terrafugia ( / ˌtɛrəˈfuːdʒiə / ) is a chinese-owned corporation , based in woburn , massachusetts , united states that is developing a roadable aircraft called the transition and a flying car called the tf-x .

the transition and tf-x are designed to be able to fold their wings , enabling the vehicles to also operate as street-legal road vehicles .

first delivery of the transition is expected in 2019 .

terrafugia

in a release issued by terrafugia , auto show director alan liebensohn said they were thrilled to have terrafugia and the transition at the show this year .
based on these factors , we conclude that terrafugia has demonstrated the requisite economic hardship .
terrafugia achieved widespread publicity after its first aircraft in 2009 ; the fixed - wing terrafugia transition is “the world’s first practical flying car” and the company is now ramping up for production .
terrafugia is taking the automobile game to a whole new level with this hybrid electric aircraft .
terrafugia flyng cars : the company said monday that its flying car has completed its first test flight . the terrafugia flying cars will be unveiled at the new york auto show this week .
just months later , in june , terrafugia was given the go ahead to certify its vehicles .
above you see terrafugia ' s transition , its first flying car that was completed in 2014 .
volvo’s parent company geely has acquired flying car startup terrafugia , bringing vehicles that transition from the roads to the skies a step closer to reality . terrafugia ' s concept car tf - x is pictured
n june 2010 , the faa granted terrafugia an exemption for the transition ' s extra takeoff weight .
we are a privately funded company . for more information about investment opportunities with terrafugia , please click here .
in the past , terrafugia has claimed its designs could be ready to fly within the next few years .
“with this achievement , terrafugia has set the stage for personal aviation , ” dietrich said at the press conference .
below is a summary of the compliance efforts and costs for each of the requirements from which terrafugia seeks exemption .
slated for delivery in 2015 , terrafugia is selling a street - legal flying car for $ 279 , 000 .
terrafugia is now taking deposits for the world’s first practical flying car , the transition ® . reserve yours today !
according to massachusetts - based terrafugia , a full - size unmanned prototype is expected to be ready by 2018 .
based in woburn , massachusetts , terrafugia’s mission is to make flying cars a practical reality . terrafugia’s core competencies are vehicle design , flight and drive testing , and the development of international certification standards . terrafugia has flown and driven two prototype vehicles , and is an active participant in astm committees f37 , f38 , f39 , and f44 . terrafugia is actively developing technologies and standards for simplified vehicle operations that will utilize the next generation of electric propulsion and automation .
the vehicle was developed by former nasa engineers and built by a small american company from massachusetts , terrafugia , inc .
terrafugia stated that it has spent approximately $ 3 . 5 million since 2006 on the development of the transition® and has had no appreciable revenue during that time . terrafugia acknowledged that it has received over 80 orders for vehicles but that due to escrow agreements for each deposit , these funds are not accessible operating funds . terrafugia ' s confidential records support its assertion that it has experienced a continuing and cumulative net loss position . additionally , one commenter agreed with terrafugia that the cost of complying with the advanced air bag requirements and the esc system requirements would represent a significant financial burden to terrafugia .
mr . dritten also questioned terrafugia ' s efforts to comply and whether the exemption sought was in the public interest . mr . dritten noted that development of the transition® began in 2006 and questioned why terrafugia had not requested an exemption earlier .
likewise , the agency does not consider the timing of terrafugia ' s petition for exemption to reflect negatively on the company ' s efforts to comply . terrafugia ' s petition is dated july 20 , 2010 . in the petition , terrafugia requested an exemption beginning with the first transition® delivery on or near december 1 , 2011 , over 16 months later . the agency considers this to be a sufficient period to carefully consider the merits of terrafugia ' s petition and make a reasoned decision .
terrafugia stated that the denial of the requested exemption will result in substantial economic hardship . the company indicated that it has spent
terrafugia is based in woburn , ma , and initial prototyping and production will be done on - site in our facility .
in october 2008 , terrafugia reported seeking reservations for airframe number 57 , and a more than us $ 8 million backlog .
the terrafugia transition is a roadable aircraft that was tested last year . darpa ' s plans for the transformer x call for the vehicle to be capable of flying on autopilot and driving off - road , among other features . credit : terrafugia .
however , massachusetts - based firm terrafugia said the tf - x will still be another eight to twelve years in development .
in this section , we provide our analysis and decision regarding terrafugia ' s temporary exemption request from the requirements of various fmvsss .
terrafugia will contribute expertise in
drive and flight integration , deployable flight surfaces , and automotive crash safety for an aircraft .
richard joined terrafugia with over 25 years of executive - level experience in all phases of financial service company operations and risk management .
terrafugia stated that it faces two challenges with an off - the - shelf esc unit . first , an esc system would add 6
the terrafugia transition
roadable aircraft
- the nearest thing to a flying car yet built - has made its first test flight .
although those rules have yet to be put in place , the faa recently granted terrafugia permission to test its tf - x outdoors .
in sum , we believe that , considering terrafugia ' s overall situation , the efforts that the company has made to date , and the plans it has in place , terrafugia has made good faith efforts to comply with the requirements from which it seeks a temporary exemption .
7 . terrafugia initially stated that it planned to begin production in late - 2011 but subsequently indicated that its production plans had been delayed .
today , degrees in hand , they have started their own company , terrafugia , flown a prototype , and are now manufacturing the vehicles .
terrafugia was founded in 2006 by students from mit ' s aeronautics and astronautics ' department to realize the dream of creating a flying car .
terrafugia is the company that has come closest to building and selling a flying car . based in woburn , ma , outside boston , it was founded in 2006 . terrafugia is latin for escape from earth . the terrafugia transition first escaped the runway in 2009 for brief takeoff - landings and has been test - flown since . terrafugia’s current thinking is to ship the first transitions in 2015 or 2016 . the price is listed at just under $ 300 , 000 , about the same as the cessna 172 , the most popular airplane built . that begs the question , is the transition underpriced , or maybe the cessna is overpriced ? either way , terrafugia reports more than 100 deposits for the transition .
one of the public comments questioned terrafugia ' s general efforts to comply . specifically , the commenter noted that terrafugia could have designed the transition® with three wheels instead of four , thus saving weight , allowing for the installation of additional safety features , and avoiding the need to comply with the safety standards required for four - wheel vehicles . the commenter also questioned why terrafugia did not request an exemption earlier in the development process .
flying - car maker terrafugia inc . made its auto - show debut in new york today and offered a “show special” discount to prospective customers .
the woburn - based firm terrafugia , ( latin for
escape the earth
) is turning fantasy into reality with its transitional roadable aircraft .
terrafugia is a growing aerospace company founded by pilots and engineers from mit and supported by a world - class network of advisers and private investors .
volvo’s parent company geely has acquired flying car startup terrafugia , bringing vehicles that transition from the roads to the skies a step closer to reality .
terrafugia co - founder and ceo carl dietrich ( pictured above in 2013 ) and board member semyon dukach both declined to comment on the news .
on november 16 , 2010 we published a notice of receipt of terrafugia ' s petition for temporary exemption in the federal register ( 75 fr 70071 ) , and provided an opportunity for public comment . we received ten comments in response to the notice , as well as a response from terrafugia .
6 . terrafugia explained that general aviation is the segment of the air transportation industry characterized by flight outside of the commercial airline system and military operations .
terrafugia began development of the transition in 2006 , flying a proof - of - concept aircraft in 2009 and a second - generation prototype in 2012 .
terrafugia intends to build flying cars . their tf - x program is aimed at producing a commercial personal aircraft and bring personal aviation into the mainstream .
the agency acknowledges that terrafugia faces impediments beyond the expense of advanced air bag technology and believes that it is consistent with the public interest to grant the requested exemption . however , in light of nhtsa ' s reexamination of the agency ' s policy regarding exemptions from the advanced air bag requirements , we do not believe that the three - year exemption requested is warranted . instead , we are granting terrafugia a one - year exemption from the advanced air bag requirements . although this period is shorter than that requested by terrafugia , this exemption will allow terrafugia to begin production and continue its efforts toward full compliance .
as a small company , terrafugia has taken a long time to get its product to market . then again , no one else has successfully sold a flying car yet . it sounds like geely’s backing and car - manufacturing facilities could greatly advance terrafugia’s vision—if the integration and cultural issues can be sorted out .
the terrafugia ' s $ 279 , 000 price point is a lot lower . but it ' s still based on assumptions about labor costs , production efficiency , the price of raw materials , and more . by way of comparison , the terrafugia ' s current price tag is about the same as that of a new cessna 172 , the most - produced aircraft in history . and its development costs were amortized before terrafugia ' s builders were even born .
“ninety percent of the total program risk is in the first flight and we’re past that , so terrafugia has taken off in more ways than one . ”
terrafugia estimated that by 2015 , the production of the transition® will provide 500 manufacturing , engineering , and support jobs to the u . s . economy .
