{"id":4969,"date":"2018-03-22T09:52:57","date_gmt":"2018-03-22T08:52:57","guid":{"rendered":"http:\/\/www.sigterritoires.fr\/?p=4969"},"modified":"2018-10-18T09:16:49","modified_gmt":"2018-10-18T07:16:49","slug":"the-spatial-temporal-cube-of-arcgis-2-hot-and-cold-spots","status":"publish","type":"post","link":"https:\/\/www.sigterritoires.fr\/index.php\/en\/the-spatial-temporal-cube-of-arcgis-2-hot-and-cold-spots\/","title":{"rendered":"The spatial-temporal cube of ArcGis : 2- Hot and Cold Spots"},"content":{"rendered":"

In the previous article (Le Cube spatio-temporel d\u2019ArcGis : 1- d\u00e9couverte<\/a>) we\u00a0discussed how to\u00a0create\u00a0a\u00a0spatial-temporal cube\u00a0from\u00a0a\u00a0cloud\u00a0of XYZ points.<\/p>\n

$\"\"$ \u00a0<\/a> The points\u00a0are\u00a0grouped\u00a0into \u00a0\u00bb\u00a0boxes\u00a0\u00a0\u00bb (bins)\u00a0corresponding\u00a0to 3D pixels.
\nWe\u00a0have\u00a0discussed how\u00a0to depict them in\u00a0an ArcGis Pro\u00a03D scene.\u00a0In\u00a0this\u00a0article we will discuss\u00a0how\u00a0to analyze\u00a0the temporal\u00a0trends\u00a0of the bins\u00a0values,\u00a0using\u00a0the analysis<\/strong>\u00a0of<\/strong>\u00a0emerging hot<\/strong>\u00a0spots<\/strong>.<\/p>\n

$\"\"$ <\/p>\n

The purpose of\u00a0this\u00a0tool\u00a0is to identify\u00a0the values grouping\u00a0trends\u00a0of the cube\u00a0built\u00a0from\u00a0your\u00a0data\u00a0,\u00a0 the so-called \u00ab\u00a0spatial aggregates\u00a0 \u00ab\u00a0.<\/p>\n

For the\u00a0description\u00a0\u00a0\u00a0of\u00a0the\u00a0mathematical method\u00a0that\u00a0 this research\u00a0tool\u00a0relies on\u00a0\u00a0\u00a0(\u00a0Getis\u00a0-Ord\u00a0Gi\u00a0*)\u00a0you\u00a0can\u00a0download t\u00e9l\u00e9charger ici l’article de Getis et Ords. <\/u>Let’s\u00a0just\u00a0say\u00a0here\u00a0that\u00a0the\u00a0research method for\u00a0the\u00a0three\u00a0axes is to\u00a0determine\u00a0wether the\u00a0occurrence values\u00a0of the points\u00a0in\u00a0your\u00a0cube\u00a0can\u00a0be\u00a0considered,\u00a0statistically,\u00a0as\u00a0grouped\u00a0(hot spots)\u00a0or\u00a0not\u00a0grouped (cold spots).<\/p>\n

