A Research on Concepts and Some Applications of Spatial Data Mining and Knowledge Discovery: A Review
Exploring Techniques and Applications of Spatial Data Mining
by Parteek Singh*,
- Published in Journal of Advances and Scholarly Researches in Allied Education, E-ISSN: 2230-7540
Volume 16, Issue No. 6, May 2019, Pages 1489 - 1496 (8)
Published by: Ignited Minds Journals
ABSTRACT
A developing consideration has been paid to spatial data mining and knowledge discovery (SDMKD). This paper displays the standards of SDMKD, proposes three new techniques, and gives their pertinence and models. To start with, the inspiration of SDMKD is informed. Second, the intension and expansion of SDMKD idea are exhibited. Third, three new techniques are proposed in this area, for example SDMKD-based image classification that coordinates spatial inductive learning from GIS database and Bayesian classification, cloud model that incorporates arbitrariness and fluffiness, data field that emanate the vitality of watched data to the universe talk. Spatial data mining is the way toward discovering intriguing and already obscure, however conceivably helpful patterns from huge spatial datasets. Extricating intriguing and valuable patterns from spatial datasets is more troublesome than removing the comparing patterns from conventional numeric and clear cut data because of the intricacy of spatial data types, spatial relationships, and spatial autocorrelation. The necessities of mining spatial databases are not the same as those of mining traditional social databases. The spatial data mining techniques are frequently gotten from spatial insights, spatial examination, machine learning, and databases, and are altered to break down enormous data sets. In this report a portion of the spatial data mining techniques have talked about alongside certain applications in genuine world. Spatial data mining is the discovery of fascinating relationships and attributes that may exist verifiably in spatial databases. In this paper, we investigate in the case of clustering methods have a task to carry out in spatial data mining.
KEYWORD
spatial data mining, knowledge discovery, techniques, GIS database, Bayesian classification, cloud model, data field, spatial datasets, spatial relationships, spatial autocorrelation
INTRODUCTION
The specialized advancement in automated data procurement and capacity brings about the development of immense databases. With the constant increment and amassing, the immense measures of the electronic data have far surpassed human capacity to totally decipher and utilize. These wonders might be increasingly genuine in geo-spatial science. So as to comprehend and utilize these data stores, a couple of techniques have been attempted, for example master framework, database management framework, spatial data investigation, machine learning, and computerized reasoning. In 1989, knowledge discovery in databases was additionally proposed. In 1995, data mining likewise shows up. As the two data mining and knowledge discovery in databases virtually point to similar techniques, individuals might want to assemble them, for example data mining and knowledge discovery (DMKD). As 80% data are geo-referenced, the need powers individuals to consider spatial attributes in DMKD and to additionally build up a branch in geo-spatial science, for example SDMKD. Spatial data are increasingly intricate, progressively alterable and greater that regular undertaking datasets. Spatial measurement implies every thing of data has a spatial reference where every element happens on the constant surface, or where the spatial-referenced relationship exists between two neighbor substances. Spatial data incorporates positional data and characteristic data, yet in addition spatial relationships among spatial substances. Also, spatial data structure is more intricate than the tables in normal social database. Other than forbidden data, there are vector and raster realistic data in spatial database. Furthermore, the highlights of realistic data are not unequivocally put away in the database. Simultaneously, contemporary GIS have just fundamental investigation functionalities, the consequences of which are unequivocal. Also, it is Since the discovered spatial knowledge can bolster and improve spatial data-referenced basic leadership, a developing consideration has been paid to the investigation, advancement and application of SDMKD. The unstable development of spatial data and across the board utilization of spatial databases underscore the requirement for the robotized discovery of spatial knowledge. Spatial data mining is the way toward discovering intriguing and beforehand obscure, yet conceivably helpful patterns from spatial databases. The unpredictability of spatial data and characteristic spatial relationships restricts the handiness of traditional data mining techniques for separating spatial patterns. Productive tools for extricating data from geo-spatial data are vital to associations which settle on choices dependent on huge spatial datasets, including NASA, the National Imagery and Mapping Agency (NIMA), the National Cancer Institute (NCI), and the United States Department of Transportation (USDOT). These associations are spread crosswise over numerous application areas including ecology and environmental management, public safety, transportation, Earth science, epidemiology, and climatology. Universally useful data mining tools, for example, Clementine and Enterprise Miner, are intended to break down enormous business databases. In spite of the fact that these tools were principally intended to distinguish client purchasing behaviors in advertise bushel data, they have likewise been utilized in breaking down logical