11 . terrafugia explained that this figure is based on identified cost vs . weight trade - offs , such as material replacement , and a minimal margin .
we ' ve been doing high - speed taxi testing ,
said cliff allen , a veteran pilot and terrafugia ' s vice president for sales .
the terrafugia transition is a two - seater car that can convert from road to air in less than a minute , without the driver leaving the vehicle .
carl dietrich , co - founder of terrafugia , told business insider that you can get a license to operate the transition in as little as 20 hours .
no one associated with terrafugia was willing to talk on the record with me , since the acquisition by geely isn’t yet a done deal . but on linkedin this month , an executive named chris jaran quietly changed his affiliation : he’d been a vice president for bell helicopters in china . now , he’s terrafugia’s new ceo .
terrafugia also provided an animation showing how the t - fx would operate . to take - off , the video shows how electric - powered propellers tilt 90 degrees
terrafugia seeks an exemption from the glazing material requirements ( s5 of fmvss no . 205 ) , which affect the transition ' s® windshield and side windows . terrafugia stated that installing compliant glazing materials , such as traditional laminated safety glass , would result in 29 pounds ( 13 . 2 kg ) of additional weight . terrafugia equipped its proof of concept vehicle with custom - made fmvss - compliant safety glass , but this vehicle was not light enough to comply with the lsa weight restrictions , and terrafugia was unable to remove sufficient weight from the aircraft to accommodate compliant glazing materials . terrafugia calculated that the removal of 29 pounds from the transition® would cost $ 420 , 500 in development costs , would increase the price of each vehicle by a minimum of $ 121 , 800 , and would delay production of the vehicles .
weighing these factors , the agency does not believe that a three - year exemption from fmvss no . 126 is warranted . instead , we are granting terrafugia a one - year exemption . although this period is shorter than that requested by the company , the exemption will allow terrafugia to begin production and continue to work towards compliance .
on march 1 , 2012 , terrafugia announced that the production prototype would make its auto show debut at the 2012 new york international auto show in april , 2012 .
the funds raised on wefunder will go directly towards getting the transition to market . we expect this infusion will enable terrafugia to complete the design of our third prototype .
with a first flight already in the books , terrafugia plans to deliver transitions to customers within 12 months , with an anticipated starting price of $ 279 , 000 .
to date , terrafugia has spent approximately $ 161 , 000 in its efforts to comply with fmvss no . 208 . terrafugia anticipated using the sales revenue generated during the exemption period to pursue the development of an advanced air bag system , ideally one that would be able to differentiate between the needs of an automotive crash and an aviation crash .
terrafugia indicated that the tires and rims it plans on using have appropriate load and speed ratings for the transition® and stated that it had already flight - tested this equipment . most of the public comments supported exempting terrafugia from the tire and rim requirements of fmvss no . 110 . one commenter expressed concern about the safety of driving the transition® without the fmvss - required safety equipment , including tires and rims , but did not specifically comment on any consequences of terrafugia ' s proposed use of motorcycle tires and rims .
terrafugia is excited to premier the new outer mold line for the tf - x™ , terrafugia ' s vision for the future of personal transportation . the tf - x™ will be a four - seat , vertical takeoff and landing ( vtol ) hybrid electric aircraft that makes flying easier and safer than ever before . visit urltoken for more information .
terrafugia is the sole registered automobile manufacturer in massachusetts . { citation needed ( lead ) | date = july 2011 } = = founding and financial history = = terrafugia was founded by graduates of the department of aeronautics and astronautics at the massachusetts institute of technology and graduates of the mit sloan school of management . their team and . . .
but terrafugia is turning most of its attention to its next model : the tf - x . the tf - x will take off , fly , and land autonomously .
in may 2013 , terrafugia said the development of the tf - x would take eight to 12 years . so far , it seems to be sticking to that timeline .
the work calls for terrafugia’s expertise in drive and flight integration , deployable flight surfaces and automotive crash safety for an aircraft . ceo carl dietrich says , “this darpa program effectively leverages terrafugia’s core competencies and enables us to grow from a pure ga [ general aviation ] company to an emerging aerospace company with both general aviation and defense development programs . ”
[ update , 2 : 30 p . m . , march 18 , 2009 : we’ve just published an extensive followup interview with carl dietrich , terrafugia’s founder and ceo . ]
13 . terrafugia stated that not being able to certify the transition® as an lsa would increase certification costs by up to $ 100 million and would force the company to dissolve .
and now terrafugia is in the process of finalizing a deal to be acquired by a chinese automaker , zhejiang geely holding group , which also owns brands like volvo and lotus .
terrafugia ' s transition was recently granted an exemption by the faa , allowing it to be classified as a ' light - sport ' craft , according to the washington post .
terrafugia said its aim is to provide ' true door - to - door transportation , ' with the vehicle capable of being parked in a home garage like an ordinary car .
with a fresh infusion of cash and ongoing flight and road testing , the terrafugia transition roadable airplane / flying car is going through design refinement and is closer to federal certification .
the model will be tested at the mit wright brothers wind tunnel , the same tunnel that was used to test models of terrafugia ' s transition . the wind tunnel test model will be used to measure drag , lift and thrust forces while simulating hovering flight , transitioning to forward flight and full forward flight ,
terrafugia said in a statement .
terrafugia had asked the faa for a waiver of weight and stall - speed limits so it can self - certify its transition flying car as a light sport aircraft ( lsa ) .
the exemptions clear the way for shipping to begin from terrafugia ' s massachusetts plant following testing . the flying car is slated to enter production this year , with shipping in 2012 .
those rules have yet to be put in place . when they are , terrafugia will have a better idea on how to proceed with getting the tf - x on the market .
after reviewing terrafugia ' s petition and the public comments , we believe that the company has made good faith efforts to comply with the standards from which it is seeking exemption . terrafugia is a new company , and the transition® is a unique , dual - purpose vehicle designed for both flying and driving . many of the impediments to compliance that terrafugia has encountered are a direct result of the dual nature of the transition® , including the need to meet the strict weight requirements of an lsa . despite these impediments , terrafugia has devoted significant resources towards compliance , has attempted to mitigate the risks associated with noncompliance , and has developed a plan for full compliance with three of the four listed fmvsss by the end of the requested three - year period .
12 . terrafugia noted that there is a physical limitation as to how much weight can be removed from the vehicle , at any cost , before it is no longer capable of safely performing its function . the dollar values provided by terrafugia are applicable until that limit is reached , past which very little can be done at any price and the product is no longer viable .
massachusetts - based firm terrafugia created the transition , a road - legal airplane . the vehicle can seat two and is small enough to fit in a garage , and comes with collapsible wings
terrafugia says that the flight took place on march 5 , and will hold a media briefing at 1430 uk time . meanwhile pictures of the flight are available on the company ' s website .
terrafugia says it plans to follow on , circa 2021 , with the tf - x , a tilt - wing rotor flying car with a plug - in hybrid powerplant ( video above ) .
the work calls for terrafugia ' s expertise in drive and flight integration , deployable flight surfaces , and automotive crash safety for an aircraft . chief executive officer carl dietrich says ,
this darpa program effectively leverages terrafugia ' s core competencies and enables us to grow from a pure ga company to an emerging aerospace company with both general aviation and defense development programs . our strong team of terrafugia engineers with recent experience designing and building a dual purpose vehicle will bring a unique perspective to the tx program that is highly valued by darpa and the other contractors on our tx team .
that question encapsulates the 11 - year saga of terrafugia , a woburn company founded by five graduates of the mit aeronautics program . terrafugia’s sleek white aircraft first flew in 2009 , and the company has benefited from millions of dollars worth of free publicity around the world . despite that , the company hasn’t managed to deliver the first of its single - prop transition vehicles into a customer’s driveway .
terrafugia stated that , to date , it has spent $ 50 , 290 towards finding a compliant rim and tire combination that would meet the speed , loading , and weight requirements for the transition® .
just how much the chinese automotive company paid for terrafugia has yet to be revealed , but experts say the move could be a step toward the ultimate travel solution for commuters , according to scmp .
i will definitely be a customer terrafugia ! i had seen your concept when you first came out a while back and hadn’t heard anything since until i saw the rss feed for slashdot just now .
the first prototype was built and flown in 2009 , followed by a second iteration in 2012 . today , terrafugia is finalizing production vehicle design and compliance testing in preparation for the first vehicle deliveries .
additionally , terrafugia stated that the transition® is currently its only product line . accordingly , a denial would force the company to delay all production until compliance is achieved . terrafugia stated that a denial would delay customer delivery and initial revenue generation by at least two years and that this delay , coupled with the sharply decreased probability of the company reaching profitability , would make additional investment capital extremely difficult to secure . terrafugia calculated that the difference between a grant and a denial of its petition was $ 19 . 4 million in revenue and indicated that a denial would likely put the company out of business .