The\u00a0result\u00a0of the\u00a0method\u00a0entails:<\/p>\n

\n
a\u00a0so\u00a0called\u00a0p-value which\u00a0is\u00a0the\u00a0\u00a0\u00a0probability\u00a0value\u00a0for\u00a0the\u00a0spatial\u00a0distribution\u00a0of dots being due to\u00a0hazard.\u00a0If p-value\u00a0is\u00a0big,\u00a0it\u00a0means\u00a0that\u00a0it is\u00a0very\u00a0likely\u00a0that\u00a0the distribution\u00a0of the 3D pixels\u00a0around\u00a0that point\u00a0is\u00a0simply\u00a0the\u00a0result\u00a0of\u00a0hazard.\u00a0A\u00a0low\u00a0p-value, on the contrary,\u00a0indicates\u00a0that it is very\u00a0likely\u00a0that\u00a0the\u00a0grouping\u00a0is\u00a0not\u00a0random,\u00a0and\u00a0therefore\u00a0the\u00a0result\u00a0of a\u00a0specific phenomenon.<\/li>\n
a\u00a0so\u00a0called\u00a0value z-score which\u00a0is\u00a0a\u00a0standard\u00a0deviation\u00a0value.\u00a0This\u00a0is\u00a0not\u00a0an\u00a0independent\u00a0value\u00a0of the p-value\u00a0but\u00a0a\u00a0complementary\u00a0value.<\/li>\n<\/ul>\n
If\u00a0you\u00a0find a weak\u00a0p-value\u00a0you\u00a0would think that there is a strong probability that\u00a0the\u00a0observed phenomenon\u00a0observed\u00a0be\u00a0significant.<\/p>\n
OK,\u00a0but how strong?\u00a0The z-score\u00a0indicates you than\u00a0if\u00a0this\u00a0value\u00a0is\u00a0more\u00a0\u00a0\u00a0than three\u00a0standard deviations\u00a0from the\u00a0mean\u00a0you\u00a0have\u00a0less\u00a0than 1% chance of\u00a0being mislead.\u00a0If\u00a0it\u00a0is\u00a0between 2\u00a0and\u00a03,\u00a0you\u00a0will have\u00a05% and\u00a0if\u00a0it\u00a0is\u00a0between 1 and 2\u00a0you\u00a0will have\u00a010%. So\u00a0it is up to you depending of the subject and your\u00a0knowledge,\u00a0determine\u00a0the\u00a0acceptable\u00a0risk\u00a0level\u00a0for\u00a0your\u00a0hypothesis. $\"\"$ <\/p>\n
We\u00a0will\u00a0keep working with\u00a0the example\u00a0of\u00a0the previous article\u00a0by using\u00a0the\u00a0cube.\u00a0To\u00a0perform\u00a0the analysis;\u00a0you\u00a0launch\u00a0the other\u00a0command\u00a0available\u00a0in\u00a0the\u00a0toolbox\u00a0Exploration<\/em><\/strong>Tools<\/em><\/strong>\u00a0for<\/em><\/strong> spatial-temporal<\/em><\/strong>\u00a0models, <\/em><\/strong>Analysis of<\/em><\/strong>\u00a0emerging <\/em><\/strong>hot spots<\/em><\/strong>.\u00a0<\/em><\/strong><\/p>\n
$\"\"$ <\/p>\n
The\u00a0first\u00a0three\u00a0fields\u00a0are\u00a0simple, input cube,\u00a0output\u00a0layer\u00a0and, for\u00a0the moment,\u00a0in\u00a0Analysis\u00a0variable\u00a0you\u00a0only have\u00a0one\u00a0choice\u00a0as\u00a0COUNT.<\/strong><\/p>\n
However,\u00a0the\u00a0following\u00a0two\u00a0fields\u00a0can\u00a0be confusing.\u00a0Indeed,\u00a0during\u00a0the construction of the cube,\u00a0in\u00a0the\u00a0previous step,\u00a0there\u00a0were\u00a0two\u00a0similar\u00a0fields.\u00a0These\u00a0fields made it\u00a0possible\u00a0to\u00a0group\u00a0the\u00a0points\u00a0by 3D pixel.\u00a0We had\u00a0defined\u00a0pixels of 40km in X\u00a0and\u00a0Y and 12\u00a0hours\u00a0in Z (time).<\/p>\n
But now this is not the matter.\u00a0Right now\u00a0you\u00a0must\u00a0indicate\u00a0(or\u00a0let\u00a0the\u00a0control\u00a0calculate\u00a0by\u00a0default)\u00a0what\u00a0is what you consider as neighbour of a 3D pixel.\u00a0Do you consider pixels located 200 km apart as neighbours or not?\u00a0Do you consider pixels\u00a0separated\u00a0by\u00a0two\u00a0days\u00a0as\u00a0neighbours\u00a0or\u00a0not?<\/p>\n
Depending\u00a0on\u00a0your\u00a0answer\u00a0(or\u00a0lack of it)\u00a0the\u00a0results\u00a0will\u00a0not\u00a0be\u00a0the\u00a0same.<\/p>\n
