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向量空间算法在信息检索中的使用

向量空间算法在信息检索中的使用向量空间模型（Vector Space Model）是一种常见的信息检索模型。

它将文本数据表示为向量的形式，利用向量运算来比较文本的相似性，从而实现检索。

向量空间模型的基本思想是：将文本集合看作向量空间中的点集，每篇文本可以表示为一个向量，向量的每个维度表示一个特征，例如单词出现的频率。

这样，文本就可以用一个向量来表示了。

在这个模型中，可以用余弦相似度（Cosine Similarity）来计算两个文本向量之间的相似度。

余弦相似度是基于向量的夹角计算的，夹角越小，余弦相似度越大，相似度也就越高。

向量空间模型在信息检索中的应用非常广泛。

这里列举几个常见的应用场景：1. 文本分类向量空间模型可以用来实现文本分类。

每个类别可以看作一个向量，在训练过程中，根据文本特征的权重调整向量的取值，最终建立一个分类模型。

分类时，将待分类文本转换成向量形式，然后通过比较其与各个类别向量的相似度来确定其所属类别。

2. 相似文本查找向量空间模型可以用来寻找相似的文本。

首先将所有的文本转换成向量形式，然后计算待查找文本与数据库中各个文本向量的相似度，最后按照相似度进行排序，选取相似度较高的文本作为结果。

3. 关键词匹配向量空间模型可以用来实现关键词匹配。

将待匹配文本表示为向量形式，然后将关键词也表示为向量形式，最后计算两个向量之间的余弦相似度，根据相似度来决定是否匹配成功。

在以上三个场景中，向量空间算法都可以很好地发挥作用，实现高效的检索和分类。

当然，这只是该算法在信息检索中的一些应用，还存在着许多其他精彩的应用场景，需要不断地探索和实践。

总之，向量空间算法是一种巧妙的算法，它将复杂的文本数据转换为简单的向量形式，从而方便地进行处理。

在信息检索中，向量空间算法已经成为了一种基础工具，可以帮助我们处理各种复杂的问题。

langchain elasticvectorsearch原理

Langchain ElasticVectorSearch是一种基于Elasticsearch的分布式向量搜索引擎，它使用了语言相关性模型（Language Model）和向量表示（Vector Representation）来实现高效的相似度匹配。