“we are passionate about continuing to lead the creation of a flying car industry and are dedicating resources to lay the foundations for our vision of personal transportation , ” says terrafugia ceo / cto carl dietrich .
terrafugia , developer of the transition roadable aircraft , has been announced by aai corp . as the largest subcontractor to develop the transformer helicopter / humvee for the defense advanced research projects agency ( darpa ) .
a key participant in the darpa program is woburn , ma - based terrafugia . you might know it as the “flying car” company , though the firm much prefers the drier term “roadable aircraft . ” terrafugia was founded in 2006 by five mit - educated pilots , and has been developing a light sport plane , called the transition , that can be driven on roads and is slated for testing and production next year . the company declined to comment on its involvement in the darpa program beyond the information in its press release this week . but it’s clear that terrafugia’s expertise in combining flying and driving vehicles is valuable here .
terrafugia described in detail its efforts to comply with the listed fmvsss as well as its plans for compliance by the end of the proposed exemption period . in particular , terrafugia provided a plan to achieve full compliance with fmvss nos . 110 , 205 , and 208 within the three - year period . although terrafugia budgeted for fmvss no . 126 compliance research and indicated that it was working towards compliance with all fmvsss by the end of the requested exemption period , the company also stated that it was currently evaluating vendors to work with to develop an esc system and indicated that further research might lead the company to petition for rulemaking on this issue . accordingly , it appears that terrafugia does not know at this time whether the transition® will be able to comply with fmvss no . 126 by the end of the requested exemption period .
the first transition ® proof of concept vehicle was flown and driven in 2009 . three years later , terrafugia designed , built , and flew a redesigned second iteration of the vehicle . that prototype has logged over 100 flight hours and over 200 successful takeoffs and landings , including a public demonstration at eaa’s airventure in oshkosh , wi in 2013 . in 2016 , the faa approved terrafugia’s request for a weight limit exemption for the transition ® , a crucial decision that will allow terrafugia to bring the vehicle to market as a light sport aircraft . the transition ® will enter production in three years with first delivery anticipated in 2019 .
one company , terrafugia , is working to get its flying car off the ground ( see what i did there ? ) by 2025 . scroll down for a closer look at the company ' s plan .
terrafugia stated that it had approached bosch engineering group about developing an esc system for the transition , ® but those discussions were terminated by bosch due to liability concerns about installing the system on an airplane . terrafugia indicated that it was in the process of evaluating other vendors . the company stated that it had also investigated the feasibility of developing an esc system in - house but had determined that such a program beyond its current capabilities . terrafugia indicated that an exemption would allow it to further investigate the issues associated with an esc system , which might result in a petition for rulemaking to reflect the aviation safety concerns of such a system .
regarding the decision to design a four - wheel , rather than three - wheel , vehicle , terrafugia stated in its petition and its response to the public comments that it was aware that using a three - wheel design would lessen its regulatory burden . however , due to the light weight of the vehicle and the exposed side area of the folded wings , the company chose a four - wheel design to increase stability and make the vehicle safer . given terrafugia ' s rationale for its decision to use a four - wheel design , the agency does not believe that this decision reflects negatively on terrafugia ' s efforts to comply with the fmvsss .
anna mracek dietrich , chief operating officer of terrafugia said the new york event was selected for the rollout of the transition because of the value the show brings in terms of exposure to future owners , investors and partners .
terrafugia management is actively involved in the creation and maintenance of the astm standards that are used by the faa for the regulation of light aircraft . in addition , terrafugia coo anna mracek dietrich participated in the aviation rulemaking committee ( arc ) which is advising the faa on the latest revision of the federal aviation regulations that pertain to aircraft less than 19 , 000 lbs . our exposure to the fmvss has been quite useful to these bodies .
terrafugia has been working on flying cars since 2006 , and has already pushed back the launch once . last summer the company said it would have to delay expected 2011 deliveries due to design challenges and problems with parts suppliers .
dietrich said terrafugia is aiming to develop a training program that could be learned over the course of a weekend . it could be taught at flight schools or other training centers , but those details have yet to be determined .
in accordance with 49 u . s . c . 30113 and the procedures in 49 cfr part 555 , terrafugia has petitioned ( dated july 20 , 2010 ) the agency for a temporary exemption from certain fmvss requirements for the transition , ® a light sport aircraft ( lsa ) that has road - going capability . in addition to its original petition , terrafugia has submitted additional information regarding its compliance efforts , which has been posted to the public docket .
additionally , terrafugia expressed concern that an esc system would create a potential hazard while the transition® is in flight . however , the agency notes that fmvss no . 126 explicitly allows vehicles to be equipped with an “esc off” control that puts the esc system into a mode in which it will no longer meet the performance requirements described in the standard . terrafugia did not discuss this provision or explain why such a control would not be feasible for the transition® .
this darpa program effectively leverages terrafugia ' s core competencies and enables us to grow from a pure ga company to an emerging aerospace company with both general aviation and defense development programs ,
said chief executive officer carl dietrich .
our strong team of terrafugia engineers with recent experience designing and building a dual purpose vehicle will bring a unique perspective to the tx program that is highly valued by darpa and the other contractors on our tx team .
terrafugia seeks an exemption from the general tire requirements ( s4 . 1 ) and rim requirements ( s4 . 4 ) of fmvss no . 110 . terrafugia stated that compliance with these requirements would cause substantial economic hardship due to the cost of reducing the weight of the vehicle in order to offset the weight of the tires and rims required by the standard , which have significantly higher speed and load ratings than that needed for the transition® . as part of its efforts to comply with the standard , terrafugia evaluated several passenger car tire and rim combinations . the company also investigated the development of a lighter custom rim and tire combination that would meet the requirements of fmvss no . 110 .
terrafugia included a schedule of its future compliance efforts during the proposed exemption period and stated that it was working toward full compliance by the end of that period . however , terrafugia noted that the success of its plan was dependent on the availability of sufficient investment capital and the willingness of third parties to work with it . the company reiterated that it was also considering petitioning nhtsa and faa for rulemakings to address the unique dual - purpose nature of the transition® .
terrafugia still has the process of light - sport certification before it , and road - legal clearance from the national highways and transportation safety administration . however the transition has already undergone extensive ground tests , and company execs seem confident .
it’s called the tf - x : terrafugia ( which is latin for “escape the earth” ) and is being created in woburn , massachusetts by a team of award - winning mit - trained aerospace engineers . check out it’s range .
terrafugia has designed and built the first prototype of the transition , ® which it described as a “roadable aircraft . ” terrafugia characterized the transition® as an lsa , as defined by the federal aviation administration ( faa ) , and stated that the vehicle ' s road - going capability will provide a significant increase in operational functionality and safety for the general aviation [ 6 ] pilot community by allowing pilots to safely continue their travel plans in the event of inclement weather .
what’s next for transition ? dietrich : delivery of first vehicle will be in 2011 . the manufacturing process is expected to create hundreds of jobs . “with this accomplishment terrafugia is poised to usher in a new era of general aviation . ”
the company also determined that , in the event of a bird strike , fmvss - compliant safety glass would either shatter or craze to a degree that would substantially inhibit the pilot ' s view . accordingly , terrafugia investigated the possibility of using an fmvss - compliant polycarbonate windshield . according to the petition , the polycarbonate material passed intrusion tests without cracking , but terrafugia was still pursuing options for a scratch - resistant coating that could meet the abrasion tests . the company stated that one vendor informed them that its coating would likely pass the abrasion tests but that such tests had not yet been performed . terrafugia indicated that it is engaged in discussions with several vendors and is planning future compliance testing of coated polycarbonate materials . in the meantime , terrafugia stated that the transition® would be equipped with polycarbonate glazing , and each vehicle would be required to undergo regular , frequent inspections , at which time windshields with degraded visibility would be identified and replaced .
mann said terrafugia was helped by the federal aviation administration ' s decision five years ago to create a separate set of standards for light sport aircraft . the standards govern the size and speed of the plane and licensing requirements for pilots , which are less restrictive than requirements for pilots of larger planes . terrafugia says an owner would need to pass a test and complete 20 hours of flying time to be able to fly the transition , a relatively low hurdle for pilots .
at this point , flying cars are still very much in the realm of science fiction . companies like terrafugia have expressed interest in this new method of consumer transportation , and while terrafugia is probably closer than anyone else , a massive wall of regulatory red tape stands in the way of turning drivers into pilots . i ' m a pretty experienced driver , but if someone told me to
squawk 1200 ,
i wouldn ' t know what the heck to do .
the job description is clear : under new ownership , get one or both of terrafugia’s products out of the hangar and into the sky . the question that remains : will this pioneering company grow in massachusetts or be shipped to china ?
terrafugia , a boston - area company that has been working on flying cars since 2006 , is being acquired by zhejiang geely holding group , an automotive manufacturer based in hangzhou , china . terms of the deal have not been disclosed .
terrafugia could be in the same boat . what it has created is an admirable execution of the flying car concept , but flying cars simply are still too costly and impractical for the dream to become more than a novelty anytime soon .
terrafugia noted that the transition® is currently its only product line . accordingly , a denial would force the company to delay all production until compliance is achieved . the company stated that a denial would delay customer delivery and initial revenue generation by at least two years and that this delay , coupled with the sharply decreased probability of the company reaching profitability , would make additional investment capital extremely difficult to secure . terrafugia calculated that the revenue difference between a grant and a denial of the exemption would be $ 19 . 4 million and would double the price point of the transition® . accordingly , terrafugia opined that a denial would likely force the company to abandon lsa certification and the development of the transition® . [ 13 ]
we wish them well , but there ' s a long way to go . for its part , the faa has released a statement that reads , in part :
the manufacturer has not yet applied for an faa airworthiness certificate , so the faa has not yet determined what level of pilot certificate and training would be required to operate the terrafugia transition as an aircraft .
that ' s a hurdle terrafugia will need to clear before it can make its first delivery .
terrafugia stated that a grant of the requested exemption would allow the company to continue with lsa certification for the transition® while pursuing lightweight compliance solutions and researching additional ways of reducing the weight of non - safety - critical systems for the aircraft .
terrafugia anticipated that the transition® will only be operated on public roadways in conjunction with a flight . the company stated that it expects that the typical recreational owner will operate the vehicle as an aircraft for at least 65 percent of its engine - on - time and will drive the vehicle on the road less than 2 , 000 miles annually . terrafugia contended that the combination of low sales volume and limited use on roadways limits the transition ' s® overall impact on motor vehicle safety .
