STATISTICA MULTIVARIATA 2

Size: px
Start display at page:

Download "STATISTICA MULTIVARIATA 2"

Transcription

1 1 / 73 STATISTICA MULTIVARIATA 2 Fabio Rapallo Dipartimento di Scienze e Innovazione Tecnologica Università del Piemonte Orientale, Alessandria (Italy) fabio.rapallo@uniupo.it Alessandria, May 2016

2 2 / 73 Summary Structure of multivariate data Principal component analysis Factor analysis (Correspondence analysis) Cluster analysis Some R commands and functions will be presented throughout the lecture.

3 Cluster analysis 3 / 73

4 4 / 73 The multivariate setting As in PCA, multivariate data are displayed here in a two-way array, or matrix, with one row for each object one column for each variable The matrix has dimensions n p, where n is the number of objects and p is the number of variables.

5 5 / 73 Why cluster analysis The goal of cluster analysis is to assign observations to groups ( clusters ) so that: observations within each group are similar to one another with respect to variables or attributes of interest; the groups themselves stand apart from one another. The objective is to divide the observations into homogeneous and distinct groups. To actually run an algorithm of this kind we need to make precise the word similar.

6 6 / 73 Why cluster analysis At the end of this lecture we will analyze the relationships between cluster analysis and PCA. However, the starting point is totally different: The main goal of PCA is to understand the correlations between the variables. The main goal of cluster analysis is to analyze the similarity between the objects.

7 7 / 73 Introductory example As an introductory example, consider the following data taken from The OCSE factbook, with 6 social and economical variables reported for all the 28 EU countries. The variables are: 1. GDP 2. Inflation 3. Life expectancy 4. Military expenses (percent over GDP) 5. Population growth 6. Unemployment

8 8 / 73 Introductory example Country GDP Inflation Life.expect Military Pop.growth Unemployment 1 Austria Belgium Bulgaria Croatia Czech Republic Denmark Estonia Finland Germany Greece Hungary Iceland Ireland Italy Latvia Lithuania Luxembourg Netherlands Norway Poland Portugal Slovakia Slovenia Spain Sweden Switzerland Ukraine United Kingdom

9 9 / 73 Introductory example With a first notion of similarity we obtain a clustering into two groups displayed in the following tree. Cluster Dendrogram Iceland Ireland Spain United Kingdom Austria Italy Germany Finland Sweden Belgium Denmark Luxembourg Switzerland Netherlands Norway Ukraine Bulgaria Estonia Latvia Greece Czech Republic Slovenia Croatia Lithuania Slovakia Portugal Hungary Poland Height

10 10 / 73 Introductory example The means of the 6 variables by groups are in the table below. class: 1 GDP Inflation Life.expect Military Pop.growth Unemployment class: 2 GDP Inflation Life.expect Military Pop.growth Unemployment The first class contains rich countries, while the second class contains the countries with lower GDP and higher Unemployment.

11 11 / 73 Introductory example But with a slightly different similarity criterion, our tree becomes totally different, as shown here. Cluster Dendrogram Ukraine Luxembourg Greece Ireland Spain Croatia Bulgaria Estonia Latvia Portugal Hungary Poland Lithuania Slovakia Switzerland Iceland United Kingdom Czech Republic Slovenia Netherlands Norway Austria Italy Germany Finland Sweden Belgium Denmark Height

12 12 / 73 The ingredients An agglomerative clustering algorithm is a multi-step procedure, merging two objects at each step. In order to define an agglomerative clustering procedure, we need to define: A distance between the experimental units. A distance or dissimilarity between groups (clusters) of experimental units.

13 13 / 73 Distances The distance between objects is a translation of the geometric notion of distance between points. Let S be a set of points in R p. A distance is a function such that d : S S R (i) d(x, y) 0 and d(x, y) = 0 if and only if x = y (ii) d(x, y) = d(y, x) (iii) d(x, y) d(x, z) + d(y, z) for all x, y, z S. (triangular inequality)

14 14 / 73 Euclidean distance Let x be the point (x 1, x 2,..., x p ) and y be the point (y 1, y 2,..., y p ). The Euclidean distance (or L 2 ) is defined as d(x, y) = p (x k y k ) 2 k=1 The Euclidean distance is denoted with x y. This is the classical distance in elementary geometry.

15 15 / 73 Other distances Manhattan (or City block, or L 1 ): Maximum (or L ): d(x, y) = p x k y k k=1 d(x, y) = max x k y k k Minkowsky with order q (or L q ): ( p ) 1 q d(x, y) = (x k y k ) q k=1

16 16 / 73 Distance matrix The distances are organized in a symmetric n n matrix with zero diagonal entries: 0 d(x 1, x 2 ) d(x 1, x n ) d(x 2, x 1 ) 0 d(x 2, x n ) d(x n, x 1 ) d(x n, x 2 ) 0

17 17 / 73 Example Let us consider a synthetic example with 9 objets and 2 variables, so that we can plot the points exactly in the two-dimensional plane X Y Y X

18 18 / 73 Example The Manhattan distances are summarized in the following matrix: > dm=dist(data,method="manhattan")

19 19 / 73 Example The squared Euclidean distances are summarized in the following matrix: > de2=dist(data,method="euclidean")^

20 20 / 73 Hierarchical agglomerative clustering All agglomerative clustering methods proceed as follows: 1. At the first stage, each experimental unit is its own class, so that we have n points in n distinct clusters. 2. At each step, the nearest clusters are merged into a unique new cluster, and thus the number of clusters reduces by one at each step. 3. At the final stage, all the n experimental units are in the same cluster.

21 21 / 73 Dissimilarities between clusters To define a distance between clusters means to define a distance (or better, dissimilarity ) between sets of points D(C A, C B ). Given two clusters C A and C B, the function D yields a non-negative real number, and we call it the distance between C A and C B. Fixed a distance d between points, the function D extends the distance d to sets of points and we require the following compatibility condition to hold: D(C A, C B ) = d(x, y) if C A = {x} and C B = {y}

22 22 / 73 Dissimilarities between clusters There are several ways to extend a distance between points. To better understand the differences we give the general formula for D, we adopt the following scheme: 1. First, we introduce the formula in the special case where one class has only one point and one class has just two points. 2. Then, we give the general formula.

23 23 / 73 Single linkage The dissimilarity between C xy = {x, y} and the point z is: D (C xy, z) = min{d(x, z), d(y, z)} In general, the dissimilarity between C A e C B is the minimum over all the pair-wise distances: D (C A, C B ) = min x i C A min {d(x i, x j )} x j C B

24 24 / 73 Complete linkage The dissimilarity between C xy = {x, y} and the point z is: D (C xy, z) = max{d(x, z), d(y, z)} In general, the dissimilarity between C A e C B is the maximum over all the pair-wise distances: D (C A, C B ) = max x i C A min {d(x i, x j )} x j C B

25 25 / 73 Average linkage The dissimilarity between C xy = {x, y} and the point z is: D (C xy, z) = d(x, z) + d(y, z) 2 In general, the dissimilarity between C A e C B is the average of all the pair-wise distances: x i C A,x j C B d(x i, x j ) D (C A, C B ) = w A w B where w A and w B are the number of points ( the weights ) of C A and C B, respectively.

