如何使用余弦度量来计算词典之间的相似度？

Question

我有一个长长的字典清单：

river 4
    ground: 1
    journey: 1
    longitude: 1
    main: 1
    world--four: 1
    contrary: 1
    cover: 1
    delaware: 1
    remarkable: 1
    vast: 1
    forty-five: 1
    crookedest: 1
    territories: 1
    spread: 1
    country: 1
    longest: 1
    fly: 1
    atlantic: 1
    crow: 1
    supply: 1
    seems: 1
    idaho: 1
    seaboard: 1
    states: 1
    ways: 1
    degrees: 1
    part: 1
    twenty-eight: 1
    pacific: 1
    branch: 1
    water: 1
    considering: 1
    six: 1
    safe: 1
    commonplace: 1
    draws: 1
    drainage-basin: 1
    uses: 1
    seventy-five: 1
    slope--a: 1
    missouri: 1
mississippi 3
    area: 1
    steamboats: 1
    germany: 1
    reading: 1
    france: 1
    proper: 1
    fifty-four: 1
    turkey: 1
    exceptionally: 1
    areas: 1
    carries: 1
    combined: 1
    flats: 1
    receives: 1
    england: 1
    italy: 1
    scotland: 1
    wales: 1
    almost: 1
    navigable: 1
    austria: 1
    region: 1
    wide: 1
    spain: 1
    subordinate: 1
    drainage-basin: 1
    hundreds: 1
    keels: 1
    portugal: 1
    water: 1
    gulf: 1
    ireland: 1
    rivers: 1
    valley: 1
    fertile: 1
    worth: 1
water 3
    steamboats: 1
    spread: 1
    country: 1
    states: 1
    longitude: 1
    fifty-four: 1
    pacific: 1
    vast: 1
    subordinate: 1
    carries: 1
    keels: 1
    flats: 1
    supply: 1
    receives: 1
    atlantic: 1
    forty-five: 1
    river: 1
    rivers: 1
    idaho: 1
    mississippi: 1
    seaboard: 1
    navigable: 1
    discharges: 1
    degrees: 1
    twenty-eight: 1
    drainage-basin: 1
    hundreds: 1
    st: 1
    gulf: 1
    draws: 1
    delaware: 1
    territories: 1
    slope--a: 1
drainage-basin 2
    area: 1
    spread: 1
    country: 1
    states: 1
    mississippi: 1
    longitude: 1
    france: 1
    proper: 1
    vast: 1
    turkey: 1
    forty-five: 1
    areas: 1
    combined: 1
    germany: 1
    exceptionally: 1
    valley: 1
    supply: 1
    fertile: 1
    atlantic: 1
    italy: 1
    river: 1
    idaho: 1
    wales: 1
    almost: 1
    seaboard: 1
    spain: 1
    austria: 1
    region: 1
    degrees: 1
    twenty-eight: 1
    wide: 1
    england: 1
    portugal: 1
    water: 1
    ireland: 1
    pacific: 1
    draws: 1
    delaware: 1
    territories: 1
    scotland: 1
    slope--a: 1
area 1
    germany: 1
    austria: 1
    mississippi: 1
    france: 1
    proper: 1
    england: 1
    turkey: 1
    exceptionally: 1
    areas: 1
    combined: 1
    scotland: 1
    italy: 1
    spain: 1
    wales: 1
    almost: 1
    fertile: 1
    region: 1
    wide: 1
    drainage-basin: 1
    portugal: 1
    ireland: 1
    valley: 1
journey 1
    ground: 1
    seems: 1
    part: 1
    cover: 1
    crow: 1
    crookedest: 1
    six: 1
    safe: 1
    uses: 1
    seventy-five: 1
    river: 1
    fly: 1
seems 1
    ground: 1
    journey: 1
    part: 1
    cover: 1
    crow: 1
    crookedest: 1
    six: 1
    safe: 1
    uses: 1
    seventy-five: 1
    river: 1
    fly: 1
states 1
    spread: 1
    country: 1
    degrees: 1
    longitude: 1
    twenty-eight: 1
    drainage-basin: 1
    vast: 1
    forty-five: 1
    water: 1
    seaboard: 1
    pacific: 1
    draws: 1
    delaware: 1
    territories: 1
    atlantic: 1
    supply: 1
    slope--a: 1
    river: 1
    idaho: 1
slope--a 1
    spread: 1
    country: 1