10 . terrafugia explained that this is based on the experience of removing weight between the proof of concept vehicle to the prototype and the fact that as more and more weight must be removed , it becomes increasingly more difficult to do so .
terrafugia’s transition ® is the only flying car in the world to have received all of the special legal considerations necessary to enter the u . s . market . driving the transition ® will require a standard u . s . driver’s license , and flying the transition ® will require a sport pilot certificate , which can be earned in as few as 20 hours of flight training . eventually , with the incorporation of autonomous flight technologies , terrafugia hopes to further reduce flight training time .
the company behind the first faa approved
roadable aircraft
– the terrafugia transition – has been selected to contribute to darpa ' s transformer ( tx ) project , a program that aims to bring flying car technology to the battlefield . terrafugia will subcontract to one of two winning teams under phase one of the program which focuses on creating a conceptual design for a four person cross between a humvee and a helicopter for use in insurgency , reconnaissance , medical evacuation and logistical supply .
terrafugia ' s flying car , on display at the new york international auto show this week , is an impressive execution of the flying car concept . but there are plenty of good reasons why we won ' t soon have roadable planes .
as soon as terrafugia begins to sell the transition , i will purchase one . i am holding out for the next model . i imagine that they have another one in the works currently . i still have time to wait , i still need to receive my private pilots certificate . so , until i get that i won’t be purchasing anything yet . i sure am very happy for terrafugia’s success . best of luck to them , and thank you for this great creation ! : )
we have also considered motor vehicle safety issues related to the exemption requested by terrafugia . we believe that , in general , the requested exemption will have a limited impact on motor vehicle safety because of the low number of vehicles expected to be produced and because each vehicle is likely to travel on public roads only infrequently . terrafugia predicted producing 200 vehicles during the exemption period and estimated that , on average , each vehicle would spend less than 2 , 000 miles on the road annually .
according to terrafugia ' s petition , one of the most significant causes of general aviation accidents and fatalities is weather , and a leading cause of weather - related accidents is when pilots using visual references , rather than flight instruments , for primary orientation and navigation ( visual flight rules or vfr ) fly into weather conditions with insufficient visibility to provide a safe visual reference ( instrument meteorological conditions or imc ) . in such situations , pilots can get disoriented and enter an unrecoverable situation that results in an often fatal accident . according to terrafugia , the transition® offers a new alternative to pilots by allowing them to divert to the nearest airport and continue the trip on the ground . although the trip may take longer , terrafugia stated that the transition® is expected to eliminate the possibility of an indeterminately long delay caused by either retracing the flight route to clearer weather or diverting and waiting for the weather to pass . accordingly , terrafugia expects that the transition® will help reduce these types of crashes , while also making general aviation more appealing and accessible to a greater number of people . additionally , because the transition® is equipped with basic fmvss occupant crash protection features , terrafugia argued that it is advancing passenger safety technology in light aircraft .
terrafugia has raised ~ $ 10 million from sophisticated accredited investors . the majority of that capital has been spent on the development of the transition . the rest is still being deployed today to get the transition through the rest of the testing program .
according to the petition , terrafugia is a small , privately held company that was incorporated in the state of delaware in 2006 and maintains headquarters in woburn , massachusetts . terrafugia states that the company employs ten full - time employees . the company identified itself as a massachusetts institute of technology ( mit ) spin - off company , but stated that it does not have access to mit ' s financial resources . the company also stated that it is not affiliated with any other aircraft or automobile manufacturer .
as of 2013 , woburn , ma - based terrafugia had raised a little over $ 10 million in financing from angel investors and $ 1 . 25 million in u . s . defense contracts . the company has raised more money since then , but the amount wasn’t disclosed ; new york - based transcendent holdings and beijing - based haiyin capital are also investors in the company . ( dietrich and terrafugia participated in a boston - area event organized by haiyin capital in the fall of 2015 . )
this breakthrough changes the world of personal mobility ,
terrafugia ceo carl dietrich told avweb .
travel now becomes a hassle - free integrated land - air experience . it ' s what aviation enthusiasts have been striving for since 1918 .
®
terrafugia’s ‘street - legal airplane , ’ transition , was approved last year by the federal aviation administration ( faa ) to be certified as a light sport aircraft , paving the way for the development of hybrid vehicles weighing up to 1 , 800 pounds .
the tx program represents an opportunity for terrafugia to rededicate members of its engineering team as its primary business , the transition light sport aircraft program , moves forward on schedule from detailed design to fabrication , testing and production in the second half of 2011 .
the agency acknowledges that terrafugia ' s petition indicated that a three - year exemption was required to comply with the fmvsss and that the company may not be able to achieve full compliance with the requirements of fmvss no . 126 and the advanced air bag requirements of fmvss no . 208 within the one - year exemption period granted by this notice . however , as stated above , this exemption will allow terrafugia to begin production and continue its efforts toward full compliance with these standards . additionally , we note that part 555 allows a manufacturer to apply for renewal of a temporary exemption , and we emphasize that our decision to grant a more limited exemption than that requested does not foreclose terrafugia from applying for such an extension at the end of the exemption period .
to date , terrafugia has not produced any vehicles for sale , but intends to begin delivery of the transition® in late - 2012 [ 7 ] and anticipates producing 200 vehicles during the three - year requested exemption period . terrafugia stated that it expects to remain a low - volume manufacturer for the foreseeable future , continuing to market the transition® as an aircraft with road - going capability , not as a “flying car . ” thus , the primary market for the transition® will be u . s . pilots .
while there are other companies out there experimenting with the futuristic hybrid vehicle , terrafugia is arguably the first to make a truly convincing prototype . offering a far more sleek and polished vehicle than any of its competitors , terrafugia ' s transition boasted a cruising range of 400 miles and a top speed of 100 mph . as well as being fitted with a full - vehicle parachute to bring the car back onto roads , the transition also uses advanced autonomous flight tech in order to stop its pilots from crashing .
geely , parent company of volvo cars , has agreed to purchase the flying - car startup terrafugia , the south china morning post reports . while the purchase amount was not disclosed , scmp reports that this deal has been in the works since last year .
despite ieee spectrum’s gloomy forecast for flying cars in 2007 as “a flimsy car and a feeble airplane” and again this year , the flying car might still happen . terrafugia is further along than any of the dozens of prototypes cobbled together in the past century .
the tx program represents an opportunity for terrafugia to rededicate members of its engineering team while its primary business , the transition light sport aircraft program , moves forward on schedule from detailed design to fabrication , testing and into production during the second half of 2011 .
terrafugia ' s prototype flying car , dubbed the transition , travels down a street with its wings folded . the vehicle can be driven like a car , and flew at 1 , 400 feet for eight minutes during its test flight on march 23 , 2012 .
getting a light plane - car hybrid off the ground seems to be an arduous process . the tf - x - - from flying - car company terrafugia - - was announced more than two years ago but will be in development for some years to come .
in ten years , terrafugia should have at least two product lines - - an evolved transition that is even easier to operate , and at least one product that has evolved out of the tf - x program which will allow a much larger segment of the population to experience the freedom of a practical flying car . i expect we will be a publicly traded company selling thousands of vehicles per year . the open development environment of tf - x will have maintained the public’s trust and terrafugia’s leadership position in a rapidly maturing flying car industry even with the entry of new much larger companies . we will be inspiring millions of people around the world to embrace a new dimension of personal freedom . flash forward another 10 years and the industry terrafugia inspired will have a measurable effect on the global gdp .
one issue is that terrafugia has been building a product for a shrinking market here in the united states . while 827 , 000 people held a pilot’s license in 1980 , that number had dropped to 584 , 000 by 2016 , according to the federal aviation administration .
the transition by terrafugia is a roadable aircraft , an airplane that can take off and land from any airport , and with the push of a button fold up its wings and drive down the road . for more information about this innovative product , please go to urltoken
in addition , us - based terrafugia said monday , the new design for the tf - x will be tested as a one - tenth scale model in a wind tunnel . the model is currently on display at the eaa airventure aviation convention in oshkosh , wisconsin .
the transition® uses an faa - certified , four cylinder , 100 horsepower , unleaded gasoline - fueled aircraft engine to power the vehicle both in the air and on the ground . terrafugia contended that the use of unleaded gasoline will provide “significant ecological and energy benefits , ” as compared to the leaded gasoline used in other general aviation aircraft . terrafugia also opined that one day a future version of the transition® might play a role in reducing highway congestion and co 2 emissions by enabling more people to shift from highway - based travel to a combination of flight and road use for mid - range trips . terrafugia stated that the transition® will cruise in the air at approximately 105 miles per hour and maintain highway speeds on the ground , while attaining between 25 and 40 miles per gallon in flight and on the road .
terrafugia also discussed the probability of children riding in the transition® . the company acknowledged that children may occasionally be driven or flown in the transition® , but that it was not expected to be a common occurrence . the company noted that most of the customers who could afford the transition® are beyond the age at which they would have young children and , as trained pilots , would understand the associated risks . terrafugia further stated that the benefit garnered by occasionally giving children the opportunity to ride in the transition® offsets the occasional , well - considered risk .