26 Centroid method The dissimilarity between C xy = {x, y} and the point z is: D (C xy, z) = d ( ) x + y 2, z In general, the dissimilarity between C A e C B is the distance between the centroids of the two clusters: D (C A, C B ) = d (x A, x B ) where x A and x B are the centroids of C A and C B, respectively. The centroid distance is generally based on the Euclidean distance, and in such case: D (C A, C B ) = x A x B 26 / 73

27 Graphical summary 27 / 73

28 28 / 73 The hierarchical algorithm step 0: we have n point in n distinct classes; step 1: we compute the dissimilarity (distance) matrix and we merge the nearest classes (points): we have now n 1 classes; step s: we compute the new dissimilarity matrix and we merge the nearest classes: we have now n s classes; step n 1: we have now only two classes and we merge them into a grand cluster containing all the experimental units.

29 29 / 73 Example We come back to our 9-points example and we proceed with the algorithm step-by-step. We use the (squared) Euclidean distance and the single linkage algorithm. Step 1: We put the points 1 and 3 into a class C1.

30 30 / 73 Example Step 2: C C We put the points 8 and 9 into another class C2.

31 31 / 73 Example Step 3: C1 C C C We add the point 2 to the class C1. We build up a new class C3 with 3 points.

32 Example X Y X Y / 73

33 33 / 73 Example Step 4: C3 C2 C C3 C C We put the points 4 and 6 into a new class C4.

34 Step 5: Example C3 C4 C2 C C3 C C C We add the point 5 to the class C4, and we define a new class C5 with 3 points. Step 6: C3 C5 C2 C1-2 C C3 C C5 C C We add the point 7 to the class C3, and we define a new class C6 with 4 points. 34 / 73

35 35 / 73 Example Y Y X X

36 36 / 73 Step 7: Example C6 C5 C2 C3-7 C C6 C C5 C C We merge the classes C5 and C6 together to form a new class C7 with 7 points. Step 8: C7 C2 C5-C6 8-9 C7 C5-C C This is the final step. We merge the classes C2 and C7 together in a single cluster containing all the 9 points.

37 37 / 73 Dissimilarity indices Note that the two extreme situations: all points are in separate clusters all points are in the same clusters are not useful. We need to decide when to stop the agglomerative algorithm. Usually we do not know the number of classes a priori. We need a measure to stop the algorithm at an appropriate step.

38 38 / 73 Dissimilarity indices (or heights) We assign a number to each step of the algorithm and we name this index as dissimilarity index or height. The dissimilarity index at step s is the dissimilarity between the two classes merged at step s. Thus we define a sequence of dissimilarity indices a 1,..., a s 1. For instance in our previous example: C1 32 {1, 3} C2 34 {8, 9} C3 130 {1, 2, 3} C4 202 {4, 6} C5 421 {4, 5, 6} C6 629 {1, 2, 3, 7} C7 901 {1, 2, 3, 4, 5, 6, 7} C {1, 2, 3, 4, 5, 6, 7, 8, 9}

39 39 / 73 The dendrogram The dendrogram is a tree representing the agglomerative process and with the heights a 1,..., a s 1 in the vertical axis. Sometimes in the vertical axis a different scale is used, namely the similarity indices: ( s i = 1 a ) i 100 d M where d M is the maximum distance at the first step.

40 40 / 73 The dendrogram This is the dendrogram for our 9 points example with (squared) Euclidean distance and the single linkage algorithm. > h=hclust(d,method="single") > plot(h,hang=-1) Cluster Dendrogram Height

41 41 / 73 The dendrogram For most methods the sequence a 1,..., a s 1 is increasing. This happens with the linkage methods, but not for the centroid method. Here is the dendrogram for the centroid method with Euclidean distance on the 9-points example. Cluster Dendrogram Height

42 42 / 73 Choosing the number of clusters To choose the number of cluster means to cut the tree at a given height. There are several criteria: At the maximal increase of the dissimilarity indices. At a given similarity level. At a given number of classes.

43 43 / 73 Choosing the number of clusters In our 9-points example, we can cut the tree in order to obtain 3 classes. > cutree(h,3) > rect.hclust(h,3) Cluster Dendrogram Height

44 44 / 73 Choosing the number of clusters The hclust function in R keeps track of the whole process: [,1] [,2] [,3] [1,] [2,] [3,] [4,] [5,] [6,] [7,] [8,]

45 45 / 73 The cophenetic matrix The dissimilarity indices can be organized in matrix (the cophenetic matrix). In the entry (i, j) there is the dissimilarity index pertaining to the first agglomeration of the points i and j

46 46 / 73 Inertia-based techniques The key idea of these techniques is as follows. In the optimal partition, the variance in each class is small compared with the total variance. We need to extend the notion of variance in the multidimensional setting, and we define the inertia of a set of points.

47 47 / 73 Inertia and its decomposition Let x 1,..., x n be n points in a space with p dimensions, and let x the centroid: x = 1 n The total inertia of x 1,..., x n is: n i=1 x i I = n x i x 2 i=1 where x i x is the Euclidean distance between x i and x. Remark. In the one-dimensional setting, the total inertia is the numerator of the variance. The contribution of the point x i to the total inertia is I(x i ): I(x i ) = x i x 2

48 48 / 73 Inertia and its decomposition Let C A and C B be a partition with two clusters with w A and w B points, respectively. We want to study the behavior of the inertia when C A and C B are merged together. The grand centroid can be computed from the centroids x A and x B as follows: x = w Ax A + w B x B w A + w B The contribution of C A to the total inertia is: I(C A ) = x i A x i x 2 = x i A x i x A + x A x 2 = = x i A x i x A 2 + w A x A x 2 = = I A + I(x A )

49 49 / 73 Inertia and its decomposition Finally we have: I(C A ) = I A + I(x A ) where I A is the inertia within the class C A ; I(x A ) is the portion of the total inertia pertaining to x A.

50 50 / 73 Inertia and its decomposition The total inertia is then decomposed in: and in general for K classes: where I = (I A + I B ) + (I(x A ) + I(x B )) I = K k=1 I k + K k=1 I(x k ) K k=1 I k is the inertia within classes; K k=1 I(x k) is the inertia between classes. TOTAL INERTIA = INERTIA WITHIN + INERTIA BETWEEN

51 51 / 73 The Ward criterion In an agglomerative algorithm, at each step two classes are merged, and since the total inertia is fixed, we conclude that the inertia within classes increases the inertia between classes decreases Under the Ward criterion, at each step are merged the two classes with the minimum increase of inertia within classes.

52 52 / 73 The Ward criterion Note that also under the Ward criterion the first and the last step are not useful at the first step each point has its own class, so that the inertia within classes is zero; the inertia between classes is equal to the total inertia; at the last step all points are in an unique class, so that the inertia within classes is equal to the total inertia; the inertia between classes is zero.

53 53 / 73 The Ward criterion One can show that the increase of inertia within classes when C A and C B are merged together is: I s = w Aw B w A + w B x A x B 2 and this is taken as a similarity index for the Ward method. Remark. The Ward criterion is a weighted version of the algorithm based on centroids.

54 54 / 73 Comparing the algorithms Single linkage. It is useful for the detection of unusual observations (outliers). Complete linkage. It produces clusters with similar diameters Average linkage. It produces classes with small variance. Ward. It produces clusters with similar cardinality.

