{"id":810,"date":"2019-09-26T10:37:43","date_gmt":"2019-09-26T10:37:43","guid":{"rendered":"http:\/\/kios.ece.ucy.ac.cy\/?post_type=kbe_knowledgebase&#038;p=810"},"modified":"2019-10-03T08:35:48","modified_gmt":"2019-10-03T08:35:48","slug":"%ce%b1%ce%bd%ce%ac%ce%ba%cf%84%ce%b7%cf%83%ce%b7-%cf%87%ce%b1%ce%bc%ce%ad%ce%bd%cf%89%ce%bd-%ce%bc%ce%b5%cf%84%cf%81%ce%ae%cf%83%ce%b5%cf%89%ce%bd-recovery-of-missing-values","status":"publish","type":"kbe_knowledgebase","link":"https:\/\/www.smartwater2020.eu\/?kbe_knowledgebase=%ce%b1%ce%bd%ce%ac%ce%ba%cf%84%ce%b7%cf%83%ce%b7-%cf%87%ce%b1%ce%bc%ce%ad%ce%bd%cf%89%ce%bd-%ce%bc%ce%b5%cf%84%cf%81%ce%ae%cf%83%ce%b5%cf%89%ce%bd-recovery-of-missing-values","title":{"rendered":"\u0391\u03bd\u03ac\u03ba\u03c4\u03b7\u03c3\u03b7 \u03a7\u03b1\u03bc\u03ad\u03bd\u03c9\u03bd \u039c\u03b5\u03c4\u03c1\u03ae\u03c3\u03b5\u03c9\u03bd\/ Recovery of Missing Values"},"content":{"rendered":"<p>\u039f\u03b9 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\u03b4\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03c9\u03bd, \u03c3\u03c5\u03c7\u03bd\u03ac \u03b1\u03c0\u03b1\u03b9\u03c4\u03b5\u03af\u03c4\u03b1\u03b9 \u03b7 \u03b1\u03cd\u03be\u03b7\u03c3\u03b7 \u03c4\u03b7\u03c2 \u03c7\u03c1\u03bf\u03bd\u03b9\u03ba\u03ae\u03c2 \u03b1\u03bd\u03ac\u03bb\u03c5\u03c3\u03b7\u03c2 \u03c4\u03c9\u03bd \u03c3\u03b7\u03bc\u03ac\u03c4\u03c9\u03bd, \u03c0\u03c1\u03bf\u03ba\u03b5\u03b9\u03bc\u03ad\u03bd\u03bf\u03c5 \u03bd\u03b1 \u03b5\u03c0\u03b5\u03be\u03b5\u03c1\u03b3\u03b1\u03c3\u03c4\u03bf\u03cd\u03bd \u03c3\u03b5 \u03bc\u03b9\u03b1 \u03c5\u03c8\u03b7\u03bb\u03cc\u03c4\u03b5\u03c1\u03b7 \u03c3\u03c5\u03c7\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 \u03b1\u03c0\u03cc \u03b5\u03ba\u03b5\u03af\u03bd\u03b7 \u03c3\u03c4\u03b7\u03bd \u03bf\u03c0\u03bf\u03af\u03b1 \u03b4\u03b5\u03b9\u03b3\u03bc\u03b1\u03c4\u03bf\u03bb\u03b5\u03b9\u03c0\u03c4\u03bf\u03cd\u03bd\u03c4\u03b1\u03b9. \u0388\u03bd\u03b1\u03c2 \u03c4\u03c1\u03cc\u03c0\u03bf\u03c2 \u03b5\u03c0\u03af\u03bb\u03c5\u03c3\u03b7\u03c2 \u03b1\u03c5\u03c4\u03bf\u03cd \u03c4\u03bf\u03c5 \u03c0\u03c1\u03bf\u03b2\u03bb\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03b1\u03bd\u03b1\u03b3\u03c9\u03b3\u03ae \u03c4\u03bf\u03c5 \u03c3\u03b5 \u03ad\u03bd\u03b1 \u03c0\u03c1\u03cc\u03b2\u03bb\u03b7\u03bc\u03b1 \u03b1\u03bd\u03ac\u03ba\u03c4\u03b7\u03c3\u03b7\u03c2 \u03b4\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03c9\u03bd , \u03cc\u03c0\u03bf\u03c5 \u03bf\u03b9 \u03bc\u03b7 \u03ba\u03b1\u03c4\u03b1\u03b3\u03b5\u03b3\u03c1\u03b1\u03bc\u03bc\u03ad\u03bd\u03b5\u03c2 \u03bc\u03b5\u03c4\u03c1\u03ae\u03c3\u03b5\u03b9\u03c2 \u03b5\u03b9\u03c3\u03ac\u03b3\u03bf\u03bd\u03c4\u03b1\u03b9 \u03bc\u03b5 \u03b4\u03bf\u03bc\u03b7\u03bc\u03ad\u03bd\u03bf \u03c4\u03c1\u03cc\u03c0\u03bf.