其工作原理可以简要概括如下：1. 数据准备阶段：首先，将待搜索的文档集合通过预训练的语言模型进行编码，将每个文档转换为一个固定长度的向量表示。

通常，可以使用诸如BERT、Word2Vec 或GloVe等模型进行编码。

这样，每个文档都被映射到一个在多维空间中的向量位置上。

2. 索引构建阶段：接下来，使用Elasticsearch将这些向量化的文档进行索引。

Elasticsearch是一个开源的分布式搜索和分析引擎，它提供了快速的全文搜索和复杂查询功能。

在Langchain ElasticVectorSearch中，通过自定义插件和扩展来支持向量搜索的特性。

3. 相似度匹配阶段：当用户提交一个查询时，Langchain ElasticVectorSearch会将查询转换为相应的向量表示。

然后，利用向量之间的距离计算方法（如余弦相似度）来度量查询向量与索引中文档向量之间的相似度。

根据相似度评分，搜索引擎可以返回与查询最相关的文档结果。

4. 结果呈现阶段：Langchain ElasticVectorSearch将根据相似度评分对搜索结果进行排序，并根据用户需求返回相应数量的最相关文档。

这些结果可以被展示给用户，通常以列表或者其他形式呈现。

总结来说，Langchain ElasticVectorSearch利用语言模型和向量表示实现了基于相似度的文档搜索。

它通过预训练的语言模型将文档编码为向量，并使用Elasticsearch 进行高效的索引和查询操作，从而提供了快速准确的相似度匹配功能。

1。

向量索引的原理

向量索引的原理向量索引是一种用于高效检索大规模向量数据的技术，它的核心思想是通过对向量数据建立索引结构，实现快速的相似度匹配和检索。

在传统的数据库中，我们可以使用B树、哈希等索引结构来加速数据的查找，但是这些索引结构仅适用于标量或者较简单的结构化数据，对于高维向量数据的索引效果并不好。

因此，为了解决高维向量数据的索引问题，研究者们提出了一系列的向量索引方法。

向量索引的基本思路是将高维向量映射到低维空间，通过对低维向量建立索引结构，实现对高维向量的快速检索。

其中最为经典的方法是局部敏感哈希（LSH），它通过将向量分成多个局部区域，并为每个区域生成一个哈希函数，从而实现将相似的向量映射到相同的哈希桶中。

当需要检索与查询向量相似的向量时，只需要在相应的哈希桶中搜索即可，大大减少了搜索的范围。

除了LSH，还有许多其他的向量索引方法，例如KD树、球树、缩略图等。

这些方法的特点各不相同，适用于不同的场景。

例如，KD树是一种二叉树，通过不断划分空间来建立索引，适用于数据维度较低的情况；而球树则通过对数据进行分解，建立一颗多叉树，适用于数据维度较高的情况。

实际应用中，向量索引通常采用多种方法相结合的方式，以充分发挥各种索引方法的优势。

例如，可以首先通过LSH进行初步检索，得到相似度较高的候选集合，然后再利用KD树、球树等方法进行进一步精确的检索。

这种分层策略既能提高检索的效果，又能降低计算复杂度。

在构建向量索引时，通常需要解决两个关键问题：哈希函数的设计和索引结构的构建。

哈希函数是向量索引的关键，它决定了向量在索引结构中的位置。

哈希函数的设计要考虑两个因素：哈希冲突的概率和相似度的保持。

哈希冲突的概率越低，索引结构的效果越好，但计算量也会增加。

而相似度的保持是指相似的向量在哈希函数的映射下保持相似，这样才能实现准确的检索。

索引结构的构建是指根据哈希函数的映射结果，将向量数据组织成索引结构。

通常情况下，索引结构可以由树状结构或者哈希表构成。

2008Synthesis reactions for Ti3SiC2 through pulse discharge

Synthesis reactions for Ti 3SiC 2through pulse dischargesintering TiH 2/Si/TiC powder mixtureYong Zou,Zheng Ming Sun *,Shuji Tada,Hitoshi HashimotoMaterials Research Institute for Sustainable Development,National Institute of Advanced Industrial Science and Technology (AIST),Nagoya 463-8560,JapanReceived 17November 2006;received in revised form 4April 2007;accepted 23April 2007Available online 4May 2007AbstractTernary compound Ti 3SiC 2was rapidly synthesized by pulse discharge sintering the powder mixture of 1TiH 2/1Si/1.8TiC without preliminary dehydrogenation.Almost single-phase dense Ti 3SiC 2was synthesized at 14008C for 20min.The grain size of synthesized Ti 3SiC 2strongly depends on sintering temperature.The synthesis mechanism of Ti 3SiC 2was revealed to be completed via the reactions among the intermediate phases of Ti 5Si 3,TiSi 2and the other reactants in the starting powder.The Ti–Si liquid reaction occurring above the Ti–Ti 5Si 3eutectic temperature at 13308C was found to assist the synthesis reaction and densiﬁcation of Ti 3SiC 2.The dehydrogenation of TiH 2was accelerated by the synthesis reactions.#2007Elsevier Ltd.All rights reserved.Keywords:A.Ceramics;B.Chemical synthesis;C:X-ray diffraction;D.Microstructure1.IntroductionTi 3SiC 2,a layered ternary carbide belonging to the ‘‘312’’family (i.e.Ti 3SiC 2,Ti 3GeC 2,Ti 3AlC 2)[1],was synthesized ﬁrstly by Jeitschko and Nowotny via chemical reaction in 1967[2].It has been determined that Ti 3SiC 2is a layered hexagonal structure in which almost close-packed planes of titanium are separated from each other by hexagonal nets of silicon;every fourth layer is a silicon layer.Carbon atoms occupy the octahedral sites between the titanium layers [3,4].Ti 3SiC 2has unusual properties that combines many of the best attributes of metals and ceramics,such as good thermal and electrical conductivity,good machinability and good resistance to thermal and mechanical shock,good mechanical properties at elevated temperatures,and possesses good oxidation resistance at high temperatures [5–12].In order to synthesize Ti 3SiC 2,various processes including chemical vapor deposition [13],arc-melting method [14],hot-isostatic-pressing (HIP)or hot-pressing (HP)[6,15–20],pulse discharge sintering (PDS)[20–27]and self-propagating high-temperature synthesis [28–30]were employed.Among these synthesis methods,pulse discharge sintering,also called spark plasma sintering (SPS),is a recent innovation and its versatility allows quick densiﬁcation to nearly theoretical density in a number of metallic,ceramic and other engineering components[31–33].In our previous work,single-phase Ti 3SiC 2was synthesized from Ti,Si,and TiC powders using PDS process at 13008C for about 15min [22,24].However,it is noticed that most synthesizing reactions employed metallic Ti powder as a starting material.TiH 2powder is an intermediate product in manufacturing crushed metallic Ti powder,so it is lower in cost than metallic Ti/locate/matresbuMaterials Research Bulletin 43(2008)968–975*Corresponding author.E-mail addresses:z.m.sun@aist.go.jp (Z.M.Sun),yzou@ (Y .Zou).0025-5408/$–see front matter #2007Elsevier Ltd.All rights reserved.doi:10.1016/j.materresbull.2007.04.028Y.Zou et al./Materials Research Bulletin43(2008)968–975969 powder and its price is only half of metallic Ti powder with the same grain size.Therefore,to synthesize Ti3SiC2closer to application with lower cost,the synthesis of Ti3SiC2from TiH2powder is a practical attempt.But the reports of adopting TiH2as starting materials are seldom[34–36].The reason of un-employing of TiH2is partly due to the long annealing time necessary for preliminarily removing hydrogen in TiH2.In Ref.