and designing data, galactic data, multi-media data, genomic data, and web data. Extricating fascinating and valuable patterns from spatial data sets is more troublesome than removing comparing patterns from customary numeric and straight out data because of the intricacy of spatial data types, spatial relationships, and spatial autocorrelation. Explicit highlights of geographical data that block the utilization of broadly useful data mining algorithms are: I) rich data types(e.g., broadened spatial items) ii) understood spatial relationships among the factors, iii) perceptions that are not autonomous, and iv) spatial autocorrelation among the highlights. The spatial data mining can be utilized to comprehend spatial data, find the connection among pace and the non-space data, set up the spatial knowledge base, exceed expectations the question, rearrange spatial database and acquire compact absolute trademark and so on. The framework structure of the spatial data mining can be partitioned into three layer structures mostly. The client interface layer is essentially utilized for info and yield, the excavator layer is chiefly used to oversee data, select calculation and capacity the mined knowledge, the data source layer, which for the most part If data mining is tied in with concentrating models from significant databases, at that point the greatest databases have an in number spatial part. For example, the Earth Observation Satellites, which are efficiently mapping the entire surface of the earth, accumulate in the region of one terabyte of data reliably. Other sweeping spatial databases may be the U.s. specification, and the atmosphere and air databases. The necessities of mining spatial databases are not equivalent to those of mining set up social databases. In particular, the idea of spatial autocorrelation that similar things tend to bundle in geographic space, is critical to spatial data mining. The total data-mining process is a mix of various sub forms which are deserving of concentrate in their right.. Some critical sub forms are data extraction and data cleaning, trademark assurance, computation layout and tuning, and the examination of the yield when the estimation is associated with the data. For spatial data, the issue of scale the degree of collection at which the data are continually inspected, is also uncommonly basic. It. is outstanding in spatial examination that vague examinations at. different degrees of scale can on occasion lead to opposing outcomes. Our inside in this part is compelled to the setup of data-mining algorithms. Explicitly we depict how conventional data-mining algorithms may be loosened up to model the spatial autocorrelation property. Here it. is fundamental to appreciate the capability between spatial data mining and spatial data examination. As the name lingerie, spatial data investigation covers a wide scope of techniques that plans with both the spatial and nori spatial characteristics of the spatial things. On the other hand spatial data mining methods are much of the time surmised from spatial insights, spatial examination, machine taking in and data bases, and are adjusted to dismember enormous data sets. Spatial Database Systems (SDBS) are database systems for the management of spatial data. Both, the number and the degree of spatial databases are rapidly creating in arrangements for instance, geo advertising, development control and natural investigations. This improvement by a wide margin outperforms human cutoff points to separate the databases with a particular ultimate objective to find certain regularities, oversees or bundles concealed in the data. Hence, motorized knowledge discovery gets the opportunity to be increasingly basic in spatial databases. Knowledge discovery in databases (KDD) is the non-minor extraction of suggested, at one time darken, and conceivably advantageous data from databases.
algorithms and their execution.
CONCEPTS
Spatial data mining and knowledge discovery (SDMKD) is the proficient extraction of covered up, understood, fascinating, already obscure, conceivably helpful, at last reasonable, spatial or non-spatial knowledge (rules, regularities, patterns, limitations) from inadequate, loud, fluffy, irregular and down to earth data in huge spatial databases. It is a conversion of databases innovation, computerized reasoning, machine learning, probabilistic insights, representation, data science, design acknowledgment and different controls. Comprehended from various perspectives, SDMKD shows numerous new interdisciplinary attributes.
Mechanism -
SDMKD is a procedure of discovering a type of rules in addition to special cases at hierarchal view-points with different edges, for example penetrating, dicing and rotating on multidimensional databases, spatial data warehousing, summing up, portraying and ordering elements, abridging and differentiating data attributes, depicting rules, anticipating future trends, etc. It is likewise a supportable procedure of spatial basic leadership. There are two mining granularities, spatial item granularity and pixel granularity (Li, Wang, Li, 2005). It might be quickly apportioned three major advances, data arrangement (situating mining objective, gathering foundation knowledge, cleaning spatial data), data mining (diminishing data measurements, choosing mining techniques, discovering knowledge), and knowledge application (translation, assessment and application of the discovered knowledge). So as to discovery the secret knowledge, it is entirely expected to utilize more than one procedure to mine the data sets simultaneously. Furthermore, it is additionally reasonable to choose the mining techniques based on the given mining task and the knowledge to be discovered.