    states: 1
    degrees: 1
    longitude: 1
    drainage-basin: 1
    vast: 1
    forty-five: 1
    water: 1
    seaboard: 1
    pacific: 1
    draws: 1
    delaware: 1
    territories: 1
    atlantic: 1
    supply: 1
    twenty-eight: 1
    river: 1
    idaho: 1
remarkable 1
    contrary: 1
    river: 1
    commonplace: 1
    ways: 1
vast 1
    spread: 1
    country: 1
    states: 1
    degrees: 1
    longitude: 1
    twenty-eight: 1
    drainage-basin: 1
    pacific: 1
    forty-five: 1
    water: 1
    seaboard: 1
    draws: 1
    delaware: 1
    territories: 1
    atlantic: 1
    supply: 1
    slope--a: 1
    river: 1
    idaho: 1
forty-five 1
    spread: 1
    longitude: 1
    country: 1
    states: 1
    degrees: 1
    slope--a: 1
    drainage-basin: 1
    vast: 1
    pacific: 1
    water: 1
    seaboard: 1
    draws: 1
    delaware: 1
    territories: 1
    atlantic: 1
    supply: 1
    twenty-eight: 1
    river: 1
    idaho: 1
crookedest 1
    ground: 1
    journey: 1
    seems: 1
    part: 1
    cover: 1
    crow: 1
    six: 1
    safe: 1
    uses: 1
    seventy-five: 1
    river: 1
    fly: 1
carries 1
    mississippi: 1
    steamboats: 1
    navigable: 1
    fifty-four: 1
    keels: 1
    hundreds: 1
    subordinate: 1
    water: 1
    gulf: 1
    flats: 1
    rivers: 1
    receives: 1
germany 1
    area: 1
    austria: 1
    mississippi: 1
    france: 1
    proper: 1
    exceptionally: 1
    turkey: 1
    england: 1
    areas: 1
    combined: 1
    scotland: 1
    italy: 1
    spain: 1
    wales: 1
    almost: 1
    fertile: 1
    region: 1
    wide: 1
    drainage-basin: 1
    portugal: 1
    ireland: 1
    valley: 1
longest 1
    main: 1
    river: 1
    world--four: 1
    branch: 1
    missouri: 1
    considering: 1
flats 1
    mississippi: 1
    steamboats: 1
    navigable: 1
    carries: 1
    fifty-four: 1
    keels: 1
    hundreds: 1
    subordinate: 1
    water: 1
    gulf: 1
    rivers: 1
    receives: 1
supply 1
    spread: 1
    longitude: 1
    country: 1
    states: 1
    degrees: 1
    slope--a: 1
    drainage-basin: 1
    vast: 1
    forty-five: 1
    water: 1
    seaboard: 1
    pacific: 1
    draws: 1
    delaware: 1
    territories: 1
    atlantic: 1
    twenty-eight: 1
    river: 1
    idaho: 1
receives 1
    mississippi: 1
    steamboats: 1
    navigable: 1
    carries: 1
    fifty-four: 1
    keels: 1
    hundreds: 1
    subordinate: 1
    water: 1
    gulf: 1
    flats: 1
    rivers: 1
crow 1
    ground: 1
    journey: 1
    seems: 1
    part: 1
    cover: 1
    crookedest: 1
    six: 1
    safe: 1
    uses: 1
    seventy-five: 1
    river: 1
    fly: 1
scotland 1
    area: 1
    germany: 1
    austria: 1
    mississippi: 1
    france: 1
    proper: 1
    exceptionally: 1
    turkey: 1
    england: 1
    areas: 1
    combined: 1
    spain: 1
    italy: 1
    wales: 1
    almost: 1
    fertile: 1
    region: 1
    wide: 1
    drainage-basin: 1
    portugal: 1
    ireland: 1
    valley: 1
country 1
    spread: 1
    idaho: 1
    states: 1
    degrees: 1
    longitude: 1
    twenty-eight: 1
    drainage-basin: 1
    vast: 1
    forty-five: 1
    water: 1
    seaboard: 1
    pacific: 1
    draws: 1
    delaware: 1
    territories: 1
    atlantic: 1
    supply: 1
    slope--a: 1
    river: 1
thames 1
    thirty-eight: 1
    rhine: 1
    lawrence: 1
    twenty-five: 1
england 1
    area: 1
    germany: 1