55 55 / 73 Comparing the algorithms As an example, We analyze (a subset of) the data in Rouncefield (1995), with the birth and death rates in 97 countries. The first lines of the data are below. Birth Death Country Albania Bulgaria Czechoslovakia Former_E._Germa Hungary Poland Romania Yugoslavia USSR Byelorussia Ukrainian_SSR...

56 56 / 73 Comparing the algorithms - Single linkage Death Cluster: 1 Birth Death Cluster: 2 Birth Death Cluster: 3 Birth Death Birth

57 57 / 73 Comparing the algorithms - Average linkage Death Cluster: 1 Birth Death Cluster: 2 Birth Death Cluster: 3 Birth Death Birth

58 58 / 73 Comparing the algorithms - Centroid method Death Cluster: 1 Birth Death Cluster: 2 Birth Death Cluster: 3 Birth Death Birth

59 59 / 73 Comparing the algorithms - Ward criterion Death Cluster: 1 Birth Death Cluster: 2 Birth Death Cluster: 3 Birth Death Birth

60 60 / 73 Warning Normalize the data In order to assign the same weight to all variables, usually the distance matrix is computed on the standardized variables, that is we replace X 1,..., X p with X 1 x 1 σ(x 1 ),..., X p x p σ(x p ) Using the original variables, the distance matrix depends essentially on the variables with the highest order of magnitude, and ignores the other variables.

61 61 / 73 Warning Normalize the data For instance, take the data of our first example. Country GDP Inflation Life.expect Military Pop.growth Unemployment 1 Austria Belgium Bulgaria Croatia Czech Republic Denmark Estonia Finland Germany Without standardization, the distance matrix would be based only on the GDP, and the clusters would not consider Inflation, Life Expectancy, etc.

62 62 / 73 Non-hierarchical methods The hierarchical methods are computationally difficult to apply when the data matrix is large (e.g., one hundred thousand experimental units), and this case often happens in Proteomics, Genomics, and Computational biology. As an alternative, we can use non-hierarchical methods, where The number of steps is considerably small; We need to choose the number of classes a priori. Among this family of algorithms, here we present the k-means algorithm.

63 The k-means algorithm Let S be the our set of points in a p-dimensional space with a distance function d. We ask for a partition of S in k classes. step 0: we randomly choose k centroids (usually k points randomly selected): x (0) 1,..., x (0) h,..., x (0) k We compute the distance between each point and each center and we assign a point to the class C h if the distance from x 0 h is minimal. This defines a first partition C (0) 1,..., C(0) h,..., C(0) k step s: we compute the centroids of C (s 1) 1,..., C (s 1) k x (s 1) 1,..., x (s 1) h,..., x (s 1) k and we compute again the distances. 63 / 73

64 64 / 73 Stopping rules The k-means algorithm needs a stopping rule. Here are some classical criteria: 1. When in two successive steps the partition does not change. 2. After a fixed number of iterations. 3. Since the inertia within classes decreases at each step I (s) within I(s+1) within we stop the algorithm when the decrease I (s+1) under a fixed threshold. within I(s) within is

65 65 / 73 The starting points With different starting points, the results will be different in general. Here are 2 results obtained on the Rouncefield data with 8 clusters. Death Death Birth Birth

66 66 / 73 The starting points Even more dramatic situations can happen.

67 67 / 73 Stability of the partition As the final partition depends on the starting centroids, we have to study the stability of the final result. A first solution is to run several execution of the k-means algorithm with different starting centroids, and to classify only the points with the same classification in all the executions, while the other points are not classified. Such groups are called stable classes.

68 68 / 73 Mixed algorithms Another approach is to apply mixed algorithms. 1. With the k-means algorithm find r clusters, with r considerably larger than the final number of clusters; 2. Apply a hierarchical method to the centroids of the r classes to reduce the number of clusters and to choose the correct number of clusters based on the dendrogram. The hierarchical method used here is usually the Ward criterion, since it can be adapted to classes with different weights.

69 69 / 73 Cluster analysis vs. PCA Although the PCA mainly works on the correlations between variables, and cluster analysis mainly works on the similarities between experimental units, nevertheless the results of the two analyses are often strictly related. To show this we run the cluster analysis on the leafs data.

70 70 / 73 Cluster analysis vs. PCA SLA Leaf-N A-mass A-area G-s Caulophyllum thalictroides Dentaria laciniate Erythronium americanum Silphium terebinthinaceum Podophyllum peltatum Baptisia leucophaea Trillium grandiflora Echinacea purpurea Silphium integrifolium Sanguinaria canadensis Sarrachenia purpurea Note: SLA in cm 2 g 1, Leaf-N in mg g 1, A-mass in nmol g 1 s 1, A-area in µmol m 2 s 1, G-s in mmol m 2 s 1.

71 71 / 73 Cluster analysis vs. PCA Running the average linkage algorithm on these data and choosing three clusters in the final partition, we get the dendrogram below. Cluster Dendrogram Sarrachenia Baptisia Silphium_t Echinacea Silphium_i Dentaria Erythronium Trillium Caulophyllum Podophyllum Sanguinaria Height

72 72 / 73 Cluster analysis vs. PCA The three groups are described as follows. > group Caulophyllum Dentaria Erythronium Silphium_t Podophyllum Baptisia Trillium Echinacea Silphium_i Sanguinaria Sarrachenia > by(data,group,colmeans) group: 1 SLA LeafN Amass Aarea Gs group: 2 SLA LeafN Amass Aarea Gs group: 3 SLA LeafN Amass Aarea Gs

73 Cluster analysis vs. PCA Finally we compare the results of the cluster analysis with the plots on the first two principal components. Second Component Sarrachenia Silphium_i Echinacea lphium_t Baptisia Caulophyl Podophyllum Sanguinaria Trillium Erythronium Dentaria Second Component SLA LeafN Amass Aarea Gs First Component First Component 73 / 73

WHO EpiData. A monthly summary of the epidemiological data on selected Vaccine preventable diseases in the WHO European Region

WHO EpiData. A monthly summary of the epidemiological data on selected Vaccine preventable diseases in the WHO European Region A monthly summary of the epidemiological data on selected Vaccine preventable diseases in the WHO European Region Table 1: Reported cases for the period January December 2018 (data as of 01 February 2019)

More information

A Markov system analysis application on labour market dynamics: The case of Greece

A Markov system analysis application on labour market dynamics: The case of Greece + A Markov system analysis application on labour market dynamics: The case of Greece Maria Symeonaki Glykeria Stamatopoulou This project has received funding from the European Union s Horizon 2020 research

More information

AD HOC DRAFTING GROUP ON TRANSNATIONAL ORGANISED CRIME (PC-GR-COT) STATUS OF RATIFICATIONS BY COUNCIL OF EUROPE MEMBER STATES

AD HOC DRAFTING GROUP ON TRANSNATIONAL ORGANISED CRIME (PC-GR-COT) STATUS OF RATIFICATIONS BY COUNCIL OF EUROPE MEMBER STATES Strasbourg, 29 May 2015 PC-GR-COT (2013) 2 EN_Rev AD HOC DRAFTING GROUP ON TRANSNATIONAL ORGANISED CRIME (PC-GR-COT) STATUS OF RATIFICATIONS BY COUNCIL OF EUROPE MEMBER STATES TO THE UNITED NATIONS CONVENTION

