Constrained self-organizing feature map to preserve feature extraction topology

In many classification problems, it is necessary to consider the specific location of an n-dimensional space from which features have been calculated. For example, considering the location of features extracted from specific areas of a two-dimensional space, as an image, could improve the understanding of a scene for a video surveillance system. In the same way, the same features extracted from different locations could mean different actions for a 3D HCI system. In this paper, we present a self-organizing feature map able to preserve the topology of locations of an n-dimensional space in which the vector of features have been extracted. The main contribution is to implicitly preserving the topology of the original space because considering the locations of the extracted features and their topology could ease the solution to certain problems. Specifically, the paper proposes the n-dimensional constrained self-organizing map preserving the input topology (nD-SOM-PINT). Features in adjacent areas of the n-dimensional space, used to extract the feature vectors, are explicitly in adjacent areas of the nD-SOM-PINT constraining the neural network structure and learning. As a study case, the neural network has been instantiate to represent and classify features as trajectories extracted from a sequence of images into a high level of semantic understanding. Experiments have been thoroughly carried out using the CAVIAR datasets (Corridor, Frontal and Inria) taken into account the global behaviour of an individual in order to validate the ability to preserve the topology of the two-dimensional space to obtain high-performance classification for trajectory classification in contrast of non-considering the location of features. Moreover, a brief example has been included to focus on validate the nD-SOM-PINT proposal in other domain than the individual trajectory. Results confirm the high accuracy of the nD-SOM-PINT outperforming previous methods aimed to classify the same datasets.

Letter from William Croswell to R. Nicholson, 1820 January 13

Draft of a one-page letter to Nicholson, a Liverpool mathematics teacher, which accompanied copies of Croswell's Mercator map.

World Map Showing Routes of Exploration and Discovery, 1790 (Image 1 of 8) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Chart of the world on Mercators projection : exhibiting all the new discoveries to the present time, with the tracks of the most distinguished navigators since the year 1700 carefully collected from the best charts, maps, voyages, &c. extant and regulated from the accurate astronomical observations made in three voyages performed under the command of Captn. James Cook in the years 1768, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79 & 80, compiled and published by A. Arrowsmith, geographer; by permission of Simon McTavish Esq[r] is correctly delineated the discoveries of Mr. McKenzie laid down from his original journal in the year 1789. It was published by A. Arrowsmith, April 1, 1790. Scale [ca. 1:20,000,000]. This layer is image 1 of 8 total images of the seven sheet source map. Covers portions of eastern Asia, Siberia, Russia, Pacific Islands, and western portions of Canada and the United States including Alaska. The image inside the map neatline is georeferenced to the surface of the earth and fit to a non-standard 'World Mercator' projection, with the central meridian at 180 degrees west. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. Note: The central meridian of this map is not the same as the Prime Meridian and may wrap the International Date Line or overlap itself when displayed in GIS software. This map shows features such as drainage, cities and other human settlements, territorial boundaries, shoreline features, and more. Relief shown by hachures. Depths shown by soundings. Includes routes, locations, and dates of James Cook's voyages. This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection and the Harvard University Library as part of the Open Collections Program at Harvard University project: Organizing Our World: Sponsored Exploration and Scientific Discovery in the Modern Age. Maps selected for the project correspond to various expeditions and represent a range of regions, originators, ground condition dates, scales, and purposes.

World Map Showing Routes of Exploration and Discovery, 1790 (Image 2 of 8) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Chart of the world on Mercators projection : exhibiting all the new discoveries to the present time, with the tracks of the most distinguished navigators since the year 1700 carefully collected from the best charts, maps, voyages, &c. extant and regulated from the accurate astronomical observations made in three voyages performed under the command of Captn. James Cook in the years 1768, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79 & 80, compiled and published by A. Arrowsmith, geographer; by permission of Simon McTavish Esq[r] is correctly delineated the discoveries of Mr. McKenzie laid down from his original journal in the year 1789. It was published by A. Arrowsmith, April 1, 1790. Scale [ca. 1:20,000,000]. This layer is image 2 of 8 total images of the seven sheet source map. Covers portions of Europe, Northern Africa, and Asia. The image inside the map neatline is georeferenced to the surface of the earth and fit to the 'World Mercator' projection. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as drainage, cities and other human settlements, territorial boundaries, shoreline features, and more. Relief shown by hachures. Depths shown by soundings. Includes routes, locations, and dates of James Cook's voyages. This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection and the Harvard University Library as part of the Open Collections Program at Harvard University project: Organizing Our World: Sponsored Exploration and Scientific Discovery in the Modern Age. Maps selected for the project correspond to various expeditions and represent a range of regions, originators, ground condition dates, scales, and purposes.