    austria: 1
    mississippi: 1
    france: 1
    proper: 1
    exceptionally: 1
    turkey: 1
    region: 1
    areas: 1
    combined: 1
    scotland: 1
    italy: 1
    spain: 1
    wales: 1
    almost: 1
    fertile: 1
    wide: 1
    drainage-basin: 1
    portugal: 1
    ireland: 1
    valley: 1
navigable 1
    mississippi: 1
    steamboats: 1
    carries: 1
    fifty-four: 1
    keels: 1
    hundreds: 1
    subordinate: 1
    water: 1
    gulf: 1
    flats: 1
    rivers: 1
    receives: 1
austria 1
    area: 1
    germany: 1
    mississippi: 1
    france: 1
    proper: 1
    region: 1
    turkey: 1
    england: 1
    areas: 1
    combined: 1
    exceptionally: 1
    scotland: 1
    italy: 1
    spain: 1
    wales: 1
    almost: 1
    fertile: 1
    wide: 1
    drainage-basin: 1
    portugal: 1
    ireland: 1
    valley: 1
rhine 1
    thirty-eight: 1
    thames: 1
    lawrence: 1
    twenty-five: 1
part 1
    ground: 1
    journey: 1
    seems: 1
    cover: 1
    crow: 1
    crookedest: 1
    six: 1
    safe: 1
    uses: 1
    seventy-five: 1
    river: 1
    fly: 1
twenty-eight 1
    spread: 1
    country: 1
    states: 1
    degrees: 1
    longitude: 1
    drainage-basin: 1
    vast: 1
    forty-five: 1
    water: 1
    seaboard: 1
    pacific: 1
    draws: 1
    delaware: 1
    territories: 1
    atlantic: 1
    supply: 1
    slope--a: 1
    river: 1
    idaho: 1
branch 1
    main: 1
    longest: 1
    river: 1
    world--four: 1
    missouri: 1
    considering: 1
hundreds 1
    mississippi: 1
    steamboats: 1
    navigable: 1
    carries: 1
    fifty-four: 1
    keels: 1
    subordinate: 1
    water: 1
    gulf: 1
    flats: 1
    rivers: 1
    receives: 1
st 1
    water: 1
    discharges: 1
considering 1
    main: 1
    longest: 1
    river: 1
    world--four: 1
    branch: 1
    missouri: 1
six 1
    ground: 1
    journey: 1
    seems: 1
    part: 1
    cover: 1
    crow: 1
    crookedest: 1
    fly: 1
    safe: 1
    uses: 1
    seventy-five: 1
    river: 1
gulf 1
    mississippi: 1
    steamboats: 1
    navigable: 1
    carries: 1
    fifty-four: 1
    keels: 1
    hundreds: 1
    subordinate: 1
    water: 1
    flats: 1
    rivers: 1
    receives: 1
ireland 1
    area: 1
    germany: 1
    austria: 1
    mississippi: 1
    france: 1
    proper: 1
    exceptionally: 1
    turkey: 1
    england: 1
    areas: 1
    combined: 1
    scotland: 1
    italy: 1
    spain: 1
    wales: 1
    almost: 1
    fertile: 1
    region: 1
    wide: 1
    drainage-basin: 1
    portugal: 1
    valley: 1
safe 1
    ground: 1
    journey: 1
    seems: 1
    part: 1
    cover: 1
    crow: 1
    crookedest: 1
    six: 1
    uses: 1
    seventy-five: 1
    river: 1
    fly: 1
commonplace 1
    contrary: 1
    river: 1
    remarkable: 1
    ways: 1
draws 1
    spread: 1
    longitude: 1
    country: 1
    states: 1
    degrees: 1
    slope--a: 1
    drainage-basin: 1
    vast: 1
    forty-five: 1
    water: 1
    seaboard: 1
    pacific: 1
    supply: 1
    delaware: 1
    territories: 1
    atlantic: 1
    twenty-eight: 1
    river: 1
    idaho: 1
delaware 1
    spread: 1
    longitude: 1
    country: 1
    states: 1
    degrees: 1
    slope--a: 1
    drainage-basin: 1
    vast: 1
    forty-five: 1
    water: 1
    seaboard: 1
    pacific: 1
    draws: 1
    territories: 1
    atlantic: 1
    supply: 1
    twenty-eight: 1
    river: 1
    idaho: 1