<\/p>\n<p>\u0397 \u03b5\u03be\u03b1\u03b3\u03c9\u03b3\u03ae \u03c3\u03c5\u03bc\u03c0\u03b5\u03c1\u03b1\u03c3\u03bc\u03ac\u03c4\u03c9\u03bd \u03b1\u03bd\u03b1\u03c6\u03bf\u03c1\u03b9\u03ba\u03ac \u03bc\u03b5 \u03c4\u03b7\u03bd \u03ba\u03b1\u03c4\u03ac\u03c3\u03c4\u03b1\u03c3\u03b7 \u03c4\u03bf\u03c5 \u03c5\u03c0\u03cc \u03c0\u03b1\u03c1\u03b1\u03ba\u03bf\u03bb\u03bf\u03cd\u03b8\u03b7\u03c3\u03b7 \u03c0\u03b5\u03c1\u03b9\u03b2\u03ac\u03bb\u03bb\u03bf\u03bd\u03c4\u03bf\u03c2 \u03c0\u03c1\u03bf\u03cb\u03c0\u03bf\u03b8\u03ad\u03c4\u03b5\u03b9 \u03c4\u03b7\u03bd \u03c0\u03bb\u03b7\u03c1\u03cc\u03c4\u03b7\u03c4\u03b1 \u03c4\u03c9\u03bd \u03bb\u03b1\u03bc\u03b2\u03b1\u03bd\u03cc\u03bc\u03b5\u03bd\u03c9\u03bd \u03b4\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03c9\u03bd. \u039b\u03cc\u03b3\u03c9 \u03c4\u03c9\u03bd \u03b4\u03b9\u03b1\u03c6\u03cc\u03c1\u03c9\u03bd \u03b1\u03b9\u03c4\u03b9\u03ce\u03bd \u03c0\u03bf\u03c5 \u03b1\u03bd\u03b1\u03c6\u03ad\u03c1\u03b8\u03b7\u03ba\u03b1\u03bd \u03c0\u03b1\u03c1\u03b1\u03c0\u03ac\u03bd\u03c9, \u03bf\u03b9 \u03c0\u03af\u03bd\u03b1\u03ba\u03b5\u03c2 \u03c4\u03c9\u03bd \u03bc\u03b5\u03c4\u03c1\u03ae\u03c3\u03b5\u03c9\u03bd \u03b5\u03bd\u03b4\u03ad\u03c7\u03b5\u03c4\u03b1\u03b9 \u03bd\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b5\u03bb\u03bb\u03b9\u03c0\u03b5\u03af\u03c2, \u03c4\u03bf \u03bf\u03c0\u03bf\u03af\u03bf \u03b5\u03b3\u03b5\u03af\u03c1\u03b5\u03b9 \u03c4\u03b7\u03bd \u03b1\u03bd\u03ac\u03b3\u03ba\u03b7 \u03b3\u03b9\u03b1 \u03b1\u03bd\u03ac\u03ba\u03c4\u03b7\u03c3\u03b7 \u03c4\u03c9\u03bd \u03c7\u03b1\u03bc\u03ad\u03bd\u03c9\u03bd \u03bc\u03b5\u03c4\u03c1\u03ae\u03c3\u03b5\u03c9\u03bd (\u03b4\u03b7\u03bb. \u03c4\u03c9\u03bd \u03ba\u03b5\u03bd\u03ce\u03bd \u03b8\u03ad\u03c3\u03b5\u03c9\u03bd \u03c3\u03c4\u03bf\u03bd \u03c0\u03af\u03bd\u03b1\u03ba\u03b1 \u03bc\u03b5\u03c4\u03c1\u03ae\u03c3\u03b5\u03c9\u03bd) \u03c0\u03c1\u03b9\u03bd \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u03b5\u03c0\u03b5\u03be\u03b5\u03c1\u03b3\u03b1\u03c3\u03af\u03b1 \u03c4\u03c9\u03bd \u03b4\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03c9\u03bd. \u0395\u03c0\u03b9\u03c0\u03bb\u03ad\u03bf\u03bd, \u03b3\u03b9\u03b1 \u03c1\u03bf\u03ad\u03c2 \u03b4\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03c9\u03bd \u03c4\u03c9\u03bd \u03bf\u03c0\u03bf\u03af\u03c9\u03bd \u03b7 \u03c3\u03c5\u03c3\u03c7\u03ad\u03c4\u03b9\u03c3\u03b7 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c5\u03c8\u03b7\u03bb\u03ae, \u03bc\u03c0\u03bf\u03c1\u03bf\u03cd\u03bd \u03bd\u03b1 \u03b5\u03c6\u03b1\u03c1\u03bc\u03bf\u03c3\u03b8\u03bf\u03cd\u03bd \u03c0\u03b9\u03bf \u03b5\u03be\u03b5\u03bb\u03b9\u03b3\u03bc\u03ad\u03bd\u03bf\u03b9 \u03b1\u03bb\u03b3\u03cc\u03c1\u03b9\u03b8\u03bc\u03bf\u03b9 \u03b1\u03bd\u03ac\u03ba\u03c4\u03b7\u03c3\u03b7\u03c2 \u03c4\u03b9\u03bc\u03ce\u03bd. \u03a3\u03c5\u03b3\u03ba\u03b5\u03ba\u03c1\u03b9\u03bc\u03ad\u03bd\u03b1, \u03b3\u03b9\u03b1 \u03ba\u03ac\u03b8\u03b5 \u03c1\u03bf\u03ae \u03b4\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03c9\u03bd \u03bc\u03b5 \u03b5\u03bb\u03bb\u03b9\u03c0\u03b5\u03af\u03c2 \u03bc\u03b5\u03c4\u03c1\u03ae\u03c3\u03b5\u03b9\u03c2 \u03b4\u03b7\u03bc\u03b9\u03bf\u03c5\u03c1\u03b3\u03b5\u03af\u03c4\u03b1\u03b9 \u03ba\u03b1\u03c4\u03ac\u03bb\u03bb\u03b7\u03bb\u03bf\u03c2 \u03c0\u03af\u03bd\u03b1\u03ba\u03b1\u03c2 (\u03bb\u03b5\u03b9\u03c4\u03bf\u03c5\u03c1\u03b3\u03af\u03b1 Hankelization), \u03bf \u03c3\u03c5\u03bd\u03b4\u03c5\u03b1\u03c3\u03bc\u03cc\u03c2 \u03c4\u03c9\u03bd \u03bf\u03c0\u03bf\u03af\u03c9\u03bd \u03c0\u03b1\u03c1\u03ac\u03b3\u03b5\u03b9 \u03ad\u03bd\u03b1 \u03c4\u03b1\u03bd\u03c5\u03c3\u03c4\u03ae 3\u03b7\u03c2 \u03c4\u03ac\u03be\u03b7\u03c2. \u0397 \u03c3\u03c5\u03bc\u03c0\u03bb\u03ae\u03c1\u03c9\u03c3\u03b7 \u03c4\u03c9\u03bd \u03bc\u03b7 \u03ba\u03b1\u03c4\u03b1\u03b3\u03b5\u03b3\u03c1\u03b1\u03bc\u03bc\u03ad\u03bd\u03c9\u03bd \u03c3\u03c4\u03bf\u03b9\u03c7\u03b5\u03af\u03c9\u03bd \u03b1\u03c5\u03c4\u03bf\u03cd \u03c4\u03bf\u03c5 \u03c4\u03b1\u03bd\u03c5\u03c3\u03c4\u03ae \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03bf\u03c0\u03bf\u03b9\u03b5\u03af\u03c4\u03b1\u03b9 \u03bc\u03ad\u03c3\u03c9 \u03ba\u03b1\u03c4\u03ac\u03bb\u03bb\u03b7\u03bb\u03c9\u03bd \u03b1\u03bb\u03b3\u03bf\u03c1\u03af\u03b8\u03bc\u03c9\u03bd \u03c3\u03c5\u03bc\u03c0\u03bb\u03ae\u03c1\u03c9\u03c3\u03b7\u03c2 \u03c4\u03b1\u03bd\u03c5\u03c3\u03c4\u03ce\u03bd. \u03a3\u03c4\u03b7 \u03c3\u03c5\u03bd\u03ad\u03c7\u03b5\u03b9\u03b1, \u03bf\u03b9 \u03b1\u03bd\u03c4\u03af\u03c3\u03c4\u03c1\u03bf\u03c6\u03b5\u03c2 \u03b4\u03b9\u03b1\u03b4\u03b9\u03ba\u03b1\u03c3\u03af\u03b5\u03c2 \u03bb\u03b1\u03bc\u03b2\u03ac\u03bd\u03bf\u03c5\u03bd \u03c7\u03ce\u03c1\u03b1, \u03cc\u03c0\u03c9\u03c2 \u03bf \u03b4\u03b9\u03b1\u03c7\u03c9\u03c1\u03b9\u03c3\u03bc\u03cc\u03c2 \u03c4\u03c9\u03bd \u00ab\u03c4\u03b5\u03bc\u03b1\u03c7\u03af\u03c9\u03bd\u00bb \u03c4\u03bf\u03c5 \u03c4\u03b1\u03bd\u03c5\u03c3\u03c4\u03ae \u03ba\u03b1\u03b9 \u03b7 \u03bc\u03b5\u03c4\u03b1\u03c4\u03c1\u03bf\u03c0\u03ae \u03c4\u03bf\u03c5 \u03ba\u03ac\u03b8\u03b5 \u03c4\u03b5\u03bc\u03b1\u03c7\u03af\u03bf\u03c5 \u03b1\u03c0\u03cc \u03c0\u03af\u03bd\u03b1\u03ba\u03b1 \u03c3\u03b5 \u03b4\u03b9\u03ac\u03bd\u03c5\u03c3\u03bc\u03b1, \u03c0\u03c1\u03bf\u03ba\u03b5\u03b9\u03bc\u03ad\u03bd\u03bf\u03c5 \u03bd\u03b1 \u03b1\u03bd\u03b1\u03ba\u03c4\u03b7\u03b8\u03bf\u03cd\u03bd \u03bf\u03b9 \u03c0\u03bb\u03ae\u03c1\u03b5\u03b9\u03c2, \u03c0\u03bb\u03ad\u03bf\u03bd, \u03c1\u03bf\u03ad\u03c2 \u03b4\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03c9\u03bd.