Knowledge to be discovered -
The knowledge is increasingly summed up, dense and justifiable than data. The regular knowledge is abridged and summed up from enormous measures of spatial data sets. The measure of spatial data is gigantic, while the volume of spatial rules is little. The more summed up the knowledge, the greater the differentiation. There are numerous sorts of knowledge that can be mined from enormous spatial data sets. Knowledge is rule in addition to specific dispersing or set of courses of action. Other than the rules, during the discovering procedure of depiction or forecast, there might be a few special cases (additionally named exceptions) that derivate such a great amount from other data perceptions (Shekhar, Lu, Zhang, 2003). They recognize and clarify special cases (shocks). For instance, spatial trend prescient modeling previously discovered the focuses that are neighborhood maximal of some non-spatial characteristic, at that point decided the (hypothetical) trend of some non-spatial trait while moving ceaselessly from the focuses. At last scarcely any deviations are discovered that a few data were away from the hypothetical trend. These deviations may stir suspicious that they are clamor, or created by an alternate component. How to clarify these exceptions? Customarily, anomalies' detection has been contemplates through measurements, and various discordancy tests have been created. A large portion of them treat anomalies as "commotion" and they attempt to dispose of the impacts of exceptions by expelling exceptions or build up some exception safe methods. Indeed, these anomalies demonstrate the rules. With regards to data mining, they are important info flag instead of commotion. At times, exceptions speak to remarkable attributes of the items that are imperative to an association. In this manner, a bit of nonexclusive knowledge is virtually as rule in addition to special case.
SPATIAL DATA MINING TASKS
Essential assignments of spatial data mining are: A. Classification
An item can be arranged utilizing its properties. Each grouped item is allocated a class. Classification is the way toward finding a lot of rules to decide the class of an article.
B. Association Rules
Find (spatially related) rules from the database. An association rule has the accompanying structure: A - >B(s%; c%), where s is the help of the standard (the likelihood, that An and B hold together in all the potential cases) and c is the certainty (the restrictive likelihood that B is valid under the state of An e. g. "in the event that the city is enormous, it is close to the waterway (with likelihood 80%)" or "on the off chance that the neighboring pixels are named water, at that point focal pixel is water (likelihood 80%)." been characterized in as the depiction of properties that are ordinary for the part being referred to however not for the entire database. On account of a spatial database, it considers of the properties of articles, yet in addition of the properties of their neighborhood up to a given level.
D. Discriminant Rules
Depict contrasts between two pieces of database e. g. discover contrasts between urban communities with high and low joblessness rate.
E. Clustering
Clustering implies it is the way toward gathering the database things in to clusters. Every one of the individuals from the cluster has comparable highlights. Individuals have a place with various clusters has different highlights.
F. Trend Detection
Discovers trends in database. A trend is a worldly example in some time arrangement data. Spatial trend is characterized as pursues: consider a non spatial trait which is the neighbor of a spatial data object. The example of changes in this trait is called spatial trend.