thirty-eight 1
    thames: 1
    rhine: 1
    lawrence: 1
    twenty-five: 1
longitude 1
    spread: 1
    country: 1
    states: 1
    degrees: 1
    slope--a: 1
    drainage-basin: 1
    vast: 1
    forty-five: 1
    water: 1
    seaboard: 1
    pacific: 1
    draws: 1
    delaware: 1
    territories: 1
    atlantic: 1
    supply: 1
    twenty-eight: 1
    river: 1
    idaho: 1
world--four 1
    main: 1
    longest: 1
    river: 1
    branch: 1
    missouri: 1
    considering: 1
lawrence 1
    thirty-eight: 1
    thames: 1
    rhine: 1
    twenty-five: 1
ground 1
    journey: 1
    seems: 1
    part: 1
    cover: 1
    crow: 1
    crookedest: 1
    six: 1
    safe: 1
    uses: 1
    seventy-five: 1
    river: 1
    fly: 1
steamboats 1
    mississippi: 1
    navigable: 1
    carries: 1
    fifty-four: 1
    keels: 1
    hundreds: 1
    subordinate: 1
    water: 1
    gulf: 1
    flats: 1
    rivers: 1
    receives: 1
spread 1
    seaboard: 1
    country: 1
    states: 1
    degrees: 1
    longitude: 1
    twenty-eight: 1
    drainage-basin: 1
    vast: 1
    forty-five: 1
    water: 1
    pacific: 1
    draws: 1
    delaware: 1
    territories: 1
    atlantic: 1
    supply: 1
    slope--a: 1
    river: 1
    idaho: 1
idaho 1
    spread: 1
    country: 1
    states: 1
    degrees: 1
    longitude: 1
    twenty-eight: 1
    drainage-basin: 1
    vast: 1
    forty-five: 1
    water: 1
    seaboard: 1
    pacific: 1
    draws: 1
    delaware: 1
    territories: 1
    atlantic: 1
    supply: 1
    slope--a: 1
    river: 1
reading 1
    mississippi: 1
    worth: 1
almost 1
    area: 1
    germany: 1
    austria: 1
    france: 1
    proper: 1
    england: 1
    turkey: 1
    exceptionally: 1
    areas: 1
    combined: 1
    scotland: 1
    italy: 1
    spain: 1
    wales: 1
    mississippi: 1
    fertile: 1
    region: 1
    wide: 1
    drainage-basin: 1
    portugal: 1
    ireland: 1
    valley: 1
contrary 1
    river: 1
    remarkable: 1
    commonplace: 1
    ways: 1
cover 1
    ground: 1
    journey: 1
    seems: 1
    part: 1
    crow: 1
    crookedest: 1
    six: 1
    safe: 1
    uses: 1
    seventy-five: 1
    river: 1
    fly: 1
france 1
    area: 1
    germany: 1
    austria: 1
    mississippi: 1
    proper: 1
    england: 1
    turkey: 1
    exceptionally: 1
    areas: 1
    combined: 1
    scotland: 1
    italy: 1
    spain: 1
    wales: 1
    almost: 1
    fertile: 1
    region: 1
    wide: 1
    drainage-basin: 1
    portugal: 1
    ireland: 1
    valley: 1
spain 1
    area: 1
    germany: 1
    austria: 1
    mississippi: 1
    france: 1
    proper: 1
    exceptionally: 1
    turkey: 1
    england: 1
    areas: 1
    combined: 1
    scotland: 1
    italy: 1
    wales: 1
    almost: 1
    fertile: 1
    region: 1
    wide: 1
    drainage-basin: 1
    portugal: 1
    ireland: 1
    valley: 1
pacific 1
    spread: 1
    longitude: 1
    country: 1
    states: 1
    degrees: 1
    slope--a: 1
    drainage-basin: 1
    vast: 1
    forty-five: 1
    water: 1
    seaboard: 1
    draws: 1
    delaware: 1
    territories: 1
    atlantic: 1
    supply: 1
    twenty-eight: 1
    river: 1
    idaho: 1
turkey 1
    area: 1
    germany: 1
    austria: 1
    mississippi: 1
    france: 1
    proper: 1
    exceptionally: 1
    england: 1
    areas: 1
    combined: 1
    scotland: 1
    italy: 1
    spain: 1
    wales: 1
    almost: 1
    fertile: 1
