<转>Spark 学习笔记：MLlib基础

MLlib：Machine Learning Library。主要内容包括：

• 数据类型
• 统计工具
  
• summary statistics
• correlations
• stratified sampling
• hypothesis testing
• random data generation 
• 分类和回归
• 线性模型（SVM，逻辑回归，线性回归）
• 朴素贝叶斯
• 决策树
• ensembles of trees（随机森林和Gradient-Boosted Trees）
• isotonic regression
• 协同过滤
• ALS(alternating least squares)　　　　　
• 聚类
• k-means
• 高斯混合模型
• power iteration clustering(PIC)
• LDA(latent Dirichlet allocation)
• 流式k-means　
• 降维
• SVD
• PCA
• 特征提取和转换
• Frequent pattern mining
• FP－growth
• 优化　　
• stochastic gradient descent
• limited-memory BFGS (L-BFGS)

  　　　　

  I.数据类型

  MLlib的数据类型主要是local vectors和local matrices，潜在的代数操作由Breeze和jblas提供。

  1.local vector 有int型和double型，下标从0开始，分为dense和sparse 两种。

  Local vector的基本类型是Vector，包括：DenseVector和SparseVector。 

  import org.apache.spark.mllib.linalg.{Vector, Vectors}    
  
  // Create a dense vector (1.0, 0.0, 3.0).
  val dv: Vector = Vectors.dense(1.0, 0.0, 3.0)
  // Create a sparse vector (1.0, 0.0, 3.0) by specifying its indices and values corresponding to nonzero entries.
  val sv1: Vector = Vectors.sparse(3, Array(0, 2), Array(1.0, 3.0))
  // Create a sparse vector (1.0, 0.0, 3.0) by specifying its nonzero entries.
  val sv2: Vector = Vectors.sparse(3, Seq((0, 1.0), (2, 3.0)))

  Scala imports scala.collection.immutable.Vector by default, so you have to import org.apache.spark.mllib.linalg.Vector explicitly to use MLlib’s Vector.

• MLlib中一个监督学习的训练样本被称为“labeled point”。

  import org.apache.spark.mllib.linalg.Vectors
  import org.apache.spark.mllib.regression.LabeledPoint
  
  // Create a labeled point with a positive label and a dense feature vector.
  val pos = LabeledPoint(1.0, Vectors.dense(1.0, 0.0, 3.0))
  
  // Create a labeled point with a negative label and a sparse feature vector.
  val neg = LabeledPoint(0.0, Vectors.sparse(3, Array(0, 2), Array(1.0, 3.0)))

•  MLlib supports reading training examples stored in LIBSVM format, which is the default format used by LIBSVM and LIBLINEAR.

  import org.apache.spark.mllib.regression.LabeledPoint
  import org.apache.spark.mllib.util.MLUtils
  import org.apache.spark.rdd.RDD
  
  val examples: RDD[LabeledPoint] = MLUtils.loadLibSVMFile(sc, "data/mllib/sample_libsvm_data.txt")

  2.local matrix

  A local matrix has integer-typed row and column indices and double-typed values, stored on a single machine. MLlib supports dense matrices, whose entry values are stored in a single double array in column major.

  import org.apache.spark.mllib.linalg.{Matrix, Matrices}
  
  // Create a dense matrix ((1.0, 2.0), (3.0, 4.0), (5.0, 6.0))
  val dm: Matrix = Matrices.dense(3, 2, Array(1.0, 3.0, 5.0, 2.0, 4.0, 6.0))

• A distributed matrix has long-typed row and column indices and double-typed values, stored distributively in one or more RDDs.It is very important to choose the right format to store large and distributed matrices.  A RowMatrix is a row-oriented distributed matrix without meaningful row indices, e.g., a collection of feature vectors. It is backed by an RDD of its rows, where each row is a local vector. We assume that the number of columns is not huge. An IndexedRowMatrix is similar to a RowMatrix but with row indices, which can be used for identifying rows and executing joins. A CoordinateMatrix is a distributed matrix stored in coordinate list (COO) format, backed by an RDD of its entries.

  import org.apache.spark.mllib.linalg.Vector
  import org.apache.spark.mllib.linalg.distributed.RowMatrix
  
  val rows: RDD[Vector] = ... // an RDD of local vectors
  // Create a RowMatrix from an RDD[Vector].
  val mat: RowMatrix = new RowMatrix(rows)
  
  // Get its size.
  val m = mat.numRows()
  val n = mat.numCols()
  
  import org.apache.spark.mllib.linalg.distributed.{IndexedRow, IndexedRowMatrix, RowMatrix}
  
  val rows: RDD[IndexedRow] = ... // an RDD of indexed rows
  // Create an IndexedRowMatrix from an RDD[IndexedRow].
  val mat: IndexedRowMatrix = new IndexedRowMatrix(rows)
  // Drop its row indices.
  val rowMat: RowMatrix = mat.toRowMatrix()
  
  import org.apache.spark.mllib.linalg.distributed.{CoordinateMatrix, MatrixEntry}
  
  val entries: RDD[MatrixEntry] = ... // an RDD of matrix entries
  // Create a CoordinateMatrix from an RDD[MatrixEntry].
  val mat: CoordinateMatrix = new CoordinateMatrix(entries)// Convert it to an IndexRowMatrix whose rows are sparse vectors.
  val indexedRowMatrix = mat.toIndexedRowMatrix()

   

• A BlockMatrix is a distributed matrix backed by an RDD of MatrixBlocks, where a MatrixBlock is a tuple of ((Int, Int), Matrix), where the (Int, Int) is the index of the block, and Matrix is the sub-matrix at the given index. BlockMatrix supports methods such as add and multiply with another BlockMatrix.A BlockMatrix can be most easily created from an IndexedRowMatrix or CoordinateMatrix by calling toBlockMatrix.

  import org.apache.spark.mllib.linalg.distributed.{BlockMatrix, CoordinateMatrix, MatrixEntry}
  
  val entries: RDD[MatrixEntry] = ... // an RDD of (i, j, v) matrix entries
  // Create a CoordinateMatrix from an RDD[MatrixEntry].
  val coordMat: CoordinateMatrix = new CoordinateMatrix(entries)
  // Transform the CoordinateMatrix to a BlockMatrix
  val matA: BlockMatrix = coordMat.toBlockMatrix().cache()
  
  // Validate whether the BlockMatrix is set up properly. Throws an Exception when it is not valid.
  // Nothing happens if it is valid.
  matA.validate()
  
  // Calculate A^T A.
  val ata = matA.transpose.multiply(matA)