If\u00a0you\u00a0do\u00a0not\u00a0fill in\u00a0the fields, the\u00a0calculation\u00a0by\u00a0default\u00a0of XY\u00a0neighbourhood\u00a0is\u00a0a\u00a0little\u00a0obscure. On the other hand, time value by default is 1.<\/p>\n
<\/p>\n
Once the request is completed,\u00a0you\u00a0will find\u00a0the new\u00a0layer\u00a0displayed\u00a0in\u00a0your\u00a02D\u00a0view\u00a0with the\u00a0following\u00a0classification\u00a0:<\/p>\n
$\"\"$ <\/p>\n
To find\u00a0the\u00a0desired results\u00a0you\u00a0have\u00a0two\u00a0groups:<\/p>\n
\n
a\u00a0group\u00a0of \u00ab\u00a0hot spots\u00a0\u00bb, where something is happening<\/li>\n
a\u00a0group\u00a0of \u00ab\u00a0cold spots\u00a0\u00bb, where nothing is happening.<\/li>\n
a\u00a0third\u00a0\u00ab\u00a0group\u00a0\u00bb\u00a0that includes\u00a0the 3D pixels which\u00a0could\u00a0not\u00a0be\u00a0classified\u00a0either as hot\u00a0or\u00a0cold, the \u00ab\u00a0No trend detected\u00a0\u00bb.<\/li>\n<\/ul>\n
<\/p>\n
Then, for\u00a0each\u00a0type (hot\u00a0or\u00a0cold)\u00a0you\u2018ll find\u00a0the 3D pixels\u00a0classified\u00a0according to:<\/p>\n
New<\/strong>\u00a0spot<\/strong>:\u00a0the\u00a0last\u00a03D pixel of the\u00a0temporal series\u00a0appears\u00a0as\u00a0a\u00a0hot\u00a0or\u00a0cold\u00a0spot,\u00a0while\u00a0in\u00a0all the\u00a0rest\u00a0of the temporal steps\u00a0this\u00a0location was\u00a0not considered as either of them.\u00a0These\u00a0are\u00a0the points\u00a0to\u00a0be monitored\u00a0in\u00a0the\u00a0next\u00a0temporal series\u00a0to verify\u00a0if they\u00a0are\u00a0truly\u00a0significant\u00a0points\u00a0or\u00a0not.<\/p>\n
Consecutive<\/strong>\u00a0Spot<\/strong>:A spot with a single uninterrupted run of statistically significant hot spot bins. Less than ninety percent of all bins are statistically significant hot spots.<\/p>\n
Intensifying spot<\/strong>: More than 90% of time steps\u00a0are\u00a0significant\u00a0and\u00a0values\u00a0increase as time increases. The\u00a0last\u00a0pixels\u00a0are\u00a0stronger\u00a0than\u00a0those\u00a0of the beginning.\u00a0The\u00a0last\u00a0time step\u00a0is\u00a0significant.<\/p>\n
Persistent<\/strong>\u00a0\u00a0<\/strong>\u00a0Spot<\/strong>: more than 90% of time steps\u00a0are\u00a0significant\u00a0but there is no increasing or decreasing trend in the temporal series.<\/p>\n
Diminishing<\/strong>\u00a0Spot<\/strong>:\u00a0More than 90% of time steps\u00a0are\u00a0significant\u00a0and\u00a0values\u00a0decrease\u00a0with time.\u00a0The\u00a0last\u00a0pixels\u00a0are\u00a0weaker\u00a0than\u00a0those\u00a0of the beginning.\u00a0The\u00a0last\u00a0time step\u00a0is\u00a0significant<\/p>\n
Sporadic<\/strong>\u00a0\u00a0<\/strong>\u00a0Spot<\/strong>:\u00a0less\u00a0than 90% of time steps\u00a0are\u00a0significant.\u00a0Significant\u00a0time steps\u00a0are\u00a0inserted\u00a0among not\u00a0significant\u00a0time steps.\u00a0If the\u00a0significant\u00a0time steps\u00a0are\u00a0hot spots\u00a0then\u00a0there\u00a0are no\u00a0cold spots\u00a0in\u00a0the series, and vice versa.<\/p>\n
\u00a0<\/strong>Oscillating<\/strong>\u00a0\u00a0<\/strong>\u00a0Spot<\/strong>:\u00a0less\u00a0than 90% of time steps\u00a0are\u00a0significant.\u00a0As\u00a0in the previous category, non-significant time steps\u00a0are\u00a0intercalated\u00a0among\u00a0significant\u00a0steps.\u00a0However,\u00a0in\u00a0the significant\u00a0time steps there are hot\u00a0as well as cold\u00a0spots.<\/p>\n
Historical<\/strong>\u00a0\u00a0\u00a0Spot<\/strong>: The most\u00a0recent\u00a0period\u00a0is\u00a0not significant,\u00a0but\u00a0at\u00a0least\u00a0ninety percent\u00a0of the time\u00a0intervals\u00a0have\u00a0been\u00a0hot\u00a0or\u00a0cold\u00a0spots statistically\u00a0significant.<\/p>\n