    region: 1
    wide: 1
    drainage-basin: 1
    portugal: 1
    ireland: 1
    valley: 1
fifty-four 1
    mississippi: 1
    steamboats: 1
    navigable: 1
    carries: 1
    hundreds: 1
    keels: 1
    subordinate: 1
    water: 1
    gulf: 1
    flats: 1
    rivers: 1
    receives: 1
subordinate 1
    mississippi: 1
    steamboats: 1
    navigable: 1
    carries: 1
    fifty-four: 1
    keels: 1
    hundreds: 1
    water: 1
    gulf: 1
    flats: 1
    rivers: 1
    receives: 1
territories 1
    spread: 1
    idaho: 1
    states: 1
    degrees: 1
    longitude: 1
    twenty-eight: 1
    drainage-basin: 1
    vast: 1
    forty-five: 1
    water: 1
    seaboard: 1
    pacific: 1
    draws: 1
    delaware: 1
    supply: 1
    atlantic: 1
    slope--a: 1
    river: 1
    country: 1
combined 1
    area: 1
    germany: 1
    austria: 1
    mississippi: 1
    france: 1
    proper: 1
    exceptionally: 1
    turkey: 1
    england: 1
    areas: 1
    scotland: 1
    italy: 1
    spain: 1
    wales: 1
    almost: 1
    fertile: 1
    region: 1
    wide: 1
    drainage-basin: 1
    portugal: 1
    ireland: 1
    valley: 1
exceptionally 1
    area: 1
    germany: 1
    austria: 1
    mississippi: 1
    france: 1
    proper: 1
    england: 1
    turkey: 1
    region: 1
    areas: 1
    combined: 1
    scotland: 1
    italy: 1
    spain: 1
    wales: 1
    almost: 1
    fertile: 1
    wide: 1
    drainage-basin: 1
    portugal: 1
    ireland: 1
    valley: 1
region 1
    area: 1
    germany: 1
    austria: 1
    mississippi: 1
    france: 1
    proper: 1
    exceptionally: 1
    turkey: 1
    england: 1
    areas: 1
    combined: 1
    scotland: 1
    italy: 1
    spain: 1
    wales: 1
    almost: 1
    fertile: 1
    wide: 1
    drainage-basin: 1
    portugal: 1
    ireland: 1
    valley: 1
twenty-five 1
    thirty-eight: 1
    thames: 1
    lawrence: 1
    rhine: 1
rivers 1
    mississippi: 1
    steamboats: 1
    navigable: 1
    carries: 1
    fifty-four: 1
    keels: 1
    hundreds: 1
    subordinate: 1
    water: 1
    gulf: 1
    flats: 1
    receives: 1
fly 1
    ground: 1
    journey: 1
    seems: 1
    part: 1
    cover: 1
    crow: 1
    crookedest: 1
    six: 1
    safe: 1
    uses: 1
    seventy-five: 1
    river: 1
atlantic 1
    spread: 1
    longitude: 1
    country: 1
    states: 1
    degrees: 1
    slope--a: 1
    drainage-basin: 1
    vast: 1
    forty-five: 1
    water: 1
    seaboard: 1
    pacific: 1
    draws: 1
    delaware: 1
    territories: 1
    river: 1
    supply: 1
    twenty-eight: 1
    idaho: 1
italy 1
    area: 1
    germany: 1
    austria: 1
    mississippi: 1
    france: 1
    proper: 1
    exceptionally: 1
    turkey: 1
    england: 1
    areas: 1
    combined: 1
    scotland: 1
    spain: 1
    wales: 1
    almost: 1
    fertile: 1
    region: 1
    wide: 1
    drainage-basin: 1
    portugal: 1
    ireland: 1
    valley: 1
main 1
    world--four: 1
    longest: 1
    river: 1
    branch: 1
    missouri: 1
    considering: 1
areas 1
    area: 1
    germany: 1
    austria: 1
    mississippi: 1
    france: 1
    proper: 1
    england: 1
    turkey: 1
    exceptionally: 1
    combined: 1
    scotland: 1
    italy: 1
    spain: 1
    wales: 1
    almost: 1
    fertile: 1
    region: 1
    wide: 1
    drainage-basin: 1
    portugal: 1
    ireland: 1
    valley: 1
seaboard 1
    spread: 1
    country: 1