[36],the mixture powders containing TiH2were annealed at9008C for6h to remove hydrogen prior to powder blending.When TiH2was used directly as a substitution for Ti in starting mixtures,without preliminary dehydrogenation,no Ti3SiC2at all was synthesized through PDS TiH2/Si/TiC powder mixture[35].The main purpose of the present work is to focus on the following issues:(1)the possibility of synthesizing single-phase dense Ti3SiC2starting from TiH2/Si/TiC powder mixture by PDS process without preliminary dehydrogenation,(2)understanding of the mechanism of the Ti3SiC2synthesis and dehydrogenation reactions during the process.2.Experimental proceduresStarting powders of TiH2(À45m m,99%),Si(À10m m,99.9%),and TiC(2–5m m,99%),were used in this study. The powders were mixed in molar ratio of TiH2:Si:TiC=1:1:1.8(Ti:Si:C=2.8:1:1.8),which is slightly off-stoichiometric.This composition is selected based on preliminary optimization experimental results for single-phase synthesis.These powders were mixed in a Turbula shaker mixer in Ar atmosphere for24h.The powder mixture was ﬁlled in a graphite mold(20mm in diameter)and sintered in vacuum by using PDS technique(PAS-V,Sodick Co. Ltd.).The sintering temperature was monitored and controlled through an infrared camera.The heating rate was controlled at508C/min,and the sintering temperature was selected in the range of900–14508C and held at these temperatures for0–20min.The powder compact was kept under a constant axial pressure of50MPa during sintering. After sintering,the samples were ground to remove surface layer for1mm in order to eliminate the carbon effect.Then the samples were analyzed by X-ray diffractometry(XRD)with Cu K a radiation at30kV and40mA to identify the phase constitution.In order to avoid the effect of preferred orientation,powder samples were taken by drilling into the bulk of the samples for quantitative analysis of phase contents by XRD.The microstructure of the synthesized samples were observed and analyzed by using scanning electron microscopy(SEM)equipped with an energy-dispersive spectroscopy(EDS)system.For the SEM observation,the samples were mechanically polished and etched in a solution of H2O:HNO3:HF(2:1:1).3.Results3.1.XRDFig.1shows the X-ray diffraction patterns of the samples sintered at1300–14508C for20min.After sintering at 13008C for20min,three phases was conﬁrmed,i.e.Ti3SiC2,Ti5Si3and TiC phases.The main peak of Ti3SiC2(104) (at2u=39.58)is the strongest in the diffraction pattern.When the sample was sintered at13508C for20min,the peak intensities of TiC are very low.At the same time,the peaks of Ti5Si3decreased to very low intensities.With an increase in sintering temperature up to14008C,the peaks of Ti5Si3and TiC almost disappeared and the near single-phase Ti3SiC2was obtained.When the sintering temperature was further increased to14508C,the peaks of TiC increased again,although the diffraction intensity is low.This result suggests that14008C is the optimum sintering temperature for single-phase Ti3SiC2synthesis by PDS technique starting from TiH2/Si/TiC powder mixture.Further synthesis experiments at this temperature for different soaking time indicated that Ti3SiC2with mass percentage greater than 98%was available for a sintering time as short as10min(results not shown).This indicates that almost single-phase Ti3SiC2can be rapidly synthesized at14008C.3.2.Phase purity and densityIn order to determine the content of Ti3SiC2in all the synthesized samples,equations for quantitative evaluation of the contents of three coexisting phases(Ti3SiC2,Ti5Si3and TiC)were derived based on experimental calibration.The details of calibration will be reported elsewhere[37].Diffraction peaks of Ti3SiC2(104),Ti5Si3(102)and TiC (111)were chosen for quantitative analysis,because they are not overlapped with any other peaks in XRD patterns ofthe mixture of these three phases.The contents of Ti 3SiC 2,TiC and Ti 5Si 3can be calculated according to the following equations:v TSC ¼I TSC I TSC þ4:159I TS þ0:818I TC(1)v TS ¼I TS 0:24I TSC þI TS þ0:197I TC (2)v TC ¼I TC1:22I TSC þ5:072I TS þI TC (3)where v TSC ,v Ts and v TC are weight percentages of Ti 3SiC 2,Ti 5Si 3and TiC,respectively.I TSC ,I TS and I TC represent the integrated diffraction peak intensities of Ti 3SiC 2(104),Ti 5Si 3(102)and TiC (111),respectively.Y.Zou et al./Materials Research Bulletin 43(2008)968–975970Fig.1.X-ray diffraction patterns of the samples sintered at various temperatures for 20min.Fig.2.Ti 5Si 3and TiC contents as functions of sintering temperature.Fig.2shows the quantitative relationship between phase contents and sintering temperature for TiC and Ti 5Si 3in all samples sintered at 1300–14508C for 20min.The contents of Ti 5Si 3and TiC,as impurity phases,showed a rapid decrease from 1300to 14008C in the narrow temperature range of 1008C.Variation in relative density of the sintered