the jenks optimization method , also called the jenks natural breaks classification method , is a data clustering method designed to determine the best arrangement of values into different classes .

this is done by seeking to minimize each class ’s average deviation from the class mean , while maximizing each class ’s deviation from the means of the other groups .

in other words , the method seeks to reduce the variance within classes and maximize the variance between classes .

the jenks optimization method is directly related to otsu 's method and fisher 's discriminant analysis .

jenks natural breaks optimization

given a vector of numeric values and the number of desired breaks , calculate the optimum breakpoints using jenks natural breaks optimization .
george f . jenks proposed jenks natural breaks in his 1977 article entitled ‘optimal data classification for choropleth maps’ .
, ( or making maps with any software ) , this page explains about
natural breaks
for setting map ranges . jenks natural breaks is also called
fisher ' s natural breaks
.
real statistics data analysis tool : the real statistics resource pack provides the jenks natural breaks data analysis tool to perform the optimization automatically .
the jenks natural breaks method was ported to c from code found in the classint r package .
i ' m looking for an implementation of the jenks optimization algorithm for data classification .
jenks natural breaks optimization addresses the problem of how to split a range of numbers into contiguous classes so as to minimize the squared deviation within each class .
observation : the jenks natural breaks algorithm is commonly used to color maps as shown in figure 9 .
the jenks natural breaks optimization method allows you to break up data points into the best possible number of groupings , with the best possible contents of each group for choropleth mapping .
the jenks natural breaks classification method seeks to reduce the variance within classes and maximize the variance between classes . urltoken urltoken
fisher ' s natural breaks uses dynamic programming to find the optimal solution and is deterministic .
you wish . here are stands displayed in 5 natural breaks classes , according to age .
different class break values between this map and the natural breaks map . each class here will
natural breaks is complicated because many steps are involved , but does not involve any higher math .
the first thing to remember about the natural breaks ( jenks ) classification is that it is an optimization method for choropleth maps . in short , it arranges each groupings so there is less variation in each class or shading .
equal intervals , quantile , natural breaks , pretty breaks – there’s a lot to choose from . but what is the difference between each of them ?
and so here’s a literate implementation of jenks natural breaks in javascript . if you can , please help to improve it by making the implementation more explanatory .
compute “natural” break values ( jenks algorythm ) on list / tuple / numpy . ndarray of integers / floats .
equal intervals , quantile , natural breaks , pretty breaks . each data classification methods generate different choropleth maps . we explain the advantages and disadvantages of using each type of choropleth map .
any pointers to any particular work that uses jenks natural break or even compares it with k - means would be great .
natural breaks classes are based on the nature of data . the range is set only when a surprise or big difference appears in data values . convergent data values put together under one class . different classes are properly distributed under this way . this method is applied to prepare this atlas , and it is calculated by the gis software according to the jenks natural breaks optimization ( jenks ) . it depends on the adequate classification by the clearest values on the map .
don ' t use multidimensional clustering algorithms for a one - dimensional problem . a single dimension is much more special than you naively think , because you can actually sort it , which makes things a lot easier . in fact , it is usually not even called clustering , but e . g . segmentation or natural breaks optimization . you might want to look at jenks natural . . .
simple - statistics , my library for literate , beginner - friendly statistics , now has a literate implementation of jenks natural breaks . in the process of understanding the implementation , i found that the matrix system is a sort of dynamic programming that cleverly solves all breaks from 1 - k when you request k breaks . thus my implementation breaks it into two parts - creating the matrices and pulling a solution out of them .
to perform the analysis for example 1 , press ctrl - m and select the multivariate analyses option from the main menu and then select jenks natural breaks from the dialog box that appears , as shown in figure 5 .
not the answer you ' re looking for ? browse other questions tagged python clustering optimization or ask your own question .
when the jenks natural breaks dialog box appears , fill in the various fields as shown in figure 5 and press the ok button . if you leave the number of iterations field blank then the algorithm will evaluate all possible partitions .
this page was updated 20 october 2002 to expand on the natural breaks description . thanks to daniel karnes of dartmouth college for pointing out the need for improvement .
the founder of the natural breaks data classification method was a cartographer by the name of george frederick jenks . he specialized in monitoring the eye movements of people when looking at a map . and the results for this map looked great too .
the jenks natural breaks algorithm , just like k - means , assigns data to one of k groups such that the within group distances are minimized . also just like k - means , one must select k prior to running the algorithm .
borden dent ( cartography - - thematic map design , fifth edition , 1999 , pages 147 - 149 ) relates that the natural breaks classes are found by an iterative search to minimize the sum of spreads of the classes . thus it is a one - dimensional example of the k - means clustering method . natural breaks , jenks ' method , and k - means are all the same in this instance .
jenks ( r1 , , lab , iter ) – performs jenks natural breaks optimization on the data in range r1 for k classes and outputs a k + 1 × 3 range , whose first k rows contain the left and right endpoints of each of the classes followed by the number of elements in the class . the last row contains the total squared deviation of the k classes , followed by the squared deviation for the data in r1 and gvf .
natural breaks ( jenks ) takes an iterative approach by comparing the sum of squared deviations between classes to the array mean . then , the algorithm uses a goodness of variance fit with 1 as a perfect fit and 0 as a poor fit .
features in each bin . here is the jenks classification for the image above .
what we don’t know is whether these four intervals is the partition of the full range that results in the smallest sum in cell t21 . as we will see shortly , the optimum solution , using jenks natural breaks optimization , is shown in figure 3 . as you can see , this is a better solution than the one shown in figure 2 ( since 3107 . 102 < 4496 . 957 ) .
if you want round numbers in your ranges , then you should choose pretty breaks . all pretty breaks does is rounds each break - point up or down . so instead of having a break point as 599 . 364 it will become 600 , 000 with pretty breaks .
the quantile style provides quantile breaks ; arguments to quantile may be passed through . . . .
the chart shows the number of acres in each unique age class . this method uses then jenks
computebayesfactors : compute bayes factors generatecontrolfile : generate control file for ' bamm ' getjenksbreaks : jenks natural breaks classification gettiprates : compute tip - specific macroevolutionary rates from ' bammdata ' . . . plotprior : plot the prior and posterior distribution of shifts setbammpriors : set bamm priors traitdependentbamm : strapp : structured rate permutations on phylogenies
create a “natural breaks” classification using two or more classes . look closely at the map . now reverse the order of the classes in the legend ( use , for example ) . what changes ? can you discover why ?
one problem is that your boss is not letting the data speak . perhaps there are three
natural
clusters . insisting on five will result in breaking apart two of the clusters . those break points will not be
natural .
i ' m not sure what mathematical definition you are using for
natural breaks ,
but one interpretation is to identify places where there are
gaps
in the data . in other words , you want to cluster the data .
the hclust style uses hclust to generate the breaks using hierarchical clustering ; the pars attribute returns the hclust object generated , and can be used to find other breaks using gethclustclassintervals ; arguments to hclust may be passed through . . . .
natural breaks
finds the
best
way to split up the ranges . suppose we had 30 counties , 15 counties with 0 - 1 values , 10 counties with 16 - 18 values , and 5 counties with 24 - 29 values . obviously , the
best
ranges are 0 - 1 , 16 - 18 , 24 - 29 . counties with similar values should have the same color .
natural breaks
is the only method that finds the
best
ranges .
given a desired number of classes , k , the natural breaks method partitions the data into k subsets that minimize the sum of the
spreads
within each subset . (
spread
is an informal term employed solely for this description . )
and this is not quibbling about style : the wikipedia article about jenks natural breaks describes an algorithm entirely unlike these ones . there’s no mention of dynamic - programming matrices , and there’s no hint in the implementations of something like the ‘sum of deviations between classes . ’ of course , there are no comments in any of the ports , so it’s hard to tell .
getclassjenks ( nbclass ) : perform a jenks classification and return bounds into an array . alias : getjenks ( nbclass )
as a result of making rounded numbers , pretty breaks will also be very picky for the number of classes you decide .
jenks is k - means in one dimension . the wikipedia article would be one of the references you seek . for work that uses the jenks method , just find any of several million maps created by arcview users over the last 20 years .
my boss has asked me to show the distribution of a variable ( square footage of 17 , 000 public library outlets / branches ) , breaking it into 5 categories using natural breaks . putting aside arguments of the
best
number of categories or the problems with categorizing a continuous variable . . . i ' ve used proc rank for creating deciles , quantiles , etc . , but the only place i ' ve seen that uses
natural breaks
( outside of distance sporting events ) is chloropleth maps . i ' ve googled for a solution . the closest i got , other than a bunch of articles on analyses using the jenks optimization in arcgis , was a post to the uga sas - listserv in 2000 . i ' ve seen a few possible links to using proc cluster , but that always seems to be when doing a multivariate analysis .
