Advanced Machine Learning
We are analyzing our data on hyper-dimensional vector spaces.
So, that's a very important notion on how to view data. Don't be scared here for example this three-dimensional cube. It looks like a star, but just try it. Just look a bit at this star, and eventually you will see that it is a cube. So, I think understanding to view data in hyper-dimensional vector spaces will change your life.
Linear Algebra
Scalar
Any number. For example: 1,5,2.5
Vector
(1,2,3)
Difference between vector and tuple:
vector contains only same data type (1,2,3).
tuple contains different data type (1,'A',2.5).
Matrix
A matrix represents a collection of numbers arranged in an order of rows and columns.
Hyper Dimensional vector spaces
Tensor:
3D tensor is like a matrix but in three dimensions. One dimension for height, one for width, one for colors, Alpha channel and focus information.
- one dimensional tensor is scalar.
- two dimensional tensor is vector.
- three dimensional tensor is matrix.
- one dimensional tensor is scalar.
- two dimensional tensor is vector.
- three dimensional tensor is matrix.
System ML(in a nutshell):
Provides a R-language(DML) for data scientists to implement machine learning algorithms. DML is expressive enough to cover a broad class of algorithms. Such as Descriptive Statistics, Classification, Clustering, Regression, Matrix Factorization, Dimensionality Reduction, Survival Model, and Deep Learning. These algorithms are pre-packaged with SystemML and available on GitHub. SystemML also supports commonly used data transformation task such as recording, demicording, bending, scaling, and missing values imputation. SystemML has a cost less compiler that automatically generates hybrid runtime execution plans. That are composed of single node and distributed operations. These plans are generated depending
on data and cluster characteristics, such as data size, data sparsity,
cluster size and memory configuration. In our previous example,
if the user specifies a small linear, then SystemML might compile
a single node plan. On the other hand, if linear is large, then SystemML might compile Hadoop or a Spark plan. The language component passes the DML script into a hierarchy of statement blocks and statements. It also performs syntactic analysis, live variable analysis, and semantic validation. We then construct a directed cyclic graph of high-level operators, called as HOPs, per statement. SystemML optimizer performs various optimizations on this HOP DAGs. For example, algebraic simplifications rewrite, interprocedural analysis, and matrix multiplication chain optimization. Each HOP DAG is compiled into a dug up low level operators called a slopes, based on memory estimation, data and cluster characteristics. Loops are back in specific operator and have corresponding real-time implementation called instructions. SystemML runs in an embeddable, standalone, and in cluster mode. It also supports various APIs in Scala, Python, and Java.
Linear
Provides a R-language(DML) for data scientists to implement machine learning algorithms. DML is expressive enough to cover a broad class of algorithms. Such as Descriptive Statistics, Classification, Clustering, Regression, Matrix Factorization, Dimensionality Reduction, Survival Model, and Deep Learning. These algorithms are pre-packaged with SystemML and available on GitHub. SystemML also supports commonly used data transformation task such as recording, demicording, bending, scaling, and missing values imputation. SystemML has a cost less compiler that automatically generates hybrid runtime execution plans. That are composed of single node and distributed operations. These plans are generated depending
on data and cluster characteristics, such as data size, data sparsity,
cluster size and memory configuration. In our previous example,
if the user specifies a small linear, then SystemML might compile
a single node plan. On the other hand, if linear is large, then SystemML might compile Hadoop or a Spark plan. The language component passes the DML script into a hierarchy of statement blocks and statements. It also performs syntactic analysis, live variable analysis, and semantic validation. We then construct a directed cyclic graph of high-level operators, called as HOPs, per statement. SystemML optimizer performs various optimizations on this HOP DAGs. For example, algebraic simplifications rewrite, interprocedural analysis, and matrix multiplication chain optimization. Each HOP DAG is compiled into a dug up low level operators called a slopes, based on memory estimation, data and cluster characteristics. Loops are back in specific operator and have corresponding real-time implementation called instructions. SystemML runs in an embeddable, standalone, and in cluster mode. It also supports various APIs in Scala, Python, and Java.
Linear
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