Objetivos. Obtener una representación compacta de los datos, para:

(1)

(2)

Segmentacion

•  Tecnica no supervisada que intenta

particionar (segmentar) a los individuos (casos) de modo tal que los grupos

formados sean heterogeneos entre si y

(3)

Objetivos

•  Obtener una representación “compacta” de los datos, para:

– Generar una clasificación – Describir los datos

– Definir “prototipos” de interes. – Resumir la infprmación.

(4)

Sin Clusterización

X₁ X₂

(5)

Con Clusterización

X₁ X₂

(6)

(7)

Complejidad del problema

Para K=3 y N=30 P(N,K)= 2 * 1014 Cantidad de objetos Cantidad de clusters Cantidad de segmentaciones posibles

(8)

(9)

Ejemplo de Espacio Métrico

M

x

y z

(10)

Métricas

•  Datos continuos: Distancia Euclidea

(11)

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

(12)

Dos tipos de segmentacion

•  Metodos jerarquicos

– Ascendentes o Aglomerativos – Decendentes o de Difusión

•  Metodos no jerarquicos o de particion

– K medias – PAM

(13)

Ejemplo

(14)

Definiciones

Objetos Dimensión del espacio Cantidad de grupos Partición Disjuntos Totalidad

(15)

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”.

(16)

Métodos Jerárquicos (HC)

Descendente Ascendente

(17)

Jerarquia de particiones

Objetos Particiones

(18)

Método

Ascendente

INICIO 1 IND. = 1 CLUST. MATRIZ DIST. UNIR 2 CLUSTERS 1 CLUSTER ? SI NO CORTAR EL DENDOGRAMA FIN

(19)

Matriz de Distancias

C₁ … C_l C_i C_j … C_n C₁ 0 … C_l 0 D(C_l,C_i) D(C_l,C_j) C_i D(C_l,C_i) 0 D(C_i,C_j) C_j D(C_l,C_i) … D(C_l,C_j) D(C_i,C_j) 0 … D(C_l,C_n) … C_n 0

(20)

Recalculo de la Matriz de

Distancias

C₁ … C_l C_i,j … C_n C₁ 0 … C_l 0 D(C_l,C_i,j)

C_i,j D(C_l,C_i,j) D(C_l,C_i,j) 0 D(C_n,C_i,j) …

(21)

Distancia entre clusters: Single

linkage

(22)

Distancia entre clusters:

Complete Linkage

(23)

(24)

Distancia entre clusters:

Average

(25)

(26)

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.

(27)

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.

(28)

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

(29)

Otros criterios

Diametro del Cluster Star index

Radio del Cluster Cut index

(30)

(31)

K-Medias (Paso 0)

(32)

K-Medias (Paso 1)

(33)

K-Medias (Paso 2)

Clusters determinados por los centros

(34)

K-Medias (Paso 3)

(35)

K-Medias (Paso 4)

Nuevos clusters

(36)

K-Medias (Paso 5)

(37)

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.

(38)

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

(39)

(40)

Dendograma

2 Clusters

3 Clusters

(41)

(42)

(43)

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

(44)

La Idea: Mean Shift como

método de Bump Hunting

Media Punto

(45)

Desplazamiento hacia la media

Media Punto

(46)

Convergencia

Moda de la densidad

(47)

Calculando el

Mean Shift

(48)

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

(49)

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

(50)

(51)

Usando una Ventana Grande

(ventana = 50% rango)

(52)

Using unaa Ventana Chica

(ventana = 35% rango)

(53)

(54)

Determinación del número de

clusters

•  Criterio de Clusterización Cúbico de

Sarle (CCC).

•  Estadístico GAP.

•  Estadístico Psuedo-F

(55)

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.

(56)

El Estadístico Pseudo F

(Calinkski-Harabasz)

Media general Media cluster i K clusters Cantidad de Objetos

(57)

Estadístico GAP

Distancias WITHIN observadas Distancias WITHIN esperadas bajo H0 (K=1) Cantidad optima de clusters clusGap

(58)

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.

(59)

Automatic and Extensive

Cropland Classification Based on

Satellite Data

(60)

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

(61)

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

(62)

Kind of Crops to be Detected

•  Arable land – Summer crops •  Soybean •  Corn – Winter crops •  Wheat •  Sunflower

•  Non arable land

Very easy Easy

Hard Hard

(63)

Remote Sensing Instruments

LON LA T NIR Band Red Band … … … … … … … … … … …

(64)

● 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

(65)

Vegetation Indices (VIs)

•  CI •  EVI •  ENVI •  NDVI Source: http://www.markelowitz.com Wavelength -1 ≤ NDVI ≤ 1 0 ≤ NDVI ≤ 1 For plants In general R ef le ct ed In te nsi ty

(66)

How is a Typical Phenological Crop

Cycle ?

Nov Jan Mar May Jul

0.0 0.2 0.4 0.6 0.8 1.0

Evolucion del cultivo

Tiempo ND VI ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ●_● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●_● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●● Start of season Time End of season Maturity of the plant Daily (2) NDVI measurements Soybea n cycle Terra measurement Aqua measurement

(67)

Double-Crop Phenological Cycle

May Jul Sep Nov Jan Mar May

0.0 0.2 0.4 0.6 0.8 1.0

Evolucion del cultivo

Tiempo ND VI ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●_● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● _● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Time Winter crop Summe rcrop Terra measurement Aqua measurement

(68)

Landsat: Big Data !

Argentina China

Landsat tile = 185km X 185 km ~

(69)

Cropland Detection Using Landsat

8 Unsupervised Approach

● −59.10 −59.09 −59.08 −59.07 −59.06 − 37.73 − 37.72 − 37.71 − 37.70 NDVI image (2014−10−16) 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ●

Visible image from

Open Street Map NDVI image

(2014-10-16) Point of

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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 ND VI −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

(71)

The Feature Space

X + Y + NDVI

Field of interest

(72)

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

(73)

−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

● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0.1 0.2 0.3 0.4 0.5 0.6

NDVI evoliution (LAndsat)

Time

ND

VI

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

(74)

Working With a Temporal Ensemble of

Images

Time N D VI ● Pixel 2 NDVI evolution NDVI_px = µ_px + α_px * Time+ β_px * Time2 Pixel-wise modelling

(75)

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 NDVI_px = µ_px + α_px * Time + β_px * Time2 ^ ^ ^ Pixel-wise modelling F alse co lo r ima ge

(76)

Clustering Based on Modelled

NDVI Temporal Evolution

−37.75 −37.74 −37.73 −37.72 −37.71 −37.70 −37.69 −59.09 −59.08 −59.07 −59.06 5 10 15 20 25 Time N D 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