samples with the sintering temperature is shown in Fig.3.The relative density was calculated by dividing the measured density (r M )with the theoretical density (r T )of each sample by taking account of the theoretical density of TiC (4.90g/cm 3),Ti 5Si 3(4.32g/cm 3),Ti 3SiC 2(4.51g/cm 3),and the volume fraction (converted from the data as shown in Fig.2)of the two or three constituent phases.The relative densityY.Zou et al./Materials Research Bulletin 43(2008)968–975971Fig.3.Dependence of the relative density on sinteringtemperature.Fig.4.SEM microstructure of the samples sintered at:(a)13008C,(b)13508C,(c)14008C and (d)14508C (sintering time:20min).of samples increases with sintering temperature.When the sintering temperature is 13008C,the relative density is 96.8%,which was improved to above 99.2%when the sintering temperature is increased to 13508C.3.3.MicrostructureFig.4shows the SEM microstructures of the samples synthesized at different sintering temperatures.When the sample was sintered at 13008C for 20min,the microstructure consists of ﬁne grains with the mean grain size of2.6m m,as shown in Fig.4(a),according to image analysis.After being sintered at 13508C for 20min,some grains grew to larger lath-like and the mean grain size is 8.9m m,as shown in Fig.4(b).With increasing sintering temperature,the lath-like grains continue to grow,with grain size of 12.3and 24.9m m,when sintered at 1400and 14508C,respectively,as shown in Fig.4(c)and (d).4.Discussion4.1.The synthesis mechanismIn order to understand the reaction mechanism during sintering process,samples of the powder mixture were heated to various intermediate temperatures under the same heating and loading procedures as in the aforementioned experiments,and cooled down immediately when the programmed temperature was reached.The high cooling rate ($2508C/min)was available due to the water-cooling of the copper electrodes which also served as upper and lower rams pressing the dies set for sintering.This high cooling rate enabled the ‘‘freezing’’of the intermediate phases during the sintering process.Fig.5shows the X-ray diffraction patterns of the starting powder and those samples heated to,and then immediately cooled down from 900,1000,1100,1200and 13008C,respectively.When the sample was heated to 9008C,the peaks of TiH 2disappeared and metallic Ti peaks were observed.At the same time,the peaks of intermediate phase Ti 5Si 3were detected,although its intensity is low.With increasing sintering temperature to 10008C,another intermediate phase,TiSi 2,was observed.When the temperature was increased to 11008C,Ti 3SiC 2Y.Zou et al./Materials Research Bulletin 43(2008)968–975972Fig.5.X-ray diffraction patterns of the TiH 2/Si/TiC powder mixture and the samples heated to and immediately cooled down from 900to 13008C.Y.Zou et al./Materials Research Bulletin43(2008)968–975973 peaks started to appear.With increasing sintering temperature to12008C,the peaks of Si disappeared,and Ti3SiC2 peaks increased considerably in intensity.When the sample was heated to13008C,the main peak of Ti3SiC2at about 2u=39.58prevailed over those of TiC.Based on these experimental observations,the reaction route through sintering TiH2/Si/TiC powder mixture for the synthesis of Ti3SiC2can be expressed as follows:TiH2¼TiþH2(4) 5Tiþ3Si¼Ti5Si3(5) Tiþ2Si¼TiSi2(6) TiSi2þTiþ4TiC¼2Ti3SiC2(7) Ti5Si3þ10TiCþ2Si¼5Ti3SiC2(8) The formation sequence of intermediate phases(i.e.Ti5Si3and TiSi2)during sintering is consistent with our previous work in whichﬁne Ti powder(À10m m)was employed[25],but it is different from the reports about using coarse metallic Ti powder(À150m m)[38].It was found that,when coarse Ti powder was employed in the starting materials,TiSi2phaseﬁrst appeared at lower sintering temperature and Ti5Si3followed when the sintering temperature was further elevated.This could be attributed to the employment of different grain size of Ti(TiH2)powder in the starting material.Different particle size of starting Ti powder leads to different contact area with Si surface,and therefore the Ti:Si ratio is different at the Ti/Si interface,which will in turn be the reaction zone.This difference might have resulted in different local chemistry for the formation of Ti5Si3or TiSi2.This result suggests that the TiH2powder with size of45m m is favorable for the formation of Ti5Si3at initial stage of reactions.4.2.Dehydrogenation reactionAs can be seen in Fig.5,the peaks of TiH2disappeared completely when the sample was heated to9008C and cooled down immediately.However,the mechanism of this extremely rapid dehydrogenation reaction as expressed by Eq.(4)is not well understood.In other words,whether the dehydrogenation reaction was caused by the heating process alone or due to other mechanisms such as the synthesis reactions is not clear.In Ref.