World Map Showing Routes of Exploration and Discovery, 1790 (Image 3 of 8) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Chart of the world on Mercators projection : exhibiting all the new discoveries to the present time, with the tracks of the most distinguished navigators since the year 1700 carefully collected from the best charts, maps, voyages, &c. extant and regulated from the accurate astronomical observations made in three voyages performed under the command of Captn. James Cook in the years 1768, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79 & 80, compiled and published by A. Arrowsmith, geographer; by permission of Simon McTavish Esq[r] is correctly delineated the discoveries of Mr. McKenzie laid down from his original journal in the year 1789. It was published by A. Arrowsmith, April 1, 1790. Scale [ca. 1:20,000,000]. This layer is image 3 of 8 total images of the seven sheet source map. Covers portions of South America, the South Pacific and the South Atlantic. The image inside the map neatline is georeferenced to the surface of the earth and fit to the 'World Mercator' projection. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as drainage, cities and other human settlements, territorial boundaries, shoreline features, and more. Relief shown by hachures. Depths shown by soundings. Includes routes, locations, and dates of James Cook's voyages. This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection and the Harvard University Library as part of the Open Collections Program at Harvard University project: Organizing Our World: Sponsored Exploration and Scientific Discovery in the Modern Age. Maps selected for the project correspond to various expeditions and represent a range of regions, originators, ground condition dates, scales, and purposes.

World Map Showing Routes of Exploration and Discovery, 1790 (Image 5 of 8) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Chart of the world on Mercators projection : exhibiting all the new discoveries to the present time, with the tracks of the most distinguished navigators since the year 1700 carefully collected from the best charts, maps, voyages, &c. extant and regulated from the accurate astronomical observations made in three voyages performed under the command of Captn. James Cook in the years 1768, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79 & 80, compiled and published by A. Arrowsmith, geographer; by permission of Simon McTavish Esq[r] is correctly delineated the discoveries of Mr. McKenzie laid down from his original journal in the year 1789. It was published by A. Arrowsmith, April 1, 1790. Scale [ca. 1:20,000,000]. This layer is image 5 of 8 total images of the seven sheet source map. Covers portions of North America, northern South America, and the western coasts of Europe and Africa. The image inside the map neatline is georeferenced to the surface of the earth and fit to the 'World Mercator' projection. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as drainage, cities and other human settlements, territorial boundaries, shoreline features, and more. Relief shown by hachures. Depths shown by soundings. Includes routes, locations, and dates of James Cook's voyages. This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection and the Harvard University Library as part of the Open Collections Program at Harvard University project: Organizing Our World: Sponsored Exploration and Scientific Discovery in the Modern Age. Maps selected for the project correspond to various expeditions and represent a range of regions, originators, ground condition dates, scales, and purposes.

World Map Showing Routes of Exploration and Discovery, 1790 (Image 4 of 8) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Chart of the world on Mercators projection : exhibiting all the new discoveries to the present time, with the tracks of the most distinguished navigators since the year 1700 carefully collected from the best charts, maps, voyages, &c. extant and regulated from the accurate astronomical observations made in three voyages performed under the command of Captn. James Cook in the years 1768, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79 & 80, compiled and published by A. Arrowsmith, geographer; by permission of Simon McTavish Esq[r] is correctly delineated the discoveries of Mr. McKenzie laid down from his original journal in the year 1789. It was published by A. Arrowsmith, April 1, 1790. Scale [ca. 1:20,000,000]. This layer is image 4 of 8 total images of the seven sheet source map. Covers portions of Southern Africa, Southeast Asia, Western Australia, and the Indian Ocean. The image inside the map neatline is georeferenced to the surface of the earth and fit to the 'World Mercator' projection. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as drainage, cities and other human settlements, territorial boundaries, shoreline features, and more. Relief shown by hachures. Depths shown by soundings. Includes routes, locations, and dates of James Cook's voyages. This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection and the Harvard University Library as part of the Open Collections Program at Harvard University project: Organizing Our World: Sponsored Exploration and Scientific Discovery in the Modern Age. Maps selected for the project correspond to various expeditions and represent a range of regions, originators, ground condition dates, scales, and purposes.

