partición o Combinatorios
• Producen grupos (clusters) mediante el agrupamiento de objetos situados en lugares cercanos del espacio al que petenecen.
• Dependen de la existencia de coordenadas de los objetos.
• Requieren definir la cantidad de grupos. • Requieren definir una función de perdida.
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Criterio del ECM Dado un conjunto de objetos queremos agruparlos en La suma de errores al cuadrado se define como:
Donde
es una matriz cc
si
es la matriz de prototipos o centroides
es la media muestral
con
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Otros criterios
Diametro del Cluster
Star index
Radio del Cluster
Cut index
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K medias kmeans
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K-Medias (Paso 0)
9 Objetos
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K-Medias (Paso 1)
Dos centros tomados al azar
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K-Medias (Paso 2)
Clusters determinados por los centros
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K-Medias (Paso 3)
Nuevos centros calculados
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K-Medias (Paso 4)
Nuevos clusters determinados por los centros
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K-Medias (Paso 5)
Nuevos centros calculados
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Desventajas de K-medias • Converge a un optimo local (no global). • La clusterización final depende de los
centros iniciales. • Requiere fijar el número de clusters
previamente.
Ventajas de K-medias • Es rápido. • Válido con grandes bases de datos.
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Métodos Mixtos
• Consisten en aplicar: – Primero: Un método combinatorio (k-medias)
con una cantidad de clusters grande (K=200). – Segundo: Un método jerarquico al resultado
del método combinatorio. Es decir, se unen los clusters hallados en el primer método.
Así, los clusters finales consisten en la unión de
los objetos pertenecientes a los clusters unidos en el segundo método.
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Ejemplo 1: Proteínas
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Dendograma 2 Clusters
3 Clusters
4 Clusters 5 Clusters
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Mapa de Europa
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K medias Vs. HC con K=5
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Mean Shift
• Técnica basada en KDE • Se originó como un método tipo “hill-
climbing” para “Bump Hunting” • Permite captar clusters con “formas”
complejas • Es (relativamente) lento • Obedece a un enfoque no-paramétrico
ms
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La Idea: Mean Shift como método de Bump Hunting
Media Punto inicial
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Desplazamiento hacia la media
Media Punto inicial
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Convergencia
Moda de la densidad
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Calculando el Mean Shift
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Clustering con Mean Shift
Se sigue (con MS) cada objeto hasta su convergencia
Cluster 1
Cluster 2
Todos los objetos que convergen al mismo punto pertenecen al mismo cluster
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Propiedades
• Convergencia asegurada para todos los objetos
• Cantidad de clusters dependiente de la ventana en la KDE
Ventana grande -> 1 Cluster
Ventana chica -> 2 Clusters
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Un Ejemplo Simple (Iris Data)
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Usando una Ventana Grande (ventana = 50% rango)
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Using unaa Ventana Chica (ventana = 35% rango)
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Un poco mas chica (20%) …
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Determinación del número de clusters
• Criterio de Clusterización Cúbico de Sarle (CCC).
• Estadístico GAP. • Estadístico Psuedo-F (Calinkski-
Harabasz).
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Validación de los clusters • Criterios externos: Comparan la
clusterización con algúna segmentación previa de referencia.
• Criterios internos: Analizan la significatividad de los clusters solo considerando los datos usados en la clusterización.
• Criterios relativos: Comparan la clusterización con otras resultantes de segmentaciones alternativas.
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El Estadístico Pseudo F (Calinkski-Harabasz)
Media general
Media cluster i
K clusters
Cantidad de Objetos
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Estadístico GAP
Distancias WITHIN observadas
Distancias WITHIN esperadas bajo H0 (K=1)
Cantidad optima de clusters
clusGap
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Feature Spaces Complejos
• El espacio de covariables puede ser tan complejo como se quiera.
• Se pueden definir nuevos features que capten comportamientos diferenciales del fenómeno.
• Es fundamental la ponderación que se da a cada feature.
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Automatic and Extensive Cropland Classification Based on
Satellite Data
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Why Automatic Crop Classification ?