here 3107 . 102 ( cell l7 ) represents the total squared deviation for the partition found using the jenks natural breaks algorithm , 27504 . 59 ( cell m7 ) is the squared deviation of the input data , as calculated by = devsq ( b3 : i22 ) and 88 . 7 % is the gvf ( cell n7 ) , as calculated by the formula = 1 - l7 / m7 .
there’s a standard algorithm we use for jenks , with existing ports in in javascript , python , and in java and fortran .
here you have php urltoken this is implementation of jenks algorithm . david drake made these functions and integrated it with google api .
the range u10 : u13 of figure 8 contains the array formula = jenks ( b3 : i22 , 4 , , 100000 ) .
when the data represent a random sample from a population consisting of two more more distinctly different subpopulations , and you know - - or can accurately guess - - how many different subpopulations there are , then natural breaks can do a good job of choosing classes which reflect the subpopulation groupings .
observation : in example 2 , we were able to go through each possible partition and calculate its squared deviation . while in example 1 , this is too time - consuming to do manually , we can use the real statistics jenks natural breaks data analysis tool , as described below , to do the calculations for us , for other problems the number of possible partitions is even too time - consuming for the computer to do .
jenks natural breaks works by optimizing the goodness of variance fit , a value from 0 to 1 where 0 = no fit and 1 = perfect fit . the key in selecting the number of classes is to find a balance between detecting differences and overfitting your data . to determine the optimum number of classes , i suggest you use a threshold gvf value you desire and use the number of classes that satisfies this value first .
it means the ranges where like areas are grouped together . obviously , we do not give a low rate area the same color as a high rate area . natural breaks minimizes the variation within each color , so the areas within each color are as close as possible in value to each other .
gvf ( r1 , r2 ) = gvf for the right endpoints ( breaks ) in range r2 based on the data in column range r1 .
i found this python implementation of the jenks natural breaks algorithm and i could make it run on my windows 7 machine . it is pretty fast and it finds the breaks in few time , considering the size of my geodata . before using this clustering algorithm for my data , i was using sklearn . clustering . kmeans ( here ) algorithm . the problem i had with kmeans , was finding the optimum k value parameter , but i
solved
it launching the algorithm for different k values and using sklearn . metrics . silhouette _ score ( here ) to find the best k .
the range k3 : n7 of figure 7 contains the output of the array formula = jenks ( b3 : i22 , , true ) . the range p10 : s14 of figure 8 contains the output of the array formula = jenks ( b3 : i22 , , true , 100000 ) .
i also read from another source that says jenks is usually used to spot gaps in ranged data . again i cannot find a reference to explain this .
try out jenks in simple - statistics . if the assortment of other algorithms included make you feel like you should create a new ‘micro library’ , you can also just use the jenks implementation as a standalone . please don’t delete the comments : if you need compression , use uglify - js as a separate step .
widely used within gis packages , these are forms of variance - minimization classification . breaks are typically uneven , and are selected to separate values where large changes in value occur . may be significantly affected by the number of classes selected and tends to have unusual class boundaries . typically the method applied is due to jenks , as described in jenks and caspall ( 1971 ) , which in turn follows fisher ( 1958 ) . see figure 4‑22 for more details . unsuitable for map comparisons
the method requires an iterative process . that is , calculations must be repeated using different breaks in the dataset to determine which set of breaks has the smallest in - class variance . the process is started by dividing the ordered data into groups . initial group divisions can be arbitrary . there are four steps that must be repeated :
i am new to this topic . as far as i know both are data clustering methods . then my question is when is jenks prefered over k - means ?
let’s be clear : the algorithms we use for jenks are directly ported from an algorithm that accepted punch cards , documented in a paper composed and published on a typewriter .
the pretty style chooses a number of breaks not necessarily equal to n using pretty , but likely to be legible ; arguments to pretty may be passed through . . . .
positioning of breaks may be pre - determined by the classification procedure ( e . g . jenks natural breaks ) , but these are often manually adjustable for some of the schemes provided — this is particularly useful if specific values or intervals are preferred , such as whole numbers or some convenient values such as 1000s , or if comparisons are to be made across a series of maps . in some instances options are provided for dealing with zero - valued and / or missing data prior to classification , but if not provided the data should be inspected in advance and subsets selected prior to classification where necessary . some authors recommend that maps with large numbers of zero or missing data values should have such regions identified in a class of their own .
so : yes , this isn’t the first implementation of jenks in javascript . and it took me several times longer to do things this way than to just get the code working .
there is no such assurance . but natural breaks makes the most epidemiologically accurate map . making the map
pretty
is important , but that would involve such factors as right number of colors ( not too few , not too many ) , right color palette ( a standard colorbrewer palette provided by vitalnet ) , high resolution so the map does not look fuzzy , and nice legend .
however , jenks and k - means are different in how they minimize within group distances . jenks takes advantage of the fact that 1 - dimensional data is sortable which makes it a faster algorithm for 1 - dimensional data . k - means is more general in that it can handle data in any dimension ; including dimensions greater than 1 where the data is not sortable .
’s thematic formatting facilities providing a wide range of options that reduce or remove the dependence on formal class boundaries . the jenks method , as implemented in a number of gis packages such as
the jenks style has been ported from jenks’ basic code , and has been checked for consistency with arcview , arcgis , and mapinfo ( with some remaining differences ) ; added here thanks to hisaji ono ; note that the sense of interval closure is reversed from the other styles , and in this implementation has to be right - closed - use cutlabels = true downstream for clarity .
using silhouette with jenks should be comparable to using it with kmeans . it ' s a heuristic and you shouldn ' t trust it blindly . imho the best is to visualize your rrsults .
the sd style chooses breaks based on pretty of the centred and scaled variables , and may have a number of classes different from n ; the returned par = includes the centre and scale values .
from jenks import jenks import numpy as np def goodness _ of _ variance _ fit ( array , classes ) : # get the break points classes = jenks ( array , classes ) # do the actual classification classified = np . array ( [ classify ( i , classes ) for i in array ] ) # max value of zones maxz = max ( classified ) # nested list of zone indices zone _ indices = [ [ idx for idx , val in enumerate ( classified ) if zone + 1 = = val ] for zone in range ( maxz ) ] # sum of squared deviations from array mean sdam = np . sum ( ( array - array . mean ( ) ) * * 2 ) # sorted polygon stats array _ sort = [ np . array ( [ array [ index ] for index in zone ] ) for zone in zone _ indices ] # sum of squared deviations of class means sdcm = sum ( [ np . sum ( ( classified - classified . mean ( ) ) * * 2 ) for classified in array _ sort ] ) # goodness of variance fit gvf = ( sdam - sdcm ) / sdam return gvf def classify ( value , breaks ) : for i in range ( 1 , len ( breaks ) ) : if value < breaks [ i ] : return i return len ( breaks ) - 1
due to numerical stability , the log likelihood is used , turning the product into a sum of logarithms , for optimization is the same , given that the log function is monotonicly increasing . by convention , loss functions are minimized with neural networks , this means we will negate it and call it the negative log - likelihood :
it depends on the number of areas , number of colors , and the cpu . remember that with 254 counties and 6 colors , there are 8 , 301 , 429 , 675 possible range combinations . it might take the computer a little while to test so many combinations . there would be even more combinations ( a lot more ) with 7 colors . vitalnet natural breaks has been designed with special programming to run as fast as possible . it runs quickly , a second or two , with a modest number of ranges or if not that many areas . but it eventually slows down with a larger number of ranges and areas . so if using natural breaks , start with a low number of ranges , and only increase the number to a large number if needed , and then be prepared for a possible wait . if needed , you can minimize the window and do other tasks .
the standard deviation classification method shows how much an attribute value varies from the mean . particularly useful for economic and physical studies such as temperature , wind and other natural phenomena with planar distributions which depend on arithmetic averages to get analyses .
the bclust style uses bclust to generate the breaks using bagged clustering ; it may be anchored using set . seed ; the pars attribute returns the bclust object generated , and can be used to find other breaks using getbclustclassintervals ; if bclust fails , a jittered input vector containing rtimes replications of var is tried — with few unique values in var , this can prove necessary ; arguments to bclust may be passed through . . . .
in addition to selection of the scheme to use , the number of breaks or intervals and the positioning of these breaks are fundamental decisions . the number of breaks is often selected as an odd value : 5 , 7 or 9 . with an even number of classes there is no central class , and with a number of classes less than 4 or 5 the level of detail obtained may be too limited . with more than 9 classes gradations may be too fine to distinguish key differences between zones , but this will depend a great deal on the data and the purpose of the classification being selected . in a number of cases the gis package provides linked frequency diagrams with breaks identified and in some cases interactively adjustable . in other cases generation of frequency diagrams should be conducted in advance to help determine the ideal number of classes and type of classification to be used .
first is proc means using the groups / clusters picked by fastclus , next is the same using the 4 jenks categories out of arcmap . the min / max are the lower and upper level of each interval .
