北航数理统计——判别分析大作业

DotA中英雄角色的基础属性的统计分析1目录摘要.........................................................2引言.........................................................31.数据整理及建模..............................................31.1数据整理.................................................31.2建模.....................................................32.数据分析....................................................72.1分析案例处理摘要........................................72.2输入和删除的变量........................................72.3特征值和判别函数........................................92.4属性值分类点图分析......................................92.5详细分类结果和交叉验证..................................93．总结........................................................18参考文献.......................................................19DotA中英雄角色的基础属性的统计分析2摘要本文通过运用统计学知识中的聚类分析和判别分析，利用DotA最新的地图版本中设定的英雄角色的基础属性对各个英雄进行了分类统计。DotA游戏中已将英雄划归为三类，分别为力量型英雄，敏捷型英雄，智力型英雄，统计结果与游戏中的实际设置基本相符，显示各个英雄的类型设定和它的基础属性有密切的关系。关键词：英雄角色的基础属性，聚类分析，判别分析，SPSSDotA中英雄角色的基础属性的统计分析3引言DotA是DefenseoftheAncients的简称，是基于魔兽争霸3：冰封王座的多人即时对战自定义地图，可支持最多10个人同时连线游戏。DotA以对立的两个小队展开对战，通常是5v5。随着DotA版本的更新，现在这款游戏中已经含有111个不同的英雄角色，每个玩家可以从这111个英雄角色中选择一个来参与游戏。DotA游戏中将英雄划归为三类，分别为力量型英雄，敏捷型英雄，智力型英雄，而每个英雄的基础属性可以用6个指标来衡量，分别是初始力量值x1，力量成长值x2，初始敏捷值x3，敏捷成长值x4，初始智力值x5，智力成长值x6。本文通过对DotA游戏中各类英雄的基础属性的判别分析，对DotA中各个英雄的类型划分进行验证。1.数据整理及建模1.1数据整理通过网上查阅得到DotA中三类英雄的基础属性如 表 关于同志近三年现实表现材料材料类招标技术评分表图表与交易pdf视力表打印pdf用图表说话 pdf 1-表3。1.2建模通过观察数据，可以得到：力量型英雄在初始力量值和力量成长值两项指标上较为突出，同样，敏捷型英雄在初始敏捷值和敏捷成长值两项指标上较为突出，智力型英雄在初始智力值和智力成长值两项指标上较为突出。但是也并不是全部英雄都是按照这个原则来区分的，通过观察数据，能够发现一些特例，例如：食人鬼魔法师的初始力量值和力量成长值均很高，但是它属于智力型英雄。通过表1-表3的数据建立的判别法则，应能判定大部分英雄的类型划分，同时也能找出其中的特例。通过分析，建立模型如下：共有3个总体𝐺1，𝐺2，𝐺3，其相应的总体均值和协方差分别由表1-表3中的数据来估计，即𝜇1̂，𝜇2̂，𝜇3̂和𝛴1̂，𝛴2̂，𝛴3̂。运用Fisher判别法建立判别法则，并用交叉验证法对判别法则进行评价。DotA中英雄角色的基础属性的统计分析4表1力量型英雄基础属性统计表英雄名称初始力量力量成长初始敏捷敏捷成长初始智力智力成长流浪剑客232.70212.00141.30撼地神牛222.50121.40161.80刚背兽222.20171.80142.80熊猫酒仙232.90162.00141.30半人马酋长233.80152.00151.60龙骑士192.80192.20151.70全能骑士202.70151.80171.80树精卫士273.30152.00171.80山岭巨人243.0090.90141.40兽王232.20181.60161.90炼金术士251.80111.20251.80神灵武士182.40202.40181.50暗夜魔王232.80182.30161.60骷髅王222.90181.70131.60末日使者263.20110.90132.10鱼人守卫212.80172.40151.50食尸鬼252.40