More information

WHO EpiData. A monthly summary of the epidemiological data on selected Vaccine preventable diseases in the European Region

WHO EpiData. A monthly summary of the epidemiological data on selected Vaccine preventable diseases in the European Region A monthly summary of the epidemiological data on selected Vaccine preventable diseases in the European Region Table : Reported measles cases for the period January December 207 (data as of 02 February

More information

WHO EpiData. A monthly summary of the epidemiological data on selected Vaccine preventable diseases in the European Region

WHO EpiData. A monthly summary of the epidemiological data on selected Vaccine preventable diseases in the European Region A monthly summary of the epidemiological data on selected Vaccine preventable diseases in the European Region Table : Reported cases for the period June 207 May 208 (data as of 0 July 208) Population in

More information

WHO EpiData. A monthly summary of the epidemiological data on selected Vaccine preventable diseases in the WHO European Region

WHO EpiData. A monthly summary of the epidemiological data on selected Vaccine preventable diseases in the WHO European Region A monthly summary of the epidemiological data on selected Vaccine preventable diseases in the WHO European Region Table : Reported cases for the period November 207 October 208 (data as of 30 November

More information

WHO EpiData. A monthly summary of the epidemiological data on selected Vaccine preventable diseases in the European Region

WHO EpiData. A monthly summary of the epidemiological data on selected Vaccine preventable diseases in the European Region A monthly summary of the epidemiological data on selected Vaccine preventable diseases in the European Region Table : Reported measles cases for the period July 207 June 208 (data as of August 208) Population

More information

WHO EpiData. A monthly summary of the epidemiological data on selected Vaccine preventable diseases in the European Region

WHO EpiData. A monthly summary of the epidemiological data on selected Vaccine preventable diseases in the European Region A monthly summary of the epidemiological data on selected Vaccine preventable diseases in the European Region Table : Reported cases for the period September 207 August 208 (data as of 0 October 208) Population

More information

Weighted Voting Games

Weighted Voting Games Weighted Voting Games Gregor Schwarz Computational Social Choice Seminar WS 2015/2016 Technische Universität München 01.12.2015 Agenda 1 Motivation 2 Basic Definitions 3 Solution Concepts Core Shapley

More information

Multivariate Analysis

Multivariate Analysis Prof. Dr. J. Franke All of Statistics 3.1 Multivariate Analysis High dimensional data X 1,..., X N, i.i.d. random vectors in R p. As a data matrix X: objects values of p features 1 X 11 X 12... X 1p 2.

More information

WHO EpiData. A monthly summary of the epidemiological data on selected vaccine preventable diseases in the European Region

WHO EpiData. A monthly summary of the epidemiological data on selected vaccine preventable diseases in the European Region A monthly summary of the epidemiological data on selected vaccine preventable diseases in the European Region Table 1: Reported measles cases for the 12-month period February 2016 January 2017 (data as

More information

Trends in Human Development Index of European Union

Trends in Human Development Index of European Union Trends in Human Development Index of European Union Department of Statistics, Hacettepe University, Beytepe, Ankara, Turkey spxl@hacettepe.edu.tr, deryacal@hacettepe.edu.tr Abstract: The Human Development

More information

The trade dispute between the US and China Who wins? Who loses?

The trade dispute between the US and China Who wins? Who loses? 1 Munich, Jan 10 th, 2019 The trade dispute between the US and China Who wins? Who loses? by Gabriel Felbermayr and Marina Steininger This report offers a brief, quantitative analysis of the potential

More information

SC4/SM4 Data Mining and Machine Learning Clustering

SC4/SM4 Data Mining and Machine Learning Clustering SC4/SM4 Data Mining and Machine Learning Clustering Dino Sejdinovic Department of Statistics Oxford Slides and other materials available at: http://www.stats.ox.ac.uk/~sejdinov/dmml Department of Statistics,

More information

Annotated Exam of Statistics 6C - Prof. M. Romanazzi

Annotated Exam of Statistics 6C - Prof. M. Romanazzi 1 Università di Venezia - Corso di Laurea Economics & Management Annotated Exam of Statistics 6C - Prof. M. Romanazzi March 17th, 2015 Full Name Matricola Total (nominal) score: 30/30 (2/30 for each question).

More information

Weekly price report on Pig carcass (Class S, E and R) and Piglet prices in the EU. Carcass Class S % + 0.3% % 98.

Weekly price report on Pig carcass (Class S, E and R) and Piglet prices in the EU. Carcass Class S % + 0.3% % 98. Weekly price report on Pig carcass (Class S, E and R) and Piglet prices in the EU Disclaimer Please note that EU prices for pig meat, are averages of the national prices communicated by Member States weighted

More information

Economic and Social Council

Economic and Social Council United Nations Economic and Social Council Distr.: General 30 August 2012 Original: English Economic Commission for Europe Inland Transport Committee Working Party on Rail Transport Sixty-sixth session

More information

Composition of capital NO051

Composition of capital NO051 Composition of capital POWSZECHNA (in million Euro) Capital position CRD3 rules A) Common equity before deductions (Original own funds without hybrid instruments and government support measures other than

More information

Composition of capital CY007 CY007 POWSZECHNACY007 BANK OF CYPRUS PUBLIC CO LTD

Composition of capital CY007 CY007 POWSZECHNACY007 BANK OF CYPRUS PUBLIC CO LTD Composition of capital POWSZECHNA (in million Euro) Capital position CRD3 rules A) Common equity before deductions (Original own funds without hybrid instruments and government support measures other than

More information

Composition of capital DE025

Composition of capital DE025 Composition of capital POWSZECHNA (in million Euro) Capital position CRD3 rules A) Common equity before deductions (Original own funds without hybrid instruments and government support measures other than

More information

Composition of capital ES060 ES060 POWSZECHNAES060 BANCO BILBAO VIZCAYA ARGENTARIA S.A. (BBVA)

Composition of capital ES060 ES060 POWSZECHNAES060 BANCO BILBAO VIZCAYA ARGENTARIA S.A. (BBVA) Composition of capital POWSZECHNA (in million Euro) Capital position CRD3 rules A) Common equity before deductions (Original own funds without hybrid instruments and government support measures other than

More information

Composition of capital LU045 LU045 POWSZECHNALU045 BANQUE ET CAISSE D'EPARGNE DE L'ETAT

Composition of capital LU045 LU045 POWSZECHNALU045 BANQUE ET CAISSE D'EPARGNE DE L'ETAT Composition of capital POWSZECHNA (in million Euro) Capital position CRD3 rules A) Common equity before deductions (Original own funds without hybrid instruments and government support measures other than

More information

Composition of capital CY006 CY006 POWSZECHNACY006 CYPRUS POPULAR BANK PUBLIC CO LTD

Composition of capital CY006 CY006 POWSZECHNACY006 CYPRUS POPULAR BANK PUBLIC CO LTD Composition of capital POWSZECHNA (in million Euro) Capital position CRD3 rules A) Common equity before deductions (Original own funds without hybrid instruments and government support measures other than