MOTIVATING SPATIAL DATA ALINING
We currently present a delineation which will be used all around this area to layout the particular thoughts in spatial data mining. We are given data in the region of two wetlands on the shores of Lake Erie in Ohio, USA, to foresee the spatial allotment of a lowland imitating winged creature, the red-winged blackbird (Agelaius phoeniceus). The names of the wetlands are Darr and Stubble, and the data was accumulated from April to June in two dynamic years, 1995 and 1996. A uniform cross section was constrained on the two wetlands, and different sorts of estimations were recorded at every one unit or pixel. The range of each pixel was five meters. The characteristics of seven characteristics were recorded at every one unit, clearly territory knowledge is vital in picking which qualities are objective and which are certainly not. For example, Vegetation Durability was picked over Vegetation Species considering the way that particular knowledge about the settling inclinations of the red-winged blackbird recommended that the choice of home zone is progressively dependent on the plant structure and its impenetrability to twist besides wave action than on the plant species. within gravity of a spatial scattering. Routinely the weighted mean center is appropriate measure for some spatial arrangements, for e.g., point of convergence of people. The weighted mean center is enrolled as the degree between the total of the headings of every one center increased by its weight (e.g., number of people in piece) moreover the aggregate of the loads. The measure center is used as a piece of certain structures. It may be used to streamline complex things (e.g., to avoid space essentials and flightiness of digitations of borderlines, a geographic thing could be addressed by its center), or for recognizing the best territory for an orchestrated development (for example a dispersal center should be detected a primary issue with the objective that make an outing to it is limited). Dissipating is a proportion of the spread of an allotment around its core interest. Consistently used proportions of dispersing and fluctuation are reach, standard deviation, change and coefficient, of contrast. Dissipating measures for geographical dispersals are routinely figured as the summation over the extent of the heaviness of geographic articles and the closeness between them. Shape is multi-dimensional, and there is no single measure to get the whole of the estimations of the shape. A robust bit of shape measures are endless supply of the shape's fringe with that of a ring of a similar zone. The Data-Mining Trinity : Data mining is a point of fact multidisciplinary zone, and there are various novel methods for concentrating structures from data. In any case, if one somehow happened to name data-mining systems, at that point the three most non questionable imprints may be plan, gathering, and collaboration norms. At the point when we delineate every one of these classes in parcel, we display some illustrative outlines where these systems may be associated. The goal of portrayal is to measure the value of a quality of an association subordinate upon the value of the association's various attributes. Various issues could be conveyed as portrayal issues. For example, determining the regions of homes in a wetland dependent on the value of various qualities (vegetation strength, water significance) is a gathering issue as often as possible moreover called the region desire issue. Additionally, predicting where to require issue territories in bad behavior activity may be given a section as a zone gauge issue. Retailers fundamentally settle a zone desire issue when they pick a region for another store. The notable portrayal in land, "Area is everything," is a pervasive sign of this issue.
are different techniques related with the previously mentioned diverse knowledge. They may incorporate, likelihood hypothesis, proof hypothesis (Dempster-Shafer), spatial measurements, fluffy sets, cloud model, unpleasant sets, neural system, hereditary algorithms, choice tree, exploratory learning, inductive learning, perception, spatial online explanatory mining (SOLAM), anomaly detection, and so forth. Some of techniques are additionally created and applied, for instance, the algorithms in spatial inductive learning incorporate AQ11 and AQ15 by Michalski, AE1 and AE9 by Hong, CLS by Hunt, ID3, C4.5 and C5.0 by Quinlan, and CN2 by Clark, and so forth. Also, the execution of data mining in spatial database is as yet should have been additionally examined. Coming up next is our proposed techniques, SDMKD-based image classification, cloud model, and data field.
SDMKD-based image classification -
In view of the mix of remote detecting and GIS, this subsection displays an approach to consolidate spatial inductive learning with Bayesian image classification in a free way, which takes learning tuple as mining granularities for learning knowledge subdivide classes into subclasses, for example pixel granularity and polygon granularity, and chooses class likelihood estimations of Bayesian classification, shape highlights, areas and heights as the learning traits. GIS data are utilized in preparing territory choice for Bayesian classification, producing learning data of two granularities, and testing region determination for classification precision assessment. What's more, the ground control focuses for image correction are likewise looked over GIS data. It actualizes inductive learning in spatial data mining by means of C5.0 calculation based on learning granularities. Figure 1 shows the guideline of the method.
Cloud model -
The cloud model is a model of the vulnerability change among subjective and quantitative examination, for example a scientific model of the vulnerability progress between a phonetic term of a subjective idea and its numerical portrayal data. A bit of cloud is comprised of heaps of cloud drops, unmistakable shape in an entire, however fluffy in detail, which is like the characteristic cloud in the sky. So the wording cloud is utilized to name the vulnerability progress model proposed here. Any of the cloud drops is a stochastic mapping in the talk universe from subjective idea, for example a predefined acknowledgment with dubious components. With the cloud model, the mapping from the talk universe to the interim [0,1] is a one- determined. Cloud model may mine spatial data with both fluffy and stochastic vulnerabilities, and the discovered knowledge is near human reasoning. Presently, in geo-spatial science, the cloud model has been additionally investigated to spatial clever inquiry, image translation, land value discovery, factors determination, component of spatial data mining, and avalanche observing and so on.