<\/p>\n<p>The limitations to which wireless sensors are subject often lead to the occurrence of non-recorded measurements. As missing we consider those measurements whose value is not stored in the measurement matrix. Specifically, the underlying causes for their occurrence are related to a sensor malfunction during the measurement\u2019s recording, or to a network failure during its transmission. Another cause could be attributed to the synchronization of data streams sampled at different frequencies. Furthermore, when processing the received data at the control center, it is often necessary to increase the temporal resolution of the signals, in order to process them at a higher frequency than that at which they were sampled. A typical way to address this problem is to reduce it into a missing data recovery problem, where the missing values are introduced in a structured way.<\/p>\n<p>Extracting conclusions regarding the condition of the monitored environment requires the completeness of the received data. However, due to the various causes mentioned before, the measurement matrices may be incomplete, which triggers the need for missing values recovery (i.e., of the missing matrix elements) before their subsequent processing. In addition, for highly correlated data streams, more sophisticated recovery algorithms can be applied. Specifically, an appropriate matrix is created for each data stream with missing values (Hankelization process), whose concatenation yields a 3rd order tensor. The completion of this tensor\u2019s missing entries is carried out by employing advanced tensor completion algorithms. Subsequently, the reverse processes are performed, such as separation of the tensor\u2019s \u201cslices\u201d and the reshaping of each slice into a vector, in order to obtain the completed data streams.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<div class=\"entry-summary\">\n<div class=\"entry-summary\">\n\u039f\u03b9 \u03c0\u03b5\u03c1\u03b9\u03bf\u03c1\u03b9\u03c3\u03bc\u03bf\u03af \u03c3\u03c4\u03bf\u03c5\u03c2 \u03bf\u03c0\u03bf\u03af\u03bf\u03c5\u03c2 \u03c5\u03c0\u03cc\u03ba\u03b5\u03b9\u03bd\u03c4\u03b1\u03b9 \u03c4\u03b1 \u03b1\u03c3\u03cd\u03c1\u03bc\u03b1\u03c4\u03b1 \u03b4\u03af\u03ba\u03c4\u03c5\u03b1 \u03b1\u03b9\u03c3\u03b8\u03b7\u03c4\u03ae\u03c1\u03c9\u03bd \u03bf\u03b4\u03b7\u03b3\u03bf\u03cd\u03bd \u03c3\u03c5\u03c7\u03bd\u03ac \u03c3\u03c4\u03b7\u03bd \u03b5\u03bc\u03c6\u03ac\u03bd\u03b9\u03c3\u03b7 \u03bc\u03b7 \u03ba\u03b1\u03c4\u03b1\u03b3\u03b5\u03b3\u03c1\u03b1\u03bc\u03bc\u03ad\u03bd\u03c9\u03bd \u03bc\u03b5\u03c4\u03c1\u03ae\u03c3\u03b5\u03c9\u03bd. \u03a9\u03c2 \u03bc\u03b7 \u03ba\u03b1\u03c4\u03b1\u03b3\u03b5\u03b3\u03c1\u03b1\u03bc\u03bc\u03ad\u03bd\u03b5\u03c2 \u03b8\u03b5\u03c9\u03c1\u03bf\u03cd\u03bc\u03b5 \u03c4\u03b9\u03c2 \u03bc\u03b5\u03c4\u03c1\u03ae\u03c3\u03b5\u03b9\u03c2 \u03b7 \u03c4\u03b9\u03bc\u03ae \u03c4\u03c9\u03bd \u03bf\u03c0\u03bf\u03af\u03c9\u03bd \u03b4\u03b5\u03bd \u03ad\u03c7\u03b5\u03b9 \u03b1\u03c0\u03bf\u03b8\u03b7\u03ba\u03b5\u03c5\u03c4\u03b5\u03af \u03c3\u03c4\u03bf\u03bd \u03c0\u03af\u03bd\u03b1\u03ba\u03b1 \u03bc\u03b5\u03c4\u03c1\u03ae\u03c3\u03b5\u03c9\u03bd. \u03a3\u03c5\u03b3\u03ba\u03b5\u03ba\u03c1\u03b9\u03bc\u03ad\u03bd\u03b1, \u03bf\u03b9 \u03b2\u03b1\u03c3\u03b9\u03ba\u03ad\u03c2 \u03b1\u03b9\u03c4\u03af\u03b5\u03c2 \u03b5\u03bc\u03c6\u03ac\u03bd\u03b9\u03c3\u03ae\u03c2 \u03c4\u03bf\u03c5\u03c2 \u03c3\u03c5\u03bd\u03b4\u03ad\u03bf\u03bd\u03c4\u03b1\u03b9 \u03bc\u03b5&hellip;\n<\/div>\n<\/div>\n","protected":false},"author":2,"featured_media":811,"comment_status":"open","ping_status":"closed","template":"","kbe_taxonomy":[97],"kbe_tags":[],"class_list":["post-810","kbe_knowledgebase","type-kbe_knowledgebase","status-publish","has-post-thumbnail","hentry","kbe_taxonomy-97","entry"],"aioseo_notices":[],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.smartwater2020.eu\/index.php?rest_route=\/wp\/v2\/kbe_knowledgebase\/810","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.smartwater2020.eu\/index.php?rest_route=\/wp\/v2\/kbe_knowledgebase"}],"about":[{"href":"https:\/\/www.smartwater2020.eu\/index.php?rest_route=\/wp\/v2\/types\/kbe_knowledgebase"}],"author":[{"embeddable":true,"href":"https:\/\/www.smartwater2020.eu\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.smartwater2020.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=810"}],"version-history":[{"count":1,"href":"https:\/\/www.smartwater2020.eu\/index.php?rest_route=\/wp\/v2\/kbe_knowledgebase\/810\/revisions"}],"predecessor-version":[{"id":812,"href":"https:\/\/www.smartwater2020.eu\/index.php?rest_route=\/wp\/v2\/kbe_knowledgebase\/810\/revisions\/812"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.smartwater2020.eu\/index.php?rest_route=\/wp\/v2\/media\/811"}],"wp:attachment":[{"href":"https:\/\/www.smartwater2020.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=810"}],"wp:term":[{"taxonomy":"kbe_taxonomy","embeddable":true,"href":"https:\/\/www.smartwater2020.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fkbe_taxonomy&post=810"},{"taxonomy":"kbe_tags","embeddable":true,"href":"https:\/\/www.smartwater2020.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fkbe_tags&post=810"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}