More information

Composition of capital DE028 DE028 POWSZECHNADE028 DekaBank Deutsche Girozentrale, Frankfurt

Composition of capital DE028 DE028 POWSZECHNADE028 DekaBank Deutsche Girozentrale, Frankfurt Composition of capital POWSZECHNA (in million Euro) Capital position CRD3 rules A) Common equity before deductions (Original own funds without hybrid instruments and government support measures other than

More information

APPLYING BORDA COUNT METHOD FOR DETERMINING THE BEST WEEE MANAGEMENT IN EUROPE. Maria-Loredana POPESCU 1

APPLYING BORDA COUNT METHOD FOR DETERMINING THE BEST WEEE MANAGEMENT IN EUROPE. Maria-Loredana POPESCU 1 APPLYING BORDA COUNT METHOD FOR DETERMINING THE BEST MANAGEMENT IN EUROPE Maria-Loredana POPESCU 1 ABSTRACT This article presents the Borda Count method and its application for ranking the regarding the

More information

Composition of capital FR015

Composition of capital FR015 Composition of capital POWSZECHNA (in million Euro) Capital position CRD3 rules A) Common equity before deductions (Original own funds without hybrid instruments and government support measures other than

More information

Composition of capital FR013

Composition of capital FR013 Composition of capital POWSZECHNA (in million Euro) Capital position CRD3 rules A) Common equity before deductions (Original own funds without hybrid instruments and government support measures other than

More information

Composition of capital DE017 DE017 POWSZECHNADE017 DEUTSCHE BANK AG

Composition of capital DE017 DE017 POWSZECHNADE017 DEUTSCHE BANK AG Composition of capital POWSZECHNA (in million Euro) Capital position CRD3 rules A) Common equity before deductions (Original own funds without hybrid instruments and government support measures other than

More information

Composition of capital ES059

Composition of capital ES059 Composition of capital POWSZECHNA (in million Euro) Capital position CRD3 rules A) Common equity before deductions (Original own funds without hybrid instruments and government support measures other than

More information

Composition of capital as of 30 September 2011 (CRD3 rules)

Composition of capital as of 30 September 2011 (CRD3 rules) Composition of capital as of 30 September 2011 (CRD3 rules) Capital position CRD3 rules September 2011 Million EUR % RWA References to COREP reporting A) Common equity before deductions (Original own funds

More information

Composition of capital as of 30 September 2011 (CRD3 rules)

Composition of capital as of 30 September 2011 (CRD3 rules) Composition of capital as of 30 September 2011 (CRD3 rules) Capital position CRD3 rules September 2011 Million EUR % RWA References to COREP reporting A) Common equity before deductions (Original own funds

More information

Composition of capital as of 30 September 2011 (CRD3 rules)

Composition of capital as of 30 September 2011 (CRD3 rules) Composition of capital as of 30 September 2011 (CRD3 rules) Capital position CRD3 rules September 2011 Million EUR % RWA References to COREP reporting A) Common equity before deductions (Original own funds

More information

Composition of capital as of 30 September 2011 (CRD3 rules)

Composition of capital as of 30 September 2011 (CRD3 rules) Composition of capital as of 30 September 2011 (CRD3 rules) Capital position CRD3 rules September 2011 Million EUR % RWA References to COREP reporting A) Common equity before deductions (Original own funds

More information

Composition of capital as of 30 September 2011 (CRD3 rules)

Composition of capital as of 30 September 2011 (CRD3 rules) Composition of capital as of 30 September 2011 (CRD3 rules) Capital position CRD3 rules September 2011 Million EUR % RWA References to COREP reporting A) Common equity before deductions (Original own funds

More information

Composition of capital as of 30 September 2011 (CRD3 rules)

Composition of capital as of 30 September 2011 (CRD3 rules) Composition of capital as of 30 September 2011 (CRD3 rules) Capital position CRD3 rules September 2011 Million EUR % RWA References to COREP reporting A) Common equity before deductions (Original own funds

More information

PLUTO The Transport Response to the National Planning Framework. Dr. Aoife O Grady Department of Transport, Tourism and Sport

PLUTO The Transport Response to the National Planning Framework. Dr. Aoife O Grady Department of Transport, Tourism and Sport PLUTO 2040 The Transport Response to the National Planning Framework Dr. Aoife O Grady Department of Transport, Tourism and Sport Dublin Economics Workshop 15 th September 2018 The Story of Pluto National

More information

Modelling structural change using broken sticks

Modelling structural change using broken sticks Modelling structural change using broken sticks Paul White, Don J. Webber and Angela Helvin Department of Mathematics and Statistics, University of the West of England, Bristol, UK Department of Economics,

More information

F M U Total. Total registrants at 31/12/2014. Profession AS 2, ,574 BS 15,044 7, ,498 CH 9,471 3, ,932

F M U Total. Total registrants at 31/12/2014. Profession AS 2, ,574 BS 15,044 7, ,498 CH 9,471 3, ,932 Profession AS 2,949 578 47 3,574 BS 15,044 7,437 17 22,498 CH 9,471 3,445 16 12,932 Total registrants at 31/12/2014 CS 2,944 2,290 0 5,234 DT 8,048 413 15 8,476 HAD 881 1,226 0 2,107 ODP 4,219 1,921 5,958

More information

Variance estimation on SILC based indicators

Variance estimation on SILC based indicators Variance estimation on SILC based indicators Emilio Di Meglio Eurostat emilio.di-meglio@ec.europa.eu Guillaume Osier STATEC guillaume.osier@statec.etat.lu 3rd EU-LFS/EU-SILC European User Conference 1

More information

c. {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}. Also {x x is a prime less than 100}.

c. {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}. Also {x x is a prime less than 100}. Mathematics for Elementary School Teachers 6th Edition Bassarear SOLUTIONS MANUAL Full download at: https://testbankreal.com/download/mathematics-elementary-school-teachers- 6th-edition-bassarear-solutions-manual/

More information

EuroGeoSurveys An Introduction

EuroGeoSurveys An Introduction EGS -ASGMI Workshop, Madrid, 2015 EuroGeoSurveys An Introduction 40 Years Listening to the Beat of the Earth Click to edit Master title Albania style EuroGeoSurveys Austria Lithuania Luxembourg Belgium

More information

NASDAQ OMX Copenhagen A/S. 3 October Jyske Bank meets 9% Core Tier 1 ratio in EU capital exercise

NASDAQ OMX Copenhagen A/S. 3 October Jyske Bank meets 9% Core Tier 1 ratio in EU capital exercise NASDAQ OMX Copenhagen A/S JYSKE BANK Vestergade 8-16 DK-8600 Silkeborg Tel. +45 89 89 89 89 Fax +45 89 89 19 99 A/S www. jyskebank.dk E-mail: jyskebank@jyskebank.dk Business Reg. No. 17616617 - meets 9%

More information

This document is a preview generated by EVS

This document is a preview generated by EVS TECHNICAL REPORT RAPPORT TECHNIQUE TECHNISCHER BERICHT CEN/TR 15641 August 2007 ICS 67.050 English Version Food analysis - Determination of pesticide residues by LC- MS/MS - Tandem mass spectrometric parameters

More information

Bathing water results 2011 Slovakia

Bathing water results 2011 Slovakia Bathing water results Slovakia 1. Reporting and assessment This report gives a general overview of water in Slovakia for the season. Slovakia has reported under the Directive 2006/7/EC since 2008. When

More information

The EuCheMS Division Chemistry and the Environment EuCheMS/DCE

The EuCheMS Division Chemistry and the Environment EuCheMS/DCE The EuCheMS Division Chemistry and the Environment EuCheMS/DCE EuCheMS Division on Chemistry and the Environment was formed as a FECS Working Party in 1977. Membership: 37 members from 34 countries. Countries

More information

Bathing water results 2011 Latvia

Bathing water results 2011 Latvia Bathing water results 2011 Latvia 1. Reporting and assessment This report gives a general overview of water in Latvia for the 2011 season. Latvia has reported under the Directive 2006/7/EC since 2008.