the fisher style uses the algorithm proposed by w . d . fisher ( 1958 ) and discussed by slocum et al . ( 2005 ) as the fisher - jenks algorithm ; added here thanks to hisaji ono .
very interesting read . as someone who struggled through the implementation of jenks [ 1 ] a few years ago in php , i can attest to the fact that it was extremely difficult to find any programming of jenks that was understandable and clear . i was able to find some examples of code , but nothing could explain what was actually happening and , as you said , there were no comments or poor comments in those examples .
in this case , it ' s a combination - the algorithm jenks arrived at is not just the math - implemented , but a clever solution that ( afaik ) has not been expressed in pure - math terms .
every implementation i could find of jenks is a port from fortran iv , with the same terrible variable names , no comments , and absolutely no evidence that the porting author knew absolutely anything about what the code was doing .
i read on this website that jenks is particularly suited for 1 - dimensional data , while k - means are for multi - dimensional . is this true ? if so can you point me to some references about this ?
the fixed style permits a
classintervals
object to be specified with given breaks , set in the fixedbreaks argument ; the length of fixedbreaks should be n + 1 ; this style can be used to insert rounded break values .
i thought jenk ' s method of optimization was k - means in one dimension ( see this comment by whuber ) . i believe there are multiple
jenk ' s
methods though , so it could be some confusions around this . your second comment also seems to be confused , if you use k - means clusters in one dimension it doesn ' t assign groups in non - contiguous rank order .
it’s a bit hard to see how round the numbers are ( it’s grouping by 5’s ) in this example because all the examples above also produce round numbers . but when you have large numbers like population estimates ( see below ) , it will generate some very pretty breaks .
a common one is “k - means , ” which ( given k ) minimizes the total within - cluster variance . this method , which has been around a long time , was rediscovered by cartographers in 1963 and so goes by the name “jenks’ method” in that community .
it destroys the objective display of the data . of the few patterns the user can test , the
prettiest
pattern will almost certainly be selected , but that has nothing to do with the correct display of the data . if the pattern resulting from natural breaks is not
pretty
, it just means there is no strong geographic pattern to the data . artificially selecting ranges to produce a
pretty
or desired pattern can easily turn into
how to lie with maps
. a valid reason to manually set map ranges is to compare two maps , to use the same ranges as in an existing map .
step 4 : individual values in each class are then systematically assigned to adjacent classes by adjusting the class boundaries to see if the tssd can be reduced . this is an iterative process , which ends when improvement in tssd falls below a threshold level , i . e . when the within class variance is as small as possible and between class variance is as large as possible . true optimization is not assured . the entire process can be optionally repeated from step 1 or 2 and tssd values compared
cartographica has added new classifications for displaying data . we have expanded the classifications from equal interval and jenks classifications to equal count , equal area , quartile distributions , quintile distributions , and classification that incorporates all unique values . the upgrades in classifications schemes gives users better capability for displaying data using chlorpleth maps .
i studied up on this and wrote it while working for a startup a few years ago , in 2009 . i found that all of the available choroplethic mapping solutions available had inadequate splits of data when asked to create a map . unfortunately , very few implementations of jenks exist outside of professional cartography packages .
jenks ( r1 , k , lab , iter ) – outputs a a k × 1 column range , whose first k− 1 rows contain the right endpoint of the first k− 1 classes ( the endpoint of the k th category is the largest element in r1 ) and whose last element is the gvf .
interesting that you mention the
combination .
when i was able to find the aforementioned image that showed the jenks method , i knew i had to understand what it meant and what the symbols were . i found it very cool that the mathematics were simple and it was the process that made the method work so well .
jenks is an algorithm designed specifically for this case that tries to maximize the similarity of numbers in groups while maximizing the distance between the groups . it tends to look good and be easily understood , so it’s popular . it’s in arcgis , qgis , and lots of other tools for maps and statistics . it’s in university lectures and textbooks .
the kmeans style uses kmeans to generate the breaks ; it may be anchored using set . seed ; the pars attribute returns the kmeans object generated ; if kmeans fails , a jittered input vector containing rtimes replications of var is tried — with few unique values in var , this can prove necessary ; arguments to kmeans may be passed through . . . .
another thing to notice is that this concept is very natural to extend to multiple output dimensions . instead of using 1 - dimensional gaussian kernels , we can also use n - dimensional gaussian kernels , by using the squared norm between the $ \ mathbf { y } $ and $ \ mathbf { y } ’ $ output vectors . if we look at the uncorrelated multivariate gaussian distribution , our kernel function turns into :
this article isn’t available online , or in print . as far as i can tell , it has never been digitized . it’s ostensibly still owned by the university of kansas geography department , so the copy that bill morris was kind enough to scan and share i can’t safely post . even if the university doesn’t assert copyright , because professor jenks passed in 1996 , it’ll be copyrighted in his name until 2072 .
note after looking into the jenks algorithm proposed in the answer , i found that the classint package in r apparently has a number of such algorithms . i post a note from its documentation to expand on the answer below . i have no idea how well these perform in practice , i post them just because of the variety of possibilities and because being in r makes them easy to try out for yourself .
my question : does anyone know whether sas has a procedure that does this ? i could probably write up code to do the iterations , but if there is a ready - made proc , there ' s no reason to do that . it also looks like the head / tail breaks approach is better ( would be more appropriate for this data , since it has a long tail ) and would be more straight - forward if i had to write something myself .
the breaks between the classes are set so that the total area of the features in each class is as close as possible to 1 / k times the total area of all features . ( this of course makes sense only for features with areas—that is , for polygonal features . ) the result usually is a map that has about the same amount of every symbol on it—a kind of visual balance . ( thought question : could you describe , in detail , an algorithm for determining the equal area cutpoints ? )
fantastic article . i like to think of this phenomenon with a positive spin though . . i can use the jenks algorithm without understanding anything about how it works , just plug it in and go . and with a few test cases i can even port it to a new language without really understanding it . i admire tom ' s work in digging in and doing it right , but as a journeyman programmer i like that i can just use it without really understanding it . sometimes cargo cults work .
for each range combination , calculate
sum of squared deviations for class means
( sdcm _ all ) , and find the smallest one . sdcm _ all is similar to sdam , but uses class means and deviations . suppose we have four counties and two ranges . for [ 4 ] [ 5 , 9 , 10 ] , sdcm _ all = ( 4 - 4 ) ^ 2 + ( 5 - 8 ) ^ 2 + ( 9 - 8 ) ^ 2 + ( 10 - 8 ) ^ 2 = 0 + 9 + 1 + 4 = 14 . for [ 4 , 5 ] [ 9 , 10 ] , sdcm _ all = ( 4 - 4 . 5 ) ^ 2 + ( 5 - 4 . 5 ) ^ 2 + ( 9 - 9 . 5 ) ^ 2 + ( 10 - 9 . 5 ) ^ 2 = 0 . 25 + 0 . 25 + 0 . 25 + 0 . 25 = 1 . for [ 4 , 5 , 9 ] [ 10 ] , sdcm _ all = ( 4 - 6 ) ^ 2 + ( 5 - 6 ) ^ 2 + ( 9 - 6 ) ^ 2 + ( 10 - 10 ) ^ 2 = 4 + 1 + 9 + 0 = 14 . [ 4 , 5 ] [ 9 , 10 ] has the smallest sdcm _ all , so is
best ranges
, minimizes variation within classes . intuitively , it makes sense to use [ 4 , 5 ] [ 9 , 10 ] , and the natural breaks algorithm automatically figures this out .
instead of using a non - parametric approach like histograms or kernel density estimation we can also use parametric distributions where we estimate the parameters to fit the assumed distribution . if the family of distributions fits the data well we can get very nice fits with relatively little amount of data , however , if the family does not fit the generating distribution properly you will get poor results . some standard distributions , for example gaussians are easy to fit by just looking at some statistics of your data . in case of the gaussian the mean $ \ hat { \ mu } = \ overline { x } = \ frac { \ sum _ { i = 1 } ^ nx _ i } { n } $ and $ \ hat { \ sigma } ^ 2 = \ frac { \ sum _ { i = 1 } ^ n ( x _ i - \ overline { x } ) ^ 2 } { n - 1 } $ will produce the most likely gaussian that generated your data . in more complicated distributions you will need to use some form of iterative optimization , for instance using gradient descent on the likelihood function to fit your parameters . below , i have illustrated a gaussian fit on our data generated by a default gaussian . notice that this animation uses smaller sample sizes .
the feature / symbol dichotomy : a gis divides the functions of representing data on a map into at least five conceptually different parts : the attributes are classified ( classification ) and associated with geometric figures ( projection ) , the classifications are associated with graphic symbols , and those symbols determine how the geometric figures will appear ( symbolization of the graphic shapes ) .
emphasize substance over form : when working with complex software , like a gis , deal with the important things first and take care of the details as late in the process as possible .
look for the familiar within the strange terminology : many disciplines have , or could have , contributed to the development and evolution of gis . many techniques may already be familiar to you under different names . do not let the terminology daunt you !
maps are statistics : symbolizing features on a map to reflect underlying data is a statistical procedure . you can use statistical techniques to help determine appropriate symbolization methods .