Data field -
The acquired spatial data are similarly inadequacy. Every datum in the idea space has its very own commitment in shaping the origination and the idea chain of importance. So it is important for the watched data to emanate their data energies from the example space to their parent space. So as to portray the data radiation, data field is proposed. Spatial data emanate energies into data field. The intensity of the data field might be estimated by its potential with a field work. This is comparable with the electric charges add to frame the electric field that each electric charge has impact on electric potential wherever in the electric field. So the capacity of data field can be gotten from the physical fields.
SPATIAL DATA MINING : AN ALGORITHMS
To help our case that the expressivity of our spatial data mining natives is good, we display how common spatial data mining algorithms could be joined with a spatial DBMS by using the database natives introduced as a piece of zone. Spatial Clustering : Clustering is the task of gathering the objects of a database into real subclasses (that is, packs) with the objective that the pieces of a bundle are as practically identical as could be normal in light of the current situation however the pieces of unmistakable bundles differentiate anyway much as could be normal from each other. Arrangements of packing in spatial databases are, e.g., the discovery of seismic faults by collecting the sections of a tremor stock or the development of topical maps in geographic data systems by gathering trademark spaces. Unmistakable sorts of spatial gathering algorithms have been proposed, for example k-medoid gathering algorithms for instance, CLARANS. This is an instance of an overall clustering computation (where a difference in a lone database thing may affect all gatherings) which can't make usage of our database natives in a typical way. On the other hand, the basic idea of a lone yield computation is to get together neighboring objects of the database into bunches subordinate upon a close by bunch be adequately performed by the SDBS. Note that close by bunch conditions are for the most part supported by our database natives, explicitly by the neighbors activity on an appropriate neighborhood diagram. Various pack conditions yield particular considerations of a gathering and assorted gathering algorithms. For instance, GDBSCAN (Generalized Density Based Spatial Clustering of Applications with Noise) depends on a thickness based thought of clusters. The key thought of a thickness based cluster is that for each purpose of a cluster its Eps-neighborhood for some given Eps > 0 needs to contain in any event a base number of focuses, for example the "thickness" in the Eps-neighborhood of focuses needs to surpass some limit. This thought of "thickness based clusters" can be summed up in two significant manners. To begin with, any idea of an area can be utilized rather than an Eps-neighborhood if the meaning of the area depends on a twofold predicate which is symmetric and reflexive. Second, rather than essentially including the articles in an area of an item different measures to characterize the "cardinality" of that area can be utilized also. While a separation based neighborhood is a characteristic idea of an area for point objects, it might be progressively suitable to utilize topological relations, for example, converges or meets to cluster spatially expanded items, for example, a lot of polygons of generally contrasting sizes. for an itemized exchange of reasonable neighborhood relations for various applications. Spatial Characterization: The errand of portrayal is to locate a conservative depiction for a chose subset of the database. In this area, we talk about the assignment of portrayal with regards to spatial databases and survey two pertinent methods. The calculation to discover spatial association rules comprises of 5 stages. Stage 2 (coarse spatial calculation) and stage 4 (refined spatial calculation) include spatial parts of the articles and are quickly analyzed in the accompanying. Stage 2 registers spatial joins of the item type to be described, (for example, town) with every one of the other indicated object types, (for example, water, street, limit or mine) utilizing a local connection, (for example, near). For every one of the applicants acquired from stage 2 (and which passed an extra channel stage 3), the careful spatial connection, for instance cover, is resolved in stage 4. At long last, a connection, for example, the one portrayed in figure 2 outcomes which is the contribution for the last advance of rule age. It is anything but difficult to see that the spatial stages 2 and 4 of this calculation can be very much
Figure 2. Input for the step of rule generation.
This paper presents the accompanying meaning of spatial portrayal as for a database and a lot of target objects which is a subset of the given database. A spatial portrayal is a depiction of the spatial and non-spatial properties which are average for the objective articles however not for the entire database. The general frequencies of the non-spatial quality qualities and the overall frequencies of the diverse article types are utilized as the intriguing properties. For example, extraordinary article types in a geographic database are networks, mountains, lakes, thruways, railways and so on. To get a spatial portrayal, the properties of the objective articles, yet in addition the properties of their neighbors (up to a given most extreme number of edges in the significant neighborhood diagram) are considered.