    states: 1
    degrees: 1
    longitude: 1
    twenty-eight: 1
    drainage-basin: 1
    vast: 1
    forty-five: 1
    water: 1
    pacific: 1
    draws: 1
    delaware: 1
    territories: 1
    atlantic: 1
    supply: 1
    slope--a: 1
    river: 1
    idaho: 1
fertile 1
    area: 1
    germany: 1
    austria: 1
    mississippi: 1
    france: 1
    proper: 1
    exceptionally: 1
    turkey: 1
    england: 1
    areas: 1
    combined: 1
    scotland: 1
    italy: 1
    spain: 1
    wales: 1
    almost: 1
    region: 1
    wide: 1
    drainage-basin: 1
    portugal: 1
    ireland: 1
    valley: 1
ways 1
    contrary: 1
    river: 1
    remarkable: 1
    commonplace: 1
discharges 1
    water: 1
    st: 1
degrees 1
    spread: 1
    country: 1
    states: 1
    longitude: 1
    twenty-eight: 1
    drainage-basin: 1
    vast: 1
    forty-five: 1
    water: 1
    seaboard: 1
    pacific: 1
    draws: 1
    delaware: 1
    territories: 1
    atlantic: 1
    supply: 1
    slope--a: 1
    river: 1
    idaho: 1
wide 1
    area: 1
    germany: 1
    austria: 1
    mississippi: 1
    france: 1
    proper: 1
    exceptionally: 1
    turkey: 1
    england: 1
    areas: 1
    combined: 1
    scotland: 1
    italy: 1
    spain: 1
    wales: 1
    almost: 1
    fertile: 1
    region: 1
    drainage-basin: 1
    portugal: 1
    ireland: 1
    valley: 1
proper 1
    area: 1
    germany: 1
    austria: 1
    mississippi: 1
    france: 1
    england: 1
    turkey: 1
    exceptionally: 1
    areas: 1
    combined: 1
    scotland: 1
    italy: 1
    spain: 1
    wales: 1
    almost: 1
    fertile: 1
    region: 1
    wide: 1
    drainage-basin: 1
    portugal: 1
    ireland: 1
    valley: 1
keels 1
    mississippi: 1
    steamboats: 1
    navigable: 1
    water: 1
    fifty-four: 1
    hundreds: 1
    subordinate: 1
    carries: 1
    gulf: 1
    flats: 1
    rivers: 1
    receives: 1
portugal 1
    area: 1
    germany: 1
    austria: 1
    mississippi: 1
    france: 1
    proper: 1
    exceptionally: 1
    turkey: 1
    england: 1
    areas: 1
    combined: 1
    scotland: 1
    italy: 1
    spain: 1
    wales: 1
    almost: 1
    fertile: 1
    region: 1
    wide: 1
    drainage-basin: 1
    ireland: 1
    valley: 1
worth 1
    mississippi: 1
    reading: 1
uses 1
    ground: 1
    journey: 1
    seems: 1
    part: 1
    cover: 1
    crow: 1
    crookedest: 1
    six: 1
    safe: 1
    fly: 1
    seventy-five: 1
    river: 1
seventy-five 1
    ground: 1
    journey: 1
    seems: 1
    part: 1
    cover: 1
    crow: 1
    crookedest: 1
    six: 1
    safe: 1
    uses: 1
    river: 1
    fly: 1
valley 1
    area: 1
    germany: 1
    austria: 1
    mississippi: 1
    france: 1
    proper: 1
    exceptionally: 1
    turkey: 1
    england: 1
    areas: 1
    combined: 1
    scotland: 1
    italy: 1
    spain: 1
    wales: 1
    almost: 1
    fertile: 1
    region: 1
    wide: 1
    drainage-basin: 1
    portugal: 1
    ireland: 1
missouri 1
    main: 1
    longest: 1
    river: 1
    branch: 1
    world--four: 1
    considering: 1
wales 1
    area: 1
    germany: 1
    austria: 1
    mississippi: 1
    france: 1
    proper: 1
    exceptionally: 1
    turkey: 1
    england: 1
    areas: 1
    combined: 1
    scotland: 1
    italy: 1
    spain: 1
    almost: 1
    fertile: 1
    region: 1
    wide: 1
    drainage-basin: 1
    portugal: 1
    ireland: 1
    valley: 1