[36],it was found that6h were needed to dehydrogenate the mixture powders containing TiH2when annealed at9008C.In order to clarify this issue, TiH2powder alone,with the same mass as used in the powder mixture for one Ti3SiC2sample synthesis,was sintered at13008C for20min with the same sintering program.The X-ray diffraction result(Fig.6)showed that the TiH2still remained after this high temperature and long time synthesis,as demonstrated by the strong diffraction peaks of TiH2 along with that of partly dehydrogenated Ti.For reference,the diffraction pattern of starting TiH2powder is also shown in theﬁgure.This result is unambiguously showing that the rapid dehydrogenation of TiH2at9008C as represented in Fig.5was not solely caused by heating.Instead,the reactions in the powder system during sintering must have played an important role in the dehydrogenation process.EDS analysis results indicated that the Ti area was not pure Ti in sample heated to9008C and cooled down,it always contained some Si.Meanwhile a powder sample was drilled from this material and analyzed by XRD,and the results indicated that the position of TiC peak did not have obvious change compared with starting TiC reactant.This implies that TiC is stable below9008C,without carbon diffusion into Ti.Therefore,the above-mentioned rapid dehydrogenation reaction is more likely to be caused by Ti–Si reaction.In other words,Si atoms started diffusing into TiH2at relatively low temperatures,such as below9008C,to substitute Ti atoms in the crystal structure.This reaction may cause the instability of Ti–H bond,and therefore the dehydrogenation reaction is accelerated.Further work is needed to thoroughly elucidate this phenomenon.4.3.Ti–Si liquid reactionIn our previous work[38,39],evidence of Ti–Si liquid reaction above Ti–Ti5Si3eutectic temperature was revealed by studying the shrinkage displacement curve during pulse discharge sintering Ti/Si/TiC powder mixture.Similar liquid phase reaction was also discussed in the literature[40–42].It is interesting to know whether such liquid reaction occurs when TiH2is used instead of Ti powder in starting materials.In order to understand this issue,similar analyzingmethod was employed,i.e.we studied the sintering process by recording shrinkage displacement curve,namely the displacement of the ram with sintering temperature,or with time,while the axial pressure applied to the powder compact was kept constant at 50MPa during sintering,as shown in Fig.7.It can be seen that the shrinkage curve is smooth when the sintering temperature is below 13508C,but there is an accelerated shrinkage when the sintering temperature is above 13508C,as marked by an arrow in Fig.7.Good reproducibility of the abrupt shrinkage in the shrinkage curve was approved at different sintering temperatures.This temperature is found to be above Ti–Ti 5Si 3eutectic temperature (13308C).Therefore,it is not unreasonable to believe that the abrupt shrinkage is caused by Ti–Si liquid reaction,which immediately ﬁlled the gaps in the powder compact under the applied pressure.On the other hand,the variation of density with sintering temperature is also evidence of this liquid reaction.That is,the relative density of sample sintered at 13008C is 96.7%,and it was rapidly improved to 99.3%when the sintering temperature was increased for only 50to 13508C.This liquid reaction above Ti–Ti 5Si 3eutectic temperature during pulse discharge sintering TiH 2/Si/TiC powder mixture greatly assisted the synthesizing reaction as well as densiﬁcation.Y.Zou et al./Materials Research Bulletin 43(2008)968–975974Fig.6.X-ray diffraction patterns of the TiH 2powder and the TiH 2sample sintered at 13008C for 20min.Fig.7.Shrinkage curves of samples sintered at 1400and 14508C for 20min,as well as the temperature curve for the 14008C sintering.Left y -axis corresponds to the sintering temperature,and right y -axis corresponds to shrinkage displacement.Y.Zou et al./Materials Research Bulletin43(2008)968–975975 5.Conclusion(1)Almost single-phase dense ternary compound Ti3SiC2was rapidly synthesized by pulse discharge sintering thepowder mixture of TiH2/Si/TiC without preliminary dehydrogenation.(2)The grain size of synthesized Ti3SiC2polycrystals strongly depend on sintering temperature.The typicalmicrostructure of almost single-phase Ti3SiC2consists of plate-like grains with mean grain size of12.3m m in length.(3)The synthesis mechanism of Ti3SiC2was revealed to be completed via the reactions among the intermediatephases of Ti5Si3and TiSi2.The rapid dehydrogenation reaction during sintering progress was found to be considerably accelerated by intermediate synthesizing reactions,at much lower temperatures.(4)Liquid formation occurred above Ti–Ti5Si3eutectic temperature during sintering process,and this liquid reactiongreatly assisted the synthesizing reaction and densiﬁcation.References[1]M.W.Barsoum,Prog.Solid State 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Compd.350(2003)303.[37]Y.Zou,Z.M.Sun,S.Tada,H.Hashimoto,J.Alloys Compd.,submitted for publication.[38]Y.Zou,Z.M.Sun,H.Hashimoto,S.Tada,Mater.Trans.47(2006)1910.[39]Y.Zou,Z.M.Sun,H.Hashimoto,S.Tada,Mater.Trans.47(2006)2987.[40]Y.Zhang,Y.C.Zhou,Y.Y.Li,Scripta Mater.49(2003)249.[41]V.Gauthier,B.Cochepin,S.Dubois,D.Vrel,J.Am.Ceram.Soc.89(2006)2899.[42]T.Y.Huang,C.C.Chen,Mater.Sci.Forum475–479(2005)1609.。