181.90151.80半人猛犸212.80152.50171.70混沌骑士202.90142.10161.20狼人222.80161.90151.60潮汐猎人223.00151.50161.70屠夫253.20141.50141.50裂魂人292.40171.70141.80沙王182.60192.10161.80斧王252.50202.20181.60地狱领主232.70171.50212.00深渊领主252.60121.30172.60不朽尸王222.10100.80272.00发条地精242.70131.20171.30船长243.00141.30181.50火凤凰172.90121.30181.80巨牙海民232.30232.10181.70牛头人酋长242.30141.50231.60精灵守卫171.90141.60231.70军团指挥官262.60181.70202.20地精撕裂者222.10161.30211.80DotA中英雄角色的基础属性的统计分析5表2敏捷性英雄基础属性统计表英雄名称初始力量力量成长初始敏捷敏捷成长初始智力智力成长复仇之魂162.30272.80151.80变体精灵192.00243.00171.50流浪剑客232.70162.20141.30娜迦海妖212.30212.80182.00隐形刺客172.00342.90141.30德鲁伊172.10242.70131.40剑圣201.90202.90141.40月之骑士151.90222.80161.90矮人狙击手161.70212.90152.60巨魔战将172.20212.80131.00赏金猎人171.80213.00191.40敌法师201.20222.80151.80黑暗游侠171.90261.90151.40熊战士232.90182.10161.50幻影长矛手181.70234.20212.00月之女祭司171.90202.80171.70圣堂刺客182.10232.70202.00蛇发女妖141.70202.50191.90地穴刺客182.00192.20182.10骷髅射手151.60223.00161.60虚空假面231.60212.70151.50冥界亚龙171.90212.50151.80闪电幽魂211.70222.00191.80灵魂守卫151.90223.20191.80剧毒术士181.90222.60151.80育母蜘蛛172.50182.20182.00幻影刺客201.90233.20131.00地穴编织者151.50142.50151.80影魔152.00202.90182.00血魔232.00243.00181.70幽鬼192.00232.20161.90地卜师231.60231.90201.60矮人直升机181.80242.80232.10鱼人夜行者211.80151.50161.90灰烬之灵192.00221.80201.80弧光守望者241.90151.80242.10DotA中英雄角色的基础属性的统计分析6表3智力型英雄基础属性统计表英雄名称初始力量力量成长初始敏捷敏捷成长初始智力智力成长众神之王191.8111.2202.7魅惑魔女161191.8162.8水晶室女161.7161.6212.9秀逗魔导师181.5161.5273.2暗影萨满191.6161.6213沉默术士172.2162.1272.5谜团172.1141203.4光之守卫161.8151.6222.8食人鬼魔法师233.2141.6172.4修补匠172131.2272.2先知191.8181.9212.9哥布林工程师172141.3222.9圣骑士201.5152.1212.8双头龙242.3101.2282.8风暴之灵171.5221.8232.6仙女龙151.7221.7252.4痛苦女王161.7182242.5受折磨的灵魂161.5231.7263巫妖181.6152183.3死亡先知192.2141.4203恶魔巫师161.7151.3223死灵飞龙222.4111.3242.5遗忘法师171.2161264痛苦之源182.1182.1182.1死灵法师162151.7222.5巫医161.8131.4242.9黑曜毁灭者191.9242263.3术士182.5101242.7暗影牧师161.9211.7273.4黑暗贤者222.3121.2292.7召唤师191.7201.9222.5极寒幽魂181.4202.2252.6蝙蝠骑士232.4151.5242.5预言者191.9151.4222.5暗影恶魔171.9182.2262.7风行者152.5171.4222.6大魔导师191.5141.6272.4天怒法师191.5180.8273.2寒冬飞龙242.1161.9252.4DotA中英雄角色的基础属性的统计分析72.数据分析利用SPSS软件分析的结果见表4-表11和图1。