我希望使用余弦度量法计算字典之间的相似性：

我想p和q是字典的钥匙。我还想添加一个函数，当你输入单词时，它会找到字典并按降序返回其他字典的相似性。相似性的期望输出是：

^{pr2}$

任何人都可以帮助或提供解决方案，或告诉如何提取共享词的价值来计算？谢谢。在

Answer 1

我不完全确定你的问题设置，但我想这可以让你开始。假设你的字典集是这样的：

import math

dict_list = {
    "water": {
        "ground": 1,
        "journey": 1,
        "longitude": 1,
        "main": 1,
        "contrary": 1,
        "cover": 1,
        "delaware": 1,
        "remarkable": 1
    },
    "mississippi": {
        "main": 1,
        "contrary": 1,
        "cover": 1,
        "delaware": 1,
        "remarkable": 1,
        "steamboats": 1,
        "germany": 1
    }
}

如果要对它们应用余弦规则，则需要设置向量，以显示两个词典中每个单词的出现情况（即，如果它出现在一个字典中，而不是另一个字典中，则另一个字典中的值必须为零）：

^{pr2}$

注意，向量元素的顺序很重要。如果你用“水”和“密西西比河”运行这个程序，你会得到：

[[1, 1, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1]]

之后，您只需应用规则：

def dot_prod(p, q):
    return sum([p[x]*q[x] for x in range(0, len(p))])

def norm(p):
    return math.sqrt(dot_prod(p, p))

def cosine_metric(p, q):
    return dot_prod(p, q)/(norm(p) * norm(q))

以及为给定字典计算它们的函数：

def find_dict(word):
    if word in dict_list.keys():
        for other_dicts in dict_list.keys():
            if other_dicts != word:
                vecs = setup_vec(dict_list[word], dict_list[other_dicts])
                print(other_dicts + " " + str(cosine_metric(vecs[0], vecs[1])))

结果如下：

find_dict('water')
0.6681531047810609

剩下的任务是对输出进行排序，这应该不难做到。在