you are in charge : always have a reason for your choice of data symbolization : do not let the computer choose .
the legend editor is a complex dialog providing access to almost all arcview’s capabilities to classify and modify the display of features . every feature has a geographic location . the view erects a graphic shape at each feature’s location in order to show it to a person . a graphic shape is a combination of a geometric shape and a symbol , which records the visual features of the shape , such as its colors , line styles , and so on . the shape is determined by the geographic data , but the means of displaying the shape are not . determining how the shape will display is the role of the legend editor . the legend editor can make this determination based on the values of one or more attributes of each feature . in this manner arcview can show data on a map .
the legend editor sets up a sequence of processes . the first is classification . this assigns features to groups according to the values of one or more of the feature attributes . the second is symbolization . this associates a symbol with each class . the figure sketches this process .
in addition , the legend editor controls how the classifications will be named or labeled in the view’s table of contents and provides capabilities to save and reload a legend .
gis software differs in how it implements the legend editor capabilities , but it must implement these capabilities at some level .
invoke the legend editor through a menu item ( theme | edit l egend ) , a button , or most simply by double - clicking on a theme’s legend in the view .
the legend editor dialog is in a separate window that can be moved outside the arcview window . however , it will never disappear behind arcview . it can remain open while you do other arcview operations ( it is “modeless ,
not a child window ) .
the legend editor will act differently on different kinds of themes : feature themes , image themes , and grid themes .
the legend editor dialog has been long in need of improvement . typically , changes to the legend type , values field , or classification type will cause unwanted side - effects , often destroying any colors or symbols you have already specified . the trick lies in specifying this fundamental information first . only when you are sure you have chosen the right kind of legend , the correct attribute ( s ) to display , and the correct number of classifications should you bother with the details of specifying the symbols themselves .
this last rule applies to all complex software : deal with the important things first and take care of the details as late in the process as possible ( or never , if you can get away with it ) .
practice editing symbols . ( you double - click on one to change it . ) can you find a way to edit multiple symbols simultaneously ?
suppose two classifications overlap ; for example , suppose one classification is 0 - 10 and the next is 5 - 20 . how does arcview resolve this conflict ; that is , how does it decide which classification to use for values within the overlapping region ?
figure out what this button does and how it is relevant to the previous question .
( optional ) the “statistics” button is handy . experiment with it . note that there are two definitions of “standard deviation” ( sd ) . one is the “root mean square” ( of the deviations from the mean ) , or “population” standard deviation . the other has been adjusted to reduce its estimation bias ; it is
n / ( n - 1 ) ) times larger than the population sd when n values are involved . which sd does arcview compute ?
when is the “advanced” button enabled ? optional ( for now ) : determine what the advanced options do .
every map is to some extent a distortion of reality . through this distortion some maps reveal patterns and other maps lie [ see monmonier or tufte , for instance ] . one of the subtlest forms of lying with maps is associated with the method of classifying numerical attributes .
we will experiment with different classification methods . the material here is background . for more information see urltoken ( section 6 ) .
for each classification type below , n numerical values are to be divided into k classifications ( “classes” ) according to the rules to be described . suppose the ordered numerical values are x
respectively . in every case the classifications consist of non - overlapping intervals of numbers .
the k classes will be constructed to contain as near to n / k values as practicable . for example , if n is 18 and k is 5 , then n / k = 3 . 6 , so the classes will contain either 3 or 4 values each . the cut points will always coincide with one of the original data values .
some intervals may contain none of the original values ( can you think of a simple example ? ) .
this is almost another kind of equal interval classification . however , the interval length is set to be some multiple of the standard deviation of the data . multiples of 1 and 0 . 5 are common ; smaller multiples may be used with lots of data .
equal length and equal number legends are conceivable for polyline and multipoint themes , but arcview does not implement these . ( the features of a
multipoint
theme consist of zero , one , or more points . )
any nonempty set of numbers can be centered by subtracting the mean of those numbers from each value . the resulting values are known as residuals . one measure of spread is the sum of squares of the residuals . it is a measure of how much the values vary about their means , and so is appropriate for identifying clusters of data .
there are many other types of classification , but ( for data sets with no “ties” ) all can be reduced to equal intervals after applying a preliminary transformation of the data , y = f ( x ) . for example , dividing y = log ( x ) into equal intervals is equivalent to dividing the range of the x’s into intervals of equal ratios , such as 1 - 2 , 2 - 4 , 4 - 8 , and so on . therefore classification methods for numerical data are usually determined by their effects on the resulting map rather than by some statistical method based purely on the data .
the classification method is an easy target for criticism when you make a map . therefore , always have a reason for selecting your method . it is not sufficient to say , “the computer chose it . ” who is in charge , you or the machine ?
experiment with the data provided in gtkav chapter 9 ( counties . shp ) . apply all five classification methods and vary the numbers of classes . each team ( computer ) will select one of the several dozen numerical attributes to study .
create a histogram of the data , by hand or using software on your computer ( such as excel or a statistics package ) . use this as a frame of reference for evaluating the maps you create . create at least two versions of this histogram by substantially varying the bin size ( or , equivalently , by varying the number of histogram bars ) . using these histograms alone , predict your answers to the next three questions . then proceed to answer those questions through experimentation with arcview’s legend editor . check your answers against your predictions .
this page was last updated 11 march 2004 . it was reformatted . the
summary of principles
section was added . minor editorial changes were made to clarify portions of the text .
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subtract the sdbc from the sdam ( sdam - sdbc ) . this equals the sum of the squared deviations from the class means .
after inspecting each of the sdbc , a decision is made to move one unit from the class with the largest sdbc toward the class with the lowest sdbc .
new class deviations are then calculated , and the process is repeated until the sum of the within class deviations reaches a minimal value .
a is the set of values that have been ordered from 1 to n .
mean i . . j is the mean of the class bounded by i and j .
when re - writing this , i had chosen to use the google charts api for our maps so , you should be able to use this to simply output a map assuming you provide all the necessary parameters .
this was kind of based on another script that was in french ( which i don ' t speak very well , at all ) . the original script had many issues and bugs and wasn ' t as flexible as i wanted it to be . so , i re - wrote it .
this one works well and is flexible in terms of the datasets . it has been tested pretty thoroughly and , as far as i can tell , is correct .
need a chance to go over it again and make improvements and / or more comments .
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unless required by applicable law or agreed to in writing , software distributed under the license is distributed on an
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example 1 : define 4 classes for the data in figure 1 which achieves this objective .
suppose , for example , that we simply divide the 160 elements in figure 1 into four intervals each containing 40 elements , as shown in figure 2 .
here , for example , cell q18 contains the formula = small ( $ b $ 3 : $ i $ 22 , 40 * ( p18 - 1 ) + 1 ) , cell r18 contains the formula = small ( $ b $ 3 : $ i $ 22 , 40 * p18 ) and cell s18 contains the formula = countifs ( $ b $ 3 : $ i $ 22 , ” > = ” & q18 , $ b $ 3 : $ i $ 22 , ” < = ” & r18 ) . note that cell r3 should contain the 120 th smallest element in figure 1 , which is 80 . 7 , but since 80 . 7 is also the 121 st smallest element , this would split 80 . 7 between interval 3 and interval 4 . this is why we are forced to make interval 3 slightly smaller and interval 4 slightly bigger .
the squared deviation of each of the four intervals is found in range t17 : t20 , with the sum in cell t21 . note that cell t17 contains the array formula
example 2 : find the optimal partition of the values 5 , 8 , 9 , 12 , 15 into 3 classes .
since this is a simpler problem than the one in example 1 , we are able to evaluate all six possible solutions , as shown in figure 4 .
in the first possible solution , shown in range b3 : d7 , the three classes are 5 , 8 and 9 - 15 . the squared deviation for the third category ( cell d6 ) , for example , is calculated by the formula = devsq ( d3 : d5 ) , with a total for all three classes of 18 , using the formula = sum ( b6 : d6 ) .
we see from figure 4 that the optimal partition is the second one , with classes 5 , 8 - 9 and 12 - 15 , since the total squared deviation of 5 is less than that of the other partitions .
where d * is the minimum total squared deviation , as described above , and d is the squared deviation of the data set , which for example 2 is 58 . 8 ( cell aa3 ) as calculated by the formula = devsq ( f3 : h5 ) . gvf takes a value between 0 and 1 . the closer to 1 the better the fit .
for example , there are 8 , 301 , 429 , 675 ways to partition 254 data elements in 6 classes . this number gets even larger the more data elements there are and the more classes we want to use . in such cases , we will need to use an iterative approach . in particular , we select a partition at random and see which class has the largest squared deviation and which class has the least squared deviation .
if , for example , we used 6 classes and class 3 had the largest squared deviation and class 5 had the smallest squared deviation , then we would move the last element in class 3 into class 4 ( in the direction of class 5 ) . if instead , class 3 had the largest squared deviation and class 1 had the smallest squared deviation , then we would move the first element in class 3 into class 2 . we repeat this process again and again , continuing until the squared deviations of none of the classes changed or until a maximum number of iterations had been reached , at which point we would select the partition with the lowest total squared deviations . in order to avoid a local minimum , from time to time we could make a random perturbation .