CLUSTERING METHODS FOR SPATIAL DATA MINING
A. Parceling Around Medoids (PAM)
PAM is like K-implies calculation. Like k-implies calculation, PAM separates data sets in to bunches however dependent on mediods. Though k-implies depends on centroids. By utilizing mediods we can diminish the divergence of articles inside a cluster. In PAM, first compute the mediod, at that point relegated the article to the closest mediod, which shapes a cluster.
B. Clustering LARge Applications (CLARA)
Contrasted with PAM, CLARA can manage a lot bigger data sets. Like PAM CLARA likewise discovers questions that are halfway situated in the clusters. The primary issue with PAM is that it finds the whole difference network at once. So for n protests, the space multifaceted nature of PAM becomes O(n2). Be that as it may, CLARA stay away from this issue. CLARA acknowledges just the genuine estimations (i.e,. n ' p data framework).
CLARA doles out articles to clusters in the accompanying manner:
• BUILD-step: Select k "halfway found" objects, to be utilized as beginning medoids. Presently the littlest conceivable
• SWAP-step: Try to decerase the normal separation between the articles and the mediods. This is finished by supplanting delegate objects. Presently an article that doesn't have a place with the example is appointed to the closest mediod.
C. Spatial dominant approach SD (CLARANS)
In SDCLARANS, every one of the data containing spatial parts are gathered. After that clustering is utilized dependent on CLARANS. It ought to be referenced that CLARANS is utilized to locate the most regular number, knat, of clusters. One may ask, how is nat k decided in any case. It is surely an exceptionally troublesome and open inquiry. The creators be that as it may, receive a heuristic of detemining nat k , which utilizes silhoutee coefflients , presented by Kaufman and Rousseeuw. Every one of the clusters in this manner acquired is handled by summing up its nonspatial parts utilizing DBLEARN. Note that this calculation contrasts from the spatial dominant speculation calculation (without clustering), in that the last requires the client to give the spatial idea chains of importance. in any case, for this situation, it tends to be said that SD(CLARANS) figures spatial chain of importance progressively. The chain of importance along these lines discovered is more "data arranged" as opposed to "human situated".
D. Non-spatial dominant approach NSD (CLARANS)
This nonspatial dominant approach initially applies nonspatial speculations and spatial clustering thereafter. DBLEARN is utilized to perform trait situated speculations of the nonspatial qualities and produce various summed up tuples. At that point, for each such generallized tuple, all the spatial parts are gathered and clustered utilizing CLARANS to discover nat k clusters. In the last advance, the clusters in this manner acquired are verified whether they cover with one another. Provided that this is true, at that point the clusters are combined, and the comparing summed up tuples are converged also. In the event that the rules to discover are nonspatial portrayals of spatial traits, at that point SD(CLARANS) has an edge. This is on the grounds that NSD(CLARANS) isolates the articles into various gatherings before clustering which may debilitate the entomb object similitude, or cluster snugness. Then again, NSD(CLARANS) is appropriate if the spatial clusters inside gatherings of data that has been summed up nonspatially is looked for. Nonetheless, the two algorithms land at a similar outcome (or rules). when PC method, database applied system and management choice help techniques and so forth have been created at certain stage. Hie spatial data mining assembled preparations that originate from machine learning, design acknowledgment, database, measurements, computerized reasoning and management data framework and so on. Various speculations, set forward the various methods of spatial data mining, for example, methods in measurements, evidence hypotheses, rule inductive, association rules, cluster investigation, spatial examination, fluffy sets, cloud speculations, unpleasant sets, neural system, choice tree and spatial data mining strategy dependent on data entropy and so on. Spatial data mining, has built up itself as a total and potential territory of research. After the idea and standard of spatial data mining and knowledge discovery (SDMKD) were advised, this paper proposed three mining techniques, SDMKD-based image classification, cloud model and data field, together with pertinent models, for example remote detecting image classification, Baota avalanche observing data mining and spatial questionable thinking. The specialized advancement in electronic spatial data securing and capacity brought about the development of tremendous databases, which made a part of data mining, SDMKD, created in geo-spatial science. This paper took the instrument of SDMKD as a procedure of discovering a type of rules in addition to special cases at hierarchal view-points with different edges.
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Parteek Singh*
VPO -Dhundwa, Tehsil Kalayat, District-Kaithal