ElasticSearch的Vector向量搜索

ElasticSearch的Vector向量搜索在Elasticsearch 7.0中，ES引入了高维向量的字段类型：dense_vector存储稠密向量，value是单一的float数值，可以是0、负数或正数，dense_vector 数组的最大长度不能超过1024，每个文档的数组长度可以不同。

sparse_vector存储稀疏向量，value是单一的float数值，可以是0、负数或正数，sparse_vector 存储的是个非嵌套类型的json对象，key是向量的位置，即integer类型的字符串，范围[0,65535]。

ElasticSearch版本：elasticsearch-7.3.0环境准备：curl -H "Content-Type: application/json" -XPUT 'http://192.168.0.1:9200/article_v1/' -d '{"settings": {"number_of_shards": 1,"number_of_replicas": 0},"mappings": {"dynamic": "strict","properties": {"id": {"type": "keyword"},"title": {"analyzer": "ik_smart","type": "text"},"title_dv": {"type": "dense_vector","dims": 200},"title_sv": {"type": "sparse_vector"}}}}'测试验证代码：# -*- coding:utf-8 -*-import osimport sysimport jiebaimport loggingimport pymongofrom elasticsearch import Elasticsearchfrom elasticsearch.serializer import TextSerializer, JSONSerializerfrom gensim.models.doc2vec import TaggedDocument, Doc2Vecdefault_encoding = 'utf-8'if sys.getdefaultencoding() != default_encoding:reload(sys)sys.setdefaultencoding(default_encoding)logging.basicConfig(format='%(asctime)s:%(levelname)s:%(message)s', level=)# 网上随便爬取一些新闻存入数据库client = pymongo.MongoClient(host='192.168.0.1', port=27017)db = client['news']es = Elasticsearch([{'host': '192.168.0.1', 'port': 9200}], timeout=3600)chinese_stop_words_file = os.path.abspath(os.getcwd() + os.sep + '..' + os.sep + 'static' + os.sep + 'dic' + os.sep + 'chinese_stop_words.txt')chinese_stop_words = [line.strip() for line in open(chinese_stop_words_file, 'r').readlines()]total_cut_word_count = 0# 句子分割def sentence_segment(sentence):global total_cut_word_countresult = []cut_words = jieba.cut(sentence)for cut_word in cut_words:if cut_word not in chinese_stop_words:result.append(cut_word)total_cut_word_count += 1return result# 准备语料库def prepare_doc_corpus():datas = db['netease_ent_news_detail'].find({"create_time": {"$ne": None}}).sort('create_time', pymongo.ASCENDING)print datas.count()for i, data in enumerate(datas):if data['title'] is not None and data['content'] is not None:title = str(data['title']).strip()yield TaggedDocument(sentence_segment(title), [data['_id']])# 训练模型def train_doc_model():corpus = prepare_doc_corpus()doc2vec = Doc2Vec(vector_size=200, min_count=2, window=5, workers=4, epochs=20)doc2vec.build_vocab(corpus)doc2vec.train(corpus, total_examples=doc2vec.corpus_count, epochs=doc2vec.epochs)doc2vec.save('doc2vec.model')def insert_data_to_es():datas = db['netease_ent_news_detail'].find({"create_time": {"$ne": None}}).sort('create_time', pymongo.ASCENDING)print datas.count()doc2vec = Doc2Vec.load('doc2vec.model')for data in datas:if data['title'] is not None and data['content'] is not None:sentence = str(data['title']).strip()title_dv = doc2vec.infer_vector(sentence_segment(sentence)).tolist()body = {"id": data['_id'], "title": data['title'], "title_dv": title_dv}es_result = es.create(index="article_v1", doc_type="_doc",id=data['_id'], body=body, ignore=[400, 409])print es_result# cosineSimilarity函数计算给定文档与索引库里文档的dense_vector相似度def search_es_dense_vertor_1(sentence):doc2vec = Doc2Vec.load('doc2vec.model')query_vector = doc2vec.infer_vector(sentence_segment(sentence)).tolist()body = {"query": {"script_score": {"query": {"match_all": {}},"script": {"source": "cosineSimilarity(params.queryVector, doc['title_dv']) + 1","params": {"queryVector": query_vector}}}},"from": 0,"size": 5}result = es.search(index="article_v1", body=body)hits = result['hits']['hits']for hit in hits:source = hit['_source']for key, value in source.items():print '%s %s' % (key, value)print '----------'# dotProduct函数计算给定文档与索引库文档点积的距离def search_es_dense_vertor_2(sentence):doc2vec = Doc2Vec.load('doc2vec.model')query_vector = doc2vec.infer_vector(sentence_segment(sentence)).tolist()body = {"query": {"script_score": {"query": {"match_all": {}},"script": {"source": "dotProduct(params.queryVector, doc['title_dv']) + 1","params": {"queryVector": query_vector}}}},"from": 0,"size": 5}result = es.search(index="article_v1", body=body)hits = result['hits']['hits']for hit in hits:source = hit['_source']for key, value in source.items():print '%s %s' % (key, value) print '----------'。