These\u00a0results\u00a0apply\u00a0to\u00a0each\u00a0temporal series\u00a0of the cube,\u00a0i.e.\u00a0at\u00a0each\u00a0column\u00a0of\u00a0it.\u00a0Therefore this\u00a0representation\u00a0is,\u00a0inevitably\u00a0in\u00a0two\u00a0dimensions.<\/p>\n
On the other hand,\u00a0each\u00a0time\u00a0series can\u00a0be\u00a0either significant\u00a0or\u00a0not,\u00a0and\u00a0with\u00a0one,\u00a0two\u00a0or\u00a0three\u00a0standard\u00a0deviations.\u00a0So, we\u00a0can\u00a0visualize\u00a0these\u00a0results\u00a0with\u00a0the\u00a03D visualization\u00a0tool\u00a0of the\u00a0spatial-temporal\u00a0cube (see previous article of this topic).<\/p>\n
You\u00a0must\u00a0have\u00a0a\u00a03D\u00a0window\u00a0(Scene)\u00a0in\u00a0your\u00a0project.\u00a0If\u00a0you\u00a0do\u00a0not,\u00a0click<\/p>\n
Insert\u00a0->-New Scene.<\/p>\n
You\u00a0must\u00a0remove\u00a0the\u00a0reference\u00a0to\u00a0a\u00a0layer\u00a0of elevation.\u00a0If you don\u2019t, the\u00a0cube columns\u00a0will be\u00a0displayed\u00a0relative to\u00a0the\u00a0ground\u00a0level\u00a0and\u00a0you will\u00a0lose\u00a0visibility\u00a0of the\u00a0correspondence\u00a0of\u00a0the different\u00a0time steps.<\/p>\n
In\u00a0the geoprocessor\u00a0window,\u00a0launch\u00a0the\u00a03D display\u00a0control.<\/p>\n
$\"\"$ <\/p>\n
<\/p>\n
Compared to the\u00a0same\u00a0order\u00a0launched\u00a0in\u00a0previous\u00a0article,\u00a0we\u00a0have made\u00a0an\u00a0analysis of\u00a0the hot\u00a0spots\u00a0in\u00a0the\u00a0\u00ab\u00a0Variable Display\u00a0\u00bb\u00a0window;\u00a0in addition to COUNT we\u00a0find\u00a0and select \u00ab\u00a0Hot and Cold Spot results\u201d.<\/p>\n
The\u00a0result\u00a0of the\u00a0order\u00a0is displayed: $\"\"$ <\/p>\n
And\u00a0the\u00a0window\u00a0key let us\u00a0see\u00a0which\u00a0are\u00a0the\u00a0displayed\u00a0classes:<\/p>\n
The\u00a0hot\u00a0spots\u00a0in red,\u00a0the cold\u00a0spots\u00a0in blue, and\u00a0with different colour intensity\u00a0that\u00a0denotes the\u00a0confidence\u00a0of the\u00a0results: one\u00a0standard deviation\u00a0= 90%, two\u00a0standard deviations\u00a0= 95%,\u00a0three\u00a0standard deviations\u00a0= 99%.<\/p>\n
With\u00a0these\u00a0two\u00a0articles\u00a0you\u00a0have\u00a0something to start\u00a0trying\u00a0the<\/p>\n
spatial-temporal analysis. In a future article we will discuss the\u00a0different\u00a0pre-processing\u00a0data\u00a0techniques to be used with\u00a0these two\u00a0tools.<\/p>\n","protected":false},"excerpt":{"rendered":"
In the previous article (Le Cube spatio-temporel d\u2019ArcGis : 1- d\u00e9couverte) we\u00a0discussed how to\u00a0create\u00a0a\u00a0spatial-temporal cube\u00a0from\u00a0a\u00a0cloud\u00a0of XYZ points. \u00a0 The points\u00a0are\u00a0grouped\u00a0into \u00a0\u00bb\u00a0boxes\u00a0\u00a0\u00bb (bins)\u00a0corresponding\u00a0to 3D pixels. We\u00a0have\u00a0discussed how\u00a0to depict them in\u00a0an ArcGis Pro\u00a03D scene.\u00a0In\u00a0this\u00a0article we will discuss\u00a0how\u00a0to analyze\u00a0the…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"sfsi_plus_gutenberg_text_before_share":"","sfsi_plus_gutenberg_show_text_before_share":"","sfsi_plus_gutenberg_icon_type":"","sfsi_plus_gutenberg_icon_alignemt":"","sfsi_plus_gutenburg_max_per_row":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[1260],"tags":[],"class_list":["post-4969","post","type-post","status-publish","format-standard","hentry","category-non-classe-en"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t