• Crops in Argentina: ~ 34.000.000 has, ~ 400.000 fields
• Screening of unknown regions • Global yield estimation and tax evasion
control • Valuable information for agro-related and
agro-insurance companies • Precise georeference of croplands • Global crop area assesment and yield
estimation
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Some Specific Classification Goals
• To assess crop share (relative proportions) in a large area (no georeference available of the fields)
• To estimate yield of an specific crop/season in a large area (no georeference available of the fields)
• To detect and to georeference fields with specific crops (no georeference available of the fields)
• To detect kind-of-crop info from specific fields (available georeference of the fields)
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Kind of Crops to be Detected
• Arable land – Summer crops
• Soybean • Corn
– Winter crops • Wheat • Sunflower
• Non arable land
Very easy Easy
Hard
Hard
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Remote Sensing Instruments
LON LAT
NIR Band
Red Band
…
… … … … … … … … … …
Spatial variables Added attributes
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●
ID Tas 3293
Estado 18
Has 8
Danio 3.4
Lat −31.8573
Lon −61.7189
Fec Sin 2012−12−19 10:10:00
ID Sin 876
Fec Siem 2012−10−30 16:33:00
Main Available Remote Sensing Instruments
• MODIS (MODerate Imaging Spectrometer) – 250m X 250m – 2 images per day – 2 satellites (Terra and Aqua) – 36 spectral bands
• LANDSAT 8 – 15m X 15m (interpolated)
– 1 image every 16 days – 1 satellite – 11 bands
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Vegetation Indices (VIs)
• CI • EVI • ENVI • NDVI
Source: http://www.markelowitz.com
Wavelength
-1 ≤ NDVI ≤ 1 0 ≤ NDVI ≤ 1 For plants In general
Ref
lect
ed In
tens
ity
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How is a Typical Phenological Crop Cycle ?
Nov Jan Mar May Jul
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Start of season
Time
End of season Maturity
of the plant
Daily (2) NDVI measurements
Soybean cycle
Terra measurement Aqua measurement
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Double-Crop Phenological Cycle
May Jul Sep Nov Jan Mar May
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Terra measurement Aqua measurement
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Landsat: Big Data ! Argentina China
Landsat tile = 185km X 185 km ~
17.500px X 14.500 px
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Cropland Detection Using Landsat 8
Unsupervised Approach
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−59.10 −59.09 −59.08 −59.07 −59.06
−37.73
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(2014-10-16)
Point of interest
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1 3 5 7 9 11 13 15 17 19 21 23 25
0.2
0.4
0.6
0.8
NDVI distribution
NDV
I
−59.10 −59.09 −59.08 −59.07 −59.06−37.73
−37.72
−37.71
−37.70
NDVI clustering
5
10
15
20
25
●
Single Image Clustering based on X + Y + NDVI
−59.10 −59.09 −59.08 −59.07 −59.06
−37.73
−37.72
−37.71
−37.70
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Feature space
25 Clusters
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The Feature Space X + Y + NDVI
Field of interest
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Field Detected
●
−59.10 −59.09 −59.08 −59.07 −59.06
−37.73
−37.72
−37.71
−37.70
5
10
15
20
25
Clusters of similar NDVI values Polygon induced by the method
Actual georeferenced field
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−59.10 −59.09 −59.08 −59.07 −59.06
−37.73
−37.72
−37.71
−37.70
0.2
0.3
0.4
0.5
0.6
0.7
0.8
−59.10 −59.09 −59.08 −59.07 −59.06
−37.73
−37.72
−37.71
−37.70
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Time series of Landsat images
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0.1
0.2
0.3
0.4
0.5
0.6
NDVI evoliution (LAndsat)
Time
NDVI
Sep 14/2014 Nov 17/2014 Jan 20/2015 Mar 25/2015 May 28/2015 Jul 31/2015 Oct 03/2015
●
●
●
●●
●
●
●●
●
●
−59.10 −59.09 −59.08 −59.07 −59.06
−37.73
−37.72
−37.71
−37.70
0.12
0.13
0.14
0.15
0.16
Cloudy image Freshly sowed field
Crop close to maturity
Whole image NDVI evolution
Cloudy Clear sky
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Working With a Temporal Ensemble of Images
Time
ND
VI
●
Pixel 2
NDVI evolution
NDVIpx = µpx + αpx * Time+ βpx * Time2
Pixel-wise modelling
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Added Attributes Based on Statistical Modelling of NDVI Temporal Evolution
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
NDVIpx = µpx + αpx * Time + βpx * Time2
^ ^ ^
Pixel-wise modelling
False color image
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Clustering Based on Modelled NDVI Temporal Evolution
−37.75 −37.74 −37.73 −37.72 −37.71 −37.70 −37.69
−59.0
9−59.0
8−59.0
7−59.0
6
5
10
15
20
25
Time
ND
VI 25 NDVI
estimated evolutions 25 clusters
2 4 6 8 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
x
1:11
Field of interest
Feature space
X +Y +µ + α + β