向量检索算法分类

向量检索算法分类向量检索算法是指通过将文本或其他信息转化为向量形式，并利用向量空间中的相似性来匹配和检索相关信息的算法。

常见的向量检索算法有以下几种：1.基于词频的向量检索算法：该算法通过计算文档中每个词的出现次数，将文档表示为一个词频向量。

这种算法简单易用，但忽略了词序和语义信息。

常见的基于词频的向量检索算法有TF-IDF（Term Frequency-InverseDocument Frequency）和BM25（Best Matching 25）。

2.基于矩阵分解的向量检索算法：该算法通过矩阵分解技术将文档表示为一个低维矩阵，从而捕捉文档中的语义信息。

常见的基于矩阵分解的向量检索算法有SVD（Singular Value Decomposition）和NMF（Non-negative Matrix Factorization）。

3.基于深度学习的向量检索算法：该算法通过深度神经网络将文档表示为一个向量，从而捕捉文档中的深层次语义信息。

常见的基于深度学习的向量检索算法有Word2Vec、GloVe（Global Vectors）和BERT（BidirectionalEncoder Representations from Transformers）。

4.基于多源数据的向量检索算法：该算法通过融合多种数据源（如文本、图像、音频等）来构建多模态向量空间，从而实现对多源数据的检索。

常见的基于多源数据的向量检索算法有CVR（Cross-Modal Video Retrieval）和图文检索算法。

基于词频的向量检索算法虽然简单，但忽略了词序和语义信息，因此在实际应用中可能存在一定的局限性。

基于矩阵分解的向量检索算法可以捕捉文档中的语义信息，但通常需要较大的计算资源和时间成本。

基于深度学习的向量检索算法可以捕捉文档中的深层次语义信息，但需要大量的训练数据和计算资源。

基于多源数据的向量检索算法可以实现对多模态数据的检索，但需要考虑不同数据源之间的融合和匹配问题。

向量索引算法

向量索引算法
向量索引算法又称为"矢量空间模型"，是一种常用的文本相似
度计算方法。

它主要通过将文本表示为向量，然后在向量空间中计算向量之间的相似度来实现文本检索或相似文本推荐等功能。

具体的向量索引算法一般包括以下几个步骤：
1. 文本预处理：将原始文本进行分词、去除停用词、词干化等操作，得到文本的词汇表。

2. 特征提取：根据预处理后的文本，构建文本的特征向量。

常用的特征提取方法有词袋模型（Bag of Words）、词频（Term Frequency）和逆文档频率（Inverse Document Frequency）等。

