From b51b07958ae236e492fbf6e16a50fc926601115c Mon Sep 17 00:00:00 2001 From: ad min Date: Mon, 7 Mar 2016 12:23:37 +0800 Subject: [PATCH] add content to lda --- "\350\201\232\347\261\273/LDA/imgs/3.2.1.png" | Bin 0 -> 12706 bytes "\350\201\232\347\261\273/LDA/imgs/3.2.2.png" | Bin 0 -> 10795 bytes "\350\201\232\347\261\273/LDA/imgs/3.2.3.png" | Bin 0 -> 24459 bytes "\350\201\232\347\261\273/LDA/imgs/3.2.4.png" | Bin 0 -> 42323 bytes "\350\201\232\347\261\273/LDA/imgs/3.2.5.png" | Bin 0 -> 13614 bytes "\350\201\232\347\261\273/LDA/imgs/3.2.6.png" | Bin 0 -> 11803 bytes "\350\201\232\347\261\273/LDA/imgs/3.2.7.png" | Bin 0 -> 6852 bytes "\350\201\232\347\261\273/LDA/imgs/3.2.8.png" | Bin 0 -> 1221 bytes "\350\201\232\347\261\273/LDA/imgs/3.2.9.png" | Bin 0 -> 4892 bytes "\350\201\232\347\261\273/LDA/imgs/alg1.png" | Bin 0 -> 70912 bytes "\350\201\232\347\261\273/LDA/imgs/alg2.png" | Bin 0 -> 67011 bytes "\350\201\232\347\261\273/LDA/lda.md" | 55 +++++++++++++++++- 12 files changed, 54 insertions(+), 1 deletion(-) create mode 100644 "\350\201\232\347\261\273/LDA/imgs/3.2.1.png" create mode 100644 "\350\201\232\347\261\273/LDA/imgs/3.2.2.png" create mode 100644 "\350\201\232\347\261\273/LDA/imgs/3.2.3.png" create mode 100644 "\350\201\232\347\261\273/LDA/imgs/3.2.4.png" create mode 100644 "\350\201\232\347\261\273/LDA/imgs/3.2.5.png" create mode 100644 "\350\201\232\347\261\273/LDA/imgs/3.2.6.png" create mode 100644 "\350\201\232\347\261\273/LDA/imgs/3.2.7.png" create mode 100644 "\350\201\232\347\261\273/LDA/imgs/3.2.8.png" create mode 100644 "\350\201\232\347\261\273/LDA/imgs/3.2.9.png" create mode 100644 "\350\201\232\347\261\273/LDA/imgs/alg1.png" create mode 100644 "\350\201\232\347\261\273/LDA/imgs/alg2.png" diff --git "a/\350\201\232\347\261\273/LDA/imgs/3.2.1.png" "b/\350\201\232\347\261\273/LDA/imgs/3.2.1.png" new file mode 100644 index 0000000000000000000000000000000000000000..9b49395ec32cc6b9ab5972e7f0db5ded4000d78d GIT binary patch literal 12706 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zR9Jo;5ZHLUzZpRPii_#)u`d9=a-dp%t>czzIJBt|BwvM^!8n^O?NLNNC1N^R(X)+m$e-kZ4>{k}1lzC6o8P+zh^#r97 zOlyP6MmGJ^?lM`72)KOvI-!MkD91t9ywFC= z8!00{1ATq#VurRqo2M}o#ym{a$IGo%GquuLBdJQPI%I7cjGd>8|JgO6J*?jcV97Jtopic_words
+ +  最大化`ELBO`就是最大化`q(z,theta,beta)`和`p(z,theta,beta|w,alpha,eta)`的`KL`距离。根据文献【3】,我们将`q`因式分解为如下**(3.2.2)**的形式: + +

topic_words

+ +  后验`z`通过`phi`来参数化,后验`theta`通过`gamma`来参数化,后验`beta`通过`lambda`来参数化。简单的说,我们把`lambda`作为“主题”。公式**(3.2.1)**分解为如下**(3.2.3)**形式: + +
topic_words