More information

40 Years Listening to the Beat of the Earth

40 Years Listening to the Beat of the Earth EuroGeoSurveys The role of EuroGeoSurveys in Europe-Africa geoscientific cooperation 40 Years Listening to the Beat of the Earth EuroGeoSurveys 32 Albania Lithuania Austria Luxembourg Belgium The Netherlands

More information

The School Geography Curriculum in European Geography Education. Similarities and differences in the United Europe.

The School Geography Curriculum in European Geography Education. Similarities and differences in the United Europe. The School Geography Curriculum in European Geography Education. Similarities and differences in the United Europe. Maria Rellou and Nikos Lambrinos Aristotle University of Thessaloniki, Dept.of Primary

More information

THE NEW DEGREE OF URBANISATION

THE NEW DEGREE OF URBANISATION THE NEW DEGREE OF URBANISATION EXECUTIVE SUMMARY This paper describes the new degree of urbanisation classification as approved by the Eurostat Labour Market Working Group in 2011. This classification

More information

EUMETSAT. A global operational satellite agency at the heart of Europe. Presentation for the Spanish Industry Day Madrid, 15 March 2012

EUMETSAT. A global operational satellite agency at the heart of Europe. Presentation for the Spanish Industry Day Madrid, 15 March 2012 EUMETSAT A global operational satellite agency at the heart of Europe Presentation for the Spanish Industry Day Madrid, Angiolo Rolli EUMETSAT Director of Administration EUMETSAT objectives The primary

More information

EuroGeoSurveys & ASGMI The Geological Surveys of Europe and IberoAmerica

EuroGeoSurveys & ASGMI The Geological Surveys of Europe and IberoAmerica EuroGeoSurveys & ASGMI The Geological Surveys of Europe and IberoAmerica Geological Surveys, what role? Legal mandate for data & information: Research Collection Management Interpretation/transformation

More information

Part 2. Cost-effective Control of Acidification and Ground-level Ozone

Part 2. Cost-effective Control of Acidification and Ground-level Ozone 8 th INTERIM REPORT Part 2 Cost-effective Control of Acidification and Ground-level Ozone Markus Amann, Imrich Bertok, Janusz Cofala, Frantisek Gyarfas, Chris Heyes, Zbigniew Klimont, Wolfgang Schöpp March

More information

04 June Dim A W V Total. Total Laser Met

04 June Dim A W V Total. Total Laser Met 4 June 218 Member State State as on 4 June 218 Acronyms are listed in the last page of this document. AUV Mass and Related Quantities Length PR T TF EM Mass Dens Pres F Torq Visc H Grav FF Dim A W V Total

More information

Bilateral Labour Agreements, 2004

Bilateral Labour Agreements, 2004 Guest Austria Canada Turkey ( 64) Canada, Czech Republic, Hungary ( 98), Belgium Italy ( 46, 54), Turkey ( 64) Bulgaria ( 99), Pol (02) Germany ( 91) Bulgaria ( 99), Mongolia ( 99), Pol ( 92), Russia (

More information

United Nations Environment Programme

United Nations Environment Programme UNITED NATIONS United Nations Environment Programme Distr. GENERAL 13 April 2016 EP ORIGINAL: ENGLISH EXECUTIVE COMMITTEE OF THE MULTILATERAL FUND FOR THE IMPLEMENTATION OF THE MONTREAL PROTOCOL Seventy-sixth

More information

10/27/2015. Content. Well-homogenized national datasets. Difference (national global) BEST (1800) Difference BEST (1911) Difference GHCN & GISS (1911)

10/27/2015. Content. Well-homogenized national datasets. Difference (national global) BEST (1800) Difference BEST (1911) Difference GHCN & GISS (1911) Content Is the global mean temperature trend too low? Victor Venema, Phil Jones, Ralf Lindau, Tim Osborn and numerous collaborators @VariabilityBlog variable-variability.blogspot.com 1. Comparison trend

More information

Publication Date: 15 Jan 2015 Effective Date: 12 Jan 2015 Addendum 6 to the CRI Technical Report (Version: 2014, Update 1)

Publication Date: 15 Jan 2015 Effective Date: 12 Jan 2015 Addendum 6 to the CRI Technical Report (Version: 2014, Update 1) Publication Date: 15 Jan 2015 Effective Date: 12 Jan 2015 This document updates the Technical Report (Version: 2014, Update 1) and details (1) Replacement of interest rates, (2) CRI coverage expansion,

More information

This document is a preview generated by EVS

This document is a preview generated by EVS TECHNICAL SPECIFICATION SPÉCIFICATION TECHNIQUE TECHNISCHE SPEZIFIKATION CEN ISO/TS 15530-3 December 2007 ICS 17.040.30 English Version Geometrical product specifications (GPS) - Coordinate measuring machines

More information

North-South Gap Mapping Assignment Country Classification / Statistical Analysis

North-South Gap Mapping Assignment Country Classification / Statistical Analysis North-South Gap Mapping Assignment Country Classification / Statistical Analysis Due Date: (Total Value: 55 points) Name: Date: Learning Outcomes: By successfully completing this assignment, you will be

More information

Gravity Analysis of Regional Economic Interdependence: In case of Japan

Gravity Analysis of Regional Economic Interdependence: In case of Japan Prepared for the 21 st INFORUM World Conference 26-31 August 2013, Listvyanka, Russia Gravity Analysis of Regional Economic Interdependence: In case of Japan Toshiaki Hasegawa Chuo University Tokyo, JAPAN

More information

USDA Dairy Import License Circular for 2018

USDA Dairy Import License Circular for 2018 USDA Dairy Import License Circular for 2018 Commodity/Note Country Name TRQ Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Grand Total Non-Cheese 21,864,781 624,064 651,121 432,669 901,074 1,202,567 907,493

More information

United Nations Environment Programme

United Nations Environment Programme UNITED NATIONS United Nations Environment Programme Distr. GENERAL UNEP/OzL.Pro/ExCom/80/3 26 October 2017 EP ORIGINAL: ENGLISH EXECUTIVE COMMITTEE OF THE MULTILATERAL FUND FOR THE IMPLEMENTATION OF THE

More information

Part A: Salmonella prevalence estimates. (Question N EFSA-Q ) Adopted by The Task Force on 28 March 2007

Part A: Salmonella prevalence estimates. (Question N EFSA-Q ) Adopted by The Task Force on 28 March 2007 The EFSA Journal (2007) 98, 1-85 Report of the Task Force on Zoonoses Data Collection on the Analysis of the baseline survey on the prevalence of Salmonella in broiler flocks of Gallus gallus, in the EU,