World Map Showing Routes of Exploration and Discovery, 1790 (Image 6 of 8) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Chart of the world on Mercators projection : exhibiting all the new discoveries to the present time, with the tracks of the most distinguished navigators since the year 1700 carefully collected from the best charts, maps, voyages, &c. extant and regulated from the accurate astronomical observations made in three voyages performed under the command of Captn. James Cook in the years 1768, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79 & 80, compiled and published by A. Arrowsmith, geographer; by permission of Simon McTavish Esq[r] is correctly delineated the discoveries of Mr. McKenzie laid down from his original journal in the year 1789. It was published by A. Arrowsmith, April 1, 1790. Scale [ca. 1:20,000,000]. This layer is image 6 of 8 total images of the seven sheet source map. Covers portions of Australia, Southeast Asia, and the South Pacific Ocean. The image inside the map neatline is georeferenced to the surface of the earth and fit to a non-standard 'World Mercator' projection, with the central meridian at 180 degrees west. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. Note: The central meridian of this map is not the same as the Prime Meridian and may wrap the International Date Line or overlap itself when displayed in GIS software. This map shows features such as drainage, cities and other human settlements, territorial boundaries, shoreline features, and more. Relief shown by hachures. Depths shown by soundings. Includes routes, locations, and dates of James Cook's voyages. This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection and the Harvard University Library as part of the Open Collections Program at Harvard University project: Organizing Our World: Sponsored Exploration and Scientific Discovery in the Modern Age. Maps selected for the project correspond to various expeditions and represent a range of regions, originators, ground condition dates, scales, and purposes.

World Map Showing Routes of Exploration and Discovery, 1790 (Image 8 of 8) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Chart of the world on Mercators projection : exhibiting all the new discoveries to the present time, with the tracks of the most distinguished navigators since the year 1700 carefully collected from the best charts, maps, voyages, &c. extant and regulated from the accurate astronomical observations made in three voyages performed under the command of Captn. James Cook in the years 1768, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79 & 80, compiled and published by A. Arrowsmith, geographer; by permission of Simon McTavish Esq[r] is correctly delineated the discoveries of Mr. McKenzie laid down from his original journal in the year 1789. It was published by A. Arrowsmith, April 1, 1790. Scale [ca. 1:20,000,000]. This layer is image 8 of 8 total images of the seven sheet source map. Covers portions of eastern Asia. The original map sheet contains multiple maps on one sheet. Because the map images are non-contiguous and possibly at differing scales, each map image was georeferenced separately. The image inside the map neatline is georeferenced to the surface of the earth and fit to the 'Mercator' projection. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as drainage, cities and other human settlements, territorial boundaries, shoreline features, and more. Relief shown by hachures. Depths shown by soundings. Includes routes, locations, and dates of James Cook's voyages. This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection and the Harvard University Library as part of the Open Collections Program at Harvard University project: Organizing Our World: Sponsored Exploration and Scientific Discovery in the Modern Age. Maps selected for the project correspond to various expeditions and represent a range of regions, originators, ground condition dates, scales, and purposes.

World Map Showing Routes of Exploration and Discovery, 1790 (Image 7 of 8) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Chart of the world on Mercators projection : exhibiting all the new discoveries to the present time, with the tracks of the most distinguished navigators since the year 1700 carefully collected from the best charts, maps, voyages, &c. extant and regulated from the accurate astronomical observations made in three voyages performed under the command of Captn. James Cook in the years 1768, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79 & 80, compiled and published by A. Arrowsmith, geographer; by permission of Simon McTavish Esq[r] is correctly delineated the discoveries of Mr. McKenzie laid down from his original journal in the year 1789. It was published by A. Arrowsmith, April 1, 1790. Scale [ca. 1:20,000,000]. This layer is image 7 of 8 total images of the seven sheet source map. Covers portions of Australia and Southeast Asia. The original map sheet contains multiple maps on one sheet. Because the map images are non-contiguous and possibly at differing scales, each map image was georeferenced separately. The image inside the map neatline is georeferenced to the surface of the earth and fit to the 'Mercator' projection. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as drainage, cities and other human settlements, territorial boundaries, shoreline features, and more. Relief shown by hachures. Depths shown by soundings. Includes routes, locations, and dates of James Cook's voyages. This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection and the Harvard University Library as part of the Open Collections Program at Harvard University project: Organizing Our World: Sponsored Exploration and Scientific Discovery in the Modern Age. Maps selected for the project correspond to various expeditions and represent a range of regions, originators, ground condition dates, scales, and purposes.