2.1分析案例处理摘要表4分析案例处理摘要表分析案例处理摘要未加权案例N百分比有效111100.0排除的缺失或越界组代码0.0至少一个缺失判别变量0.0缺失或越界组代码还有至少一个缺失判别变量0.0合计0.0合计111100.02.2输入和删除的变量通过表5-表7可知，在判别分析过程中，剔除了“基础敏捷值”这一变量，因为“基础敏捷值”这一变量的F值没有达到要输入的最小值3.84。表5输入和删除的变量统计表输入的/删除的变量a,b,c,d步骤输入的Wilks的Lambda统计量df1df2df3精确F统计量df1df2Sig.1智力成长.31512108.000117.2662108.000.0002敏捷成长.18222108.00071.8924214.000.0003力量成长.14032108.00059.1316212.000.0004基础智力.12642108.00047.6688210.000.0005基础力量.11552108.00040.48110208.000.000在每个步骤中，输入了最小化整体Wilk的Lambda的变量。a.步骤的最大数目是12。b.要输入的最小偏F是3.84。c.要删除的最大偏F是2.71。d.F级、容差或VIN不足以进行进一步计算。DotA中英雄角色的基础属性的统计分析8表6分析中的变量统计表分析中的变量步骤容差要删除的FWilks的Lambda1智力成长1.000117.2662智力成长.95989.260.4863智力成长.86048.924.2694智力成长.84932.553.204基础智力.8715.742.1405智力成长.84527.276.176基础智力.8675.968.128基础力量.8674.924.126表7不在分析中的变量统计表不在分析中的变量步骤容差最小容差要输入的FWilks的Lambda0基础力量1.0001.00031.661.630力量成长1.0001.00046.602.537基础敏捷1.0001.00032.339.625敏捷成长1.0001.00057.167.486基础智力1.0001.00051.337.513智力成长1.0001.000117.266.3151基础力量.994.99423.631.219力量成长.910.91034.684.191基础敏捷.997.99726.892.210敏捷成长.959.95939.164.182基础智力.949.9497.341.2772基础力量.916.8849.497.154力量成长.891.86015.961.140基础敏捷.712.6852.719.173基础智力.927.9236.905.1613基础力量.871.8484.693.128基础敏捷.678.678.737.138基础智力.871.8385.742.1264基础力量.867.7944.924.115基础敏捷.675.674.555.1255基础敏捷.672.653.514.114DotA中英雄角色的基础属性的统计分析92.3特征值和判别函数表8特征值表特征值函数特征值方差的%累积%正则相关性12.860a69.669.6.86121.249a30.4100.0.745a.分析中使用了前2个典型判别式函数。表9判别函数系数表标准化的典型判别式函数系数函数12基础力量-.266.292力量成长.102.598敏捷成长-.235-.575基础智力.400.004智力成长.742.002由表9可知Fisher判别法构造的两个判别函数为：𝑦1=−0.266x1+0.102x2−0.235x4+0.4x5+0.742x6𝑦2=0.292x1+0.598x2−0.575x4+0.004x5+0.002x62.4属性值分类点图分析图1为基础属性值分类点图，从图中我们可以清楚地看到基础属性值的分类情况，可见三个类型的中心点距离较远，区分效果较好。2.5详细分类结果和交叉验证表10为详细分类结果和交叉验证表，详细分类中，一共出现了10次实际值和预测值不相符的情况。交叉验证中，一共出现了11次错判。这些结果也反映在表11分类结果汇总中。DotA中英雄角色的基础属性的统计分析10图1基础属性值分类点图表10详细分类结果和交叉验证表按照案例顺序的统计量案例数目实际组最高组第二最高组判别式得分预测组P(D>d|G=g)P(G=g|D=d)到质心的平方Mahalanobis距离组P(G=g|D=d)到质心的平方Mahalanobis距离函数1函数2pdf初始111.3092.9302.3472.0707.512-2.5901.143211.9802.981.0412.0178.118-.8981.500313**.2422.6042.8361.3413.979.696.519411.3482.9692.1132.0319.009-2.5361.454511.3232.9992.2612.00117.398-1.5252.858611.7022.813.7092.1853.666-1.281.603781111.884.52222.943.999.2471.30122.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