More information

Measuring Instruments Directive (MID) MID/EN14154 Short Overview

Measuring Instruments Directive (MID) MID/EN14154 Short Overview Measuring Instruments Directive (MID) MID/EN14154 Short Overview STARTING POSITION Approval vs. Type examination In the past, country specific approvals were needed to sell measuring instruments in EU

More information

How Well Are Recessions and Recoveries Forecast? Prakash Loungani, Herman Stekler and Natalia Tamirisa

How Well Are Recessions and Recoveries Forecast? Prakash Loungani, Herman Stekler and Natalia Tamirisa How Well Are Recessions and Recoveries Forecast? Prakash Loungani, Herman Stekler and Natalia Tamirisa 1 Outline Focus of the study Data Dispersion and forecast errors during turning points Testing efficiency

More information

Drawing the European map

Drawing the European map Welcome in Europe Objectif: mieux connaitre l'espace géographique et civilisationnel européen Opérer la distinction entre pays d'europe et pays de l'union Européenne Tâche intermédiaire: restitution de

More information

USDA Dairy Import License Circular for 2018 Commodity/

USDA Dairy Import License Circular for 2018 Commodity/ USDA Dairy Import License Circular for 2018 Commodity/ Grand Country Name TRQ Jan Feb Mar Apr May Jun Jul Aug Sep Note Total Non-Cheese 21,864,781 624,064 651,121 432,669 901,074 1,202,567 907,493 1,117,261

More information

Modelling and projecting the postponement of childbearing in low-fertility countries

Modelling and projecting the postponement of childbearing in low-fertility countries of childbearing in low-fertility countries Nan Li and Patrick Gerland, United Nations * Abstract In most developed countries, total fertility reached below-replacement level and stopped changing notably.

More information

This document is a preview generated by EVS

This document is a preview generated by EVS TECHNICAL SPECIFICATION SPÉCIFICATION TECHNIQUE TECHNISCHE SPEZIFIKATION CEN/TS 16272-5 April 2014 ICS 93.100 English Version Railway applications - Track - Noise barriers and related devices acting on

More information

CropCast Europe Weekly Report

CropCast Europe Weekly Report CropCast Europe Weekly Report Kenny Miller Monday, June 05, 2017 Europe Hot Spots Abundant showers should ease dryness across northern and central UK as well as across western Norway and Sweden. Improvements

More information

Программа Организации Объединенных Наций по окружающей среде

Программа Организации Объединенных Наций по окружающей среде ОРГАНИЗАЦИЯ ОБЪЕДИНЕННЫХ НАЦИЙ EP Программа Организации Объединенных Наций по окружающей среде Distr. GENERAL UNEP/OzL.Pro/ExCom/73/3/Corr.1 20 October 2014 RUSSIAN ORIGINAL: ENGLISH ИСПОЛНИТЕЛЬНЫЙ КОМИТЕТ

More information

Identification of Very Shallow Groundwater Regions in the EU to Support Monitoring

Identification of Very Shallow Groundwater Regions in the EU to Support Monitoring Identification of Very Shallow Groundwater Regions in the EU to Support Monitoring Timothy Negley Paul Sweeney Lucy Fish Paul Hendley Andrew Newcombe ARCADIS Syngenta Ltd. Syngenta Ltd. Phasera Ltd. ARCADIS

More information

USDA Dairy Import License Circular for 2018

USDA Dairy Import License Circular for 2018 USDA Dairy Import License Circular for 2018 Commodity/Note Country Name TRQ Jan Feb Mar Apr May Jun Grand Total Non-Cheese 21,864,781 624,064 651,121 432,669 901,074 1,202,567 907,493 4,718,988 BUTTER

More information

MB of. Cable. Wholesale. FWBA (fixed OAOs. connections of which Full unbundled. OAO owning. Internet. unbundled broadband

MB of. Cable. Wholesale. FWBA (fixed OAOs. connections of which Full unbundled. OAO owning. Internet. unbundled broadband ECTA Broadband scorecard end of March 2009 Incumbent retail and resale xdsl connections Incumbent wholesale xdsl connections Entrant xdsl connections Broadband cable FTTH/B Other fixed broadband Mobile

More information

ORGANISATION FOR ECONOMIC CO-OPERATION AND DEVELOPMENT

ORGANISATION FOR ECONOMIC CO-OPERATION AND DEVELOPMENT ORGANISATION FOR ECONOMIC CO-OPERATION AND DEVELOPMENT Pursuant to Article 1 of the Convention signed in Paris on 14th December 1960, and which came into force on 30th September 1961, the Organisation

More information

Use of the ISO Quality standards at the NMCAs Results from questionnaires taken in 2004 and 2011

Use of the ISO Quality standards at the NMCAs Results from questionnaires taken in 2004 and 2011 Use of the ISO 19100 Quality standards at the NMCAs Results from questionnaires taken in 2004 and 2011 Eurogeographics Quality Knowledge Exchange Network Reference: History Version Author Date Comments

More information

Comparison of Turkey and European Union Countries Health Indicators by Using Fuzzy Clustering Analysis

Comparison of Turkey and European Union Countries Health Indicators by Using Fuzzy Clustering Analysis International Journal of Business and Social Research Issue 04, Volume 10, 2014 Comparison of Turkey and European Union Countries Health Indicators by Using Fuzzy Clustering Analysis Nesrin Alptekin 1

More information

Regional economy upgrading triple helix at work? Some selected cases from the Czech republic (and Central Eastern Europe) Pavel Ptáček

Regional economy upgrading triple helix at work? Some selected cases from the Czech republic (and Central Eastern Europe) Pavel Ptáček Regional economy upgrading triple helix at work? Some selected cases from the Czech republic (and Central Eastern Europe) Pavel Ptáček Department of Geography Palacký University in Olomouc, Czech republic

More information

Supplementary Appendix for. Version: February 3, 2014

Supplementary Appendix for. Version: February 3, 2014 Supplementary Appendix for When Do Governments Resort to Election Violence? Version: February 3, 2014 This appendix provides supplementary information not included in the published draft. Supplementary

More information

Almería 23 rd -25 th October th Joint Workshop of the European Union Reference Laboratories for Residues of Pesticides

Almería 23 rd -25 th October th Joint Workshop of the European Union Reference Laboratories for Residues of Pesticides General European Commission Proficiency Test Scheme EURL-FV Scientific Group Samples and Protocol INFORMATION EUPT Web Page Data Analysis Reports 1 2 3 4 5 ACTIVITY DATE Publishing the Calendar and Matrix

More information

Canadian Imports of Honey

Canadian Imports of Honey of 0409000029 - Honey, natural, in containers of a weight > 5 kg, nes (Kilogram) Argentina 236,716 663,087 2,160,216 761,990 35.27% 202.09% /0 76,819 212,038 717,834 257,569 35.88% 205.69% /0 United States

More information

Refinement of the OECD regional typology: Economic Performance of Remote Rural Regions

Refinement of the OECD regional typology: Economic Performance of Remote Rural Regions [Preliminary draft April 2010] Refinement of the OECD regional typology: Economic Performance of Remote Rural Regions by Lewis Dijkstra* and Vicente Ruiz** Abstract To account for differences among rural