World Map Showing Routes of Exploration and Discovery, 1850 (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: The world, on Mercator's projection, by David H. Burr. It was published by J. Haven, 86 State St. in 1850. Scale [ca. 1:74,000,000]. The image inside the map neatline is georeferenced to the surface of the earth and fit to a non-standard 'Mercator' projection with the central meridian at 90 degrees west. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. "Showing the different routes to California, and distance by each, routes of different navigators, route of the contemplated Pacific R. Road, distances to China, Europe, & c." This map shows features such as drainage, cities and other human settlements, shoreline features, and more. Relief shown by abbreviated form lines. Includes historical notes, ship ill., tables of distances, "Nicaragua route" distances, and text on "Pacific Railroad." Insets: Map of the Nicaragua route -- Map of the proposed rail road from St. Louis to the bay of St. Francisco. This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection and the Harvard University Library as part of the Open Collections Program at Harvard University project: Organizing Our World: Sponsored Exploration and Scientific Discovery in the Modern Age. Maps selected for the project correspond to various expeditions and represent a range of regions, originators, ground condition dates, scales, and purposes.

World Map Showing the Voyages of the Vettor Pisani, 1882-1885 (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Viaggio della R[a] Corvetta 'Vettor Pisani', negli anni 1882-1883-1884-1885 (comandante G. Palumbo). It was published by Stab. Lit. Bruno e Salomone in 1885. Scale [ca. 1:250,500]. World map showing the voyages of the Vettor Pisani. The image inside the map neatline is georeferenced to the surface of the earth and fit to a non-standard 'Mercator' projection with the central meridian at 160 degrees east. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as drainage, cities and other human settlements, ship route with dates, territorial boundaries, shoreline features, and more. This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection and the Harvard University Library as part of the Open Collections Program at Harvard University project: Organizing Our World: Sponsored Exploration and Scientific Discovery in the Modern Age. Maps selected for the project correspond to various expeditions and represent a range of regions, originators, ground condition dates, scales, and purposes.

Archaeological Map, Carthage, Tunisia, ca. 1895 (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Carte archéologique et topographique des ruines de Carthage : dressée d'après les relevés de M. l'adjoint du génie Bordy, avec le concours de MM. le R. P. Delattre, ... le général Dolot,... P. Gauckler. It was published by Service géographique de l'armée, ca. 1895. Scale 1:5,000. Covers Carthage, Tunis, Tunisia. Map in French.The image inside the map neatline is georeferenced to the surface of the earth and fit to the Universal Transverse Mercator (UTM Zone 32N, meters, WGS 1984) projected coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as drainage, cities and towns, villages, roads, railroads and stations, selected buildings and built-up areas, shoreline features, and more. Relief shown by contours and hachures. Overprinted to show archaeological sites.This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of originators, ground condition dates, scales, and map purposes.

Nile River and Birkat Qārūn Regions, Egypt, 1854 (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Carte hydrographique de la Moyenne Égypte, où sont indiqués les travaux exécutés ou à exécuter, d'après les ordres de Son Altesse Mehémet-Ali, Vice-Roi d'Egypte. Avec le projet de communication directe des deux mers au travers de l'Isthme, par M. Linant de Bellefonds ; gravée par Schwaerzlé et Erhard. It was published by Dépôt de la Guerre in 1854. Scale 1:250,000. Covers a portion of the Nile River region near Birkat Qārūn, Banī Suwayf, Al Fayyūm, and Al Minyā. Map in French.The image inside the map neatline is georeferenced to the surface of the earth and fit to the Egypt Red Belt projected coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as drainage, canals, roads, cities and other human settlements, administrative boundaries, ruins and historical sites, and more. Relief shown by hachures. Includes also text and notes.This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of originators, ground condition dates, scales, and map purposes.

Talfīq al-akhbār wa-talqīḥ al-āthār fī waqāʻiʻ Qāzān wa-Bulghār wa-mulūk al-Tatār

athar M. M. al-Ramzī.