+ +  我们现在将上面的期望扩展为变分参数的函数形式。这反映了变分目标只依赖于,即词`w`出现在文档`d`中的次数。当使用`VB`算法时,文档可以通过它们的词频来概括,如公式**(3.2.4)** + +
topic_words

+ +  上面的公式中,`W`表示词的数量,`D`表示文档的数量。`l`表示文档`d`对`ELBO`所做的贡献。`L`可以通过坐标上升法来最优化,它的更新公式如**(3.2.5)**: + +
topic_words

+ +  `log(theta)`和`log(beta)`的期望通过下面的公式**(3.2.6)**计算: + +
topic_words

+ +  通过`EM`算法,我们可以将这些更新分解成`E-步`和`M-步`。`E-步`固定`lambda`来更新`gamma`和`phi`;`M-步`通过给定`phi`来更新`lambda`。批`VB`算法的过程如下**(算法1)**所示: + +
topic_words

+ +### 3.2.2 在线变分贝叶斯 + +  批量变分贝叶斯算法需要固定的内存,并且比吉布斯采样更快。但是它仍然需要在每次迭代时处理所有的文档,这在处理大规模文档时,速度会很慢,并且也不适合流式数据的处理。 +文献【5】提出了一种在线变分推导算法。设定`gamma(n_d,lambda)`和`phi(n_d,lambda)`分别表示`gamma_d`和`phi_d`的值,我们的目的就是设定`phi`来最大化下面的公式**(3.2.7)** + +
topic_words

+ +  我们在**算法2**中介绍了在线`VB`算法。因为词频的第t个向量是可观察的,我们在`E-步`通过固定`lambda`来找到`gamma_t`和`phi_t`的局部最优解。 +然后,我们计算`lambda_cap`。如果整个语料库由单个文档重复`D`次组成,那么这样的`lambda_cap`设置是最优的。之后,我们通过`lambda`之前的值以及`lambda_cap`来更新`lambda`。我们给`lambda_cap`设置的权重如公式**(3.2.8)**所示: + +
topic_words

+ +  在线`VB`算法的实现流程如下**算法2**所示 + +
topic_words

+ +  同时在在线`VB`算法中,`alpha`和`eta`通过下面公式**(3.2.9)**来更新: + +
topic_words

+ # 4 LDA代码实现 ## 4.1 LDA使用实例 @@ -526,6 +577,8 @@ this.graph = Graph(docTermVertices, edges).partitionBy(PartitionStrategy.EdgePar // 计算 N_{wj} gamma_{wjk} val N_wj = edgeContext.attr // E-STEP: 计算 gamma_{wjk} 通过N_{wj}来计算 + //此处的edgeContext.srcAttr为当前迭代的N_kj , edgeContext.dstAttr为当前迭代的N_wk, + //后面通过M-步,会更新这两个值,作为下一次迭代的当前值 val scaledTopicDistribution: TopicCounts = computePTopic(edgeContext.srcAttr, edgeContext.dstAttr, N_k, W, eta, alpha) *= N_wj edgeContext.sendToDst((false, scaledTopicDistribution)) @@ -534,7 +587,7 @@ this.graph = Graph(docTermVertices, edges).partitionBy(PartitionStrategy.EdgePar ```   上述代码中,`W`表示词数,`N_k`表示所有文档中,出现在主题`k`中的词的词频总数,后续的实现会使用方法`computeGlobalTopicTotals`来更新这个值。`N_wj`表示词`w`出现在文档`j`中的词频数,为已知数。`E-步`就是利用公式**(3.1.6)**去更新`gamma`。 代码中使用`computePTopic`方法来实现这个更新。`edgeContext`通过方法`sendToDst`将`scaledTopicDistribution`发送到目标顶点, -通过方法`sendToSrc`发送到源节点以便于后续的`M-步`计算更新的`N_kj`和`N_wk`。下面我们看看`computePTopic`方法。 +通过方法`sendToSrc`发送到源顶点以便于后续的`M-步`更新的`N_kj`和`N_wk`。下面我们看看`computePTopic`方法。 ```scala private[clustering] def computePTopic(