More information

Applying cluster analysis to 2011 Census local authority data

Applying cluster analysis to 2011 Census local authority data Applying cluster analysis to 2011 Census local authority data Kitty.Lymperopoulou@manchester.ac.uk SPSS User Group Conference November, 10 2017 Outline Basic ideas of cluster analysis How to choose variables

More information

Aerospace part number guide

Aerospace part number guide TRELLEBORG SEALING SOLUTIONS Aerospace part number guide YOUR PARTNER FOR SEALING TECHNOLOGY Your Partner for Sealing Technology Trelleborg Sealing Solutions is a major international sealing force, uniquely

More information

RISK ASSESSMENT METHODOLOGIES FOR LANDSLIDES

RISK ASSESSMENT METHODOLOGIES FOR LANDSLIDES RISK ASSESSMENT METHODOLOGIES FOR LANDSLIDES Jean-Philippe MALET Olivier MAQUAIRE CNRS & CERG. Welcome to Paris! 1 Landslide RAMs Landslide RAM A method based on the use of available information to estimate

More information

DISTILLED SPIRITS - IMPORTS BY VALUE DECEMBER 2017

DISTILLED SPIRITS - IMPORTS BY VALUE DECEMBER 2017 DISTILLED SPIRITS - IMPORTS BY VALUE DECEMBER 2017 U.S. DUTIABLE IMPORTS OF DISTILLED SPIRITS (U.S. DOLLARS) Ea-Value-17-12 SUMMARY: IMPORTS ENTERED FOR CONSUMPTION CLASS DECEMBER DECEMBER PERCENT JANUARY

More information

DISTILLED SPIRITS - IMPORTS BY VOLUME DECEMBER 2017

DISTILLED SPIRITS - IMPORTS BY VOLUME DECEMBER 2017 DISTILLED SPIRITS - IMPORTS BY VOLUME DECEMBER 2017 U.S. DUTIABLE IMPORTS OF DISTILLED SPIRITS (PROOF GALLONS) Ea-17-12 SUMMARY: IMPORTS ENTERED FOR CONSUMPTION CLASS DECEMBER DECEMBER PERCENT JANUARY

More information

E-SURFMAR Report. Jean ROLLAND Michel TREMANT Pierre BLOUCH Jon TURTON

E-SURFMAR Report. Jean ROLLAND Michel TREMANT Pierre BLOUCH Jon TURTON E-SURFMAR Report Jean ROLLAND Michel TREMANT Pierre BLOUCH Jon TURTON DBCP 28-Fremantle 2nd-6th October 2012 E-SURFMAR EUMETNET Members 29 European Meteorological Services. Austria, Belgium, Croatia, Cyprus,

More information

The European regional Human Development and Human Poverty Indices Human Development Index

The European regional Human Development and Human Poverty Indices Human Development Index n 02/2011 The European regional Human Development and Human Poverty Indices Contents 1. Introduction...1 2. The United Nations Development Programme Approach...1 3. Regional Human Development and Poverty

More information

This document is a preview generated by EVS

This document is a preview generated by EVS TECHNICAL SPECIFICATION SPÉCIFICATION TECHNIQUE TECHNISCHE SPEZIFIKATION CEN ISO/TS 15883-5 November 2005 ICS 11.080.10 English Version Washer-disinfectors - Part 5: Test soils and methods for demonstrating

More information

Structural equation modeling in evaluation of technological potential of European Union countries in the years

Structural equation modeling in evaluation of technological potential of European Union countries in the years Structural equation modeling in evaluation of technological potential of European Union countries in the years 2008-2012 Adam P. Balcerzak 1, Michał Bernard Pietrzak 2 Abstract The abilities of countries

More information

Unsupervised machine learning

Unsupervised machine learning Chapter 9 Unsupervised machine learning Unsupervised machine learning (a.k.a. cluster analysis) is a set of methods to assign objects into clusters under a predefined distance measure when class labels

More information

About the Authors Geography and Tourism: The Attraction of Place p. 1 The Elements of Geography p. 2 Themes of Geography p. 4 Location: The Where of

About the Authors Geography and Tourism: The Attraction of Place p. 1 The Elements of Geography p. 2 Themes of Geography p. 4 Location: The Where of Preface p. ix About the Authors p. xi Geography and Tourism: The Attraction of Place p. 1 The Elements of Geography p. 2 Themes of Geography p. 4 Location: The Where of Geography p. 4 Place and Space:

More information

Appendix B: Detailed tables showing overall figures by country and measure

Appendix B: Detailed tables showing overall figures by country and measure 44 country and measure % who report that they are very happy Source: World Values Survey, 2010-2014 except United States, Pew Research Center 2012 Gender and Generations survey and Argentina 32% 32% 36%

More information

EUMETSAT Satellite Programmes Use of McIDAS at EUMETSAT

EUMETSAT Satellite Programmes Use of McIDAS at EUMETSAT EUMETSAT Satellite Programmes Use of McIDAS at EUMETSAT Marianne König Peter Miu McIDAS Users' Group Meeting, 07-10 May 2012 Slide 1 EUMETSAT Headquarters Darmstadt McIDAS Users' Group Meeting, 07-10 May

More information

Securing EUMETSAT s Mission from an Evolving Space Environment

Securing EUMETSAT s Mission from an Evolving Space Environment Securing EUMETSAT s Mission from an Evolving Space Environment ESPI 12 th Autumn Conference Andrew Monham 1 EUMETSAT: Intergovernmental Organisation of 30 Member States Presentation Contents AUSTRIA BELGIU

More information

Governments that have requested pre-export notifications pursuant to article 12, paragraph 10 (a), of the 1988 Convention

Governments that have requested pre-export notifications pursuant to article 12, paragraph 10 (a), of the 1988 Convention Annex X Governments that have requested pre-export notifications pursuant to article 12, paragraph 10 (a), of the 1988 Convention 1. Governments of all exporting countries and territories are reminded

More information

E-SURFMAR Report. Jean ROLLAND Gilbert EMZIVAT Pierre BLOUCH Jon TURTON

E-SURFMAR Report. Jean ROLLAND Gilbert EMZIVAT Pierre BLOUCH Jon TURTON E-SURFMAR Report Jean ROLLAND Gilbert EMZIVAT Pierre BLOUCH Jon TURTON DBCP 30 WEIHAI 27-31 October 2014 E-SURFMAR EUMETNET members 31 European Meteorological Services. Austria, Belgium, Croatia, Cyprus,

More information

ICC Rev August 2010 Original: English. Agreement. International Coffee Council 105 th Session September 2010 London, England

ICC Rev August 2010 Original: English. Agreement. International Coffee Council 105 th Session September 2010 London, England ICC 105-7 Rev. 1 31 August 2010 Original: English Agreement E International Coffee Council 105 th Session 21 24 September 2010 London, England Obstacles to consumption Background 1. In accordance with

More information

European regulations for winter equipment on trucks and buses Winter 2015/2016

European regulations for winter equipment on trucks and buses Winter 2015/2016 European regulations for Country Tire regulations Snow chain regulations Further information Albania Snow chains for drive axle must be carried in the vehicle. Use according to traffic signs and road Austria

More information