3. 向量化表示：将提取到的特征转化为向量表示。

一种常见的方法是使用TF-IDF将词袋模型的特征向量转化为稀疏向量。

4. 建立索引：将向量化表示的文本存储到索引数据结构中。

常用的索引结构有倒排索引（Inverted Index）和KD树等。

5. 查询匹配：对于给定的查询文本，将其进行预处理和特征提取，并转化为向量表示。

然后在索引数据结构中查找与查询向量最相似的文本向量。

6. 相似度计算：通过计算查询向量与文本向量之间的相似度，可以得到查询结果的排序。

常见的向量索引算法有倒排索引算法、LSH（局部敏感哈希）算法、KD-树算法等。

不同的算法有不同的适用场景和优劣势，具体选择哪种算法需要根据实际需求来考虑。

稀疏算子编译

稀疏算子（Sparse Operator）是指只对部分元素进行操作的算子，例如矩阵乘法中的稀疏矩阵。

在编译过程中，稀疏算子的处理通常涉及到如何有效地存储和计算稀疏矩阵，以及如何优化稀疏算子的计算性能。

以下是一些编译中处理稀疏算子的常见方法：
1.压缩存储：对于稀疏矩阵，可以使用压缩存储方法来减少存储空间的使用。

例
如，可以使用三元组表示法或行主序存储法等。

2.稀疏算子优化：针对稀疏算子进行优化，可以显著提高计算性能。

例如，可以
使用快速傅里叶变换（FFT）等算法加速稀疏矩阵乘法等操作。

3.代码生成优化：在编译器中，可以根据稀疏算子的特性生成优化的代码。

例如，
可以使用向量化指令、并行计算等技术来加速稀疏算子的计算。

4.内存优化：对于大规模的稀疏矩阵，内存的使用也是一个重要的问题。

可以使
用内存优化技术，例如缓存优化、内存对齐等，来提高内存的使用效率。

5.并行计算：对于大规模的稀疏矩阵操作，可以使用并行计算技术来加速计算。

例如，可以将稀疏矩阵分成多个子矩阵，并使用多线程或分布式计算等技术进行并行处理。

总之，在编译过程中处理稀疏算子需要综合考虑存储、计算和内存等多个方面，并使用各种优化技术来提高计算性能和内存使用效率。

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3
cross sections obey tree-level unitarity, as is the hallmark of all gauge theories. Of course, it might be that the appearance of vector leptoquarks is simply some low energy manifestation of a more fundamental theory at a higher scale and that these particles may even be composite. In this case so-called ‘anomalous’ couplings in both the gV V and ggV V vertices can appear. One possible coupling of this type is an ‘anomalous chromomagnetic moment’, usually described in the literature by the parameter κ, which takes the value of unity in the more realistic gauge theory case. Among these ‘anomalous couplings’, the term which induces κ is quite special in that it is the only one that conserves CP and is of dimension 4.
2ห้องสมุดไป่ตู้
Figure 1: Production cross section for a pair of 1 TeV vector leptoquarks at the LHC as a function of κ. The dotted(dashed) curve corresponds to the gg(qq¯) production subprocess whereas the solid curve is their sum.
ABSTRACT The search reaches for both scalar(S) and vector(V ) leptoquarks at future hadron colliders are summarized. In particular we evaluate the production cross sections of both leptoquark types at TeV33 and LHC as well as the proposed 60 and 200 TeV colliders through both quark-antiquark annihilation and gluongluon fusion: qq¯, gg → SS, V V . Experiments at these machines should easily discover such particles if their masses are not in excess of the few TeV range.
The vector leptoquark(V ) case is not as straightforward. In order to calculate the gg → V V cross section we need to determine both the trilinear gV V and quartic ggV V couplings, which may naively at ﬁrst glance appear to be unknown. (For the qq¯ subprocess, only the gV V coupling is required.) However, in any realistic model wherein vector leptoquarks appear and are fundamental objects, they will be the gauge bosons of an extended gauge group like SU(5). In this case the gV V and ggV V couplings are completely ﬁxed by extended gauge invariance. These particular couplings will also insure that the subprocess
2 Leptoquark Pair Production
Leptoquarks can be produced either singly or in pairs in hadronic collisions. The cross section for single production, however, relies on the size of the a priori unknown Yukawa couplings of the leptoquark and is therefore model dependent. Pair production, on the otherhand, proceeds through QCD interactions and thus depends only on the leptoquark spin and the fact that it is a color triplet ﬁeld. It has been shown in Ref.[6] that this mechanism will be dominant unless the Yukawa couplings, which are governed by the electroweak interactions, are rather large, i.e., of order electromagnetic strength or greater. This is an important result in that the production of both scalar and vector leptoquarks at hadron colliders is not dependent upon the electroweak properties of these particles. Of course, the converse is also true, i.e., the production properties cannot be used to probe the detailed nature of the leptoquark type.
1Work supported by the Department of Energy, contract DE–AC03–76SF00515.
1
1 Introduction
Many extensions of the standard model(SM) which place quarks and leptons on a symmetric footing predict the existence of leptoquarks, which are spin-0 or 1, color-triplet objects that couple to a qℓ or q¯ℓ pair[1]. While these particles may be sought indirectly through their inﬂuence on low energy processes[2], the most promising approach is via direct production at colliders. In particular, searches for leptoquarks at LEP[3], HERA[4], and the Tevatron[5] have already been performed, in most cases concentrating on the speciﬁc scenario of scalar leptoquarks. Based on both the direct and indirect searches we might expect that if leptoquarks exist their masses must be above a few hundred GeV, and possibly up in the TeV range. In this paper we will examine the search reach for both scalar and vector leptoquarks at future hadron colliders. The production rates for leptoquarks at such colliders will be shown to be suﬃciently large so that particles of this type in the TeV mass range and above become accessible. In addition, we will see that the size of the production cross section alone is suﬃcient to distinguish scalar from vector leptoquark types.
To appear in the Proceedings of the 1996 DPF/DPB Summer Study on New Directions for High Energy Physics-Snowmass96, Snowmass, CO, 25 June-12 July, 1996.