How to use Polynomial Regression in rapidminer correctly
Hello, everyone. This is my first forum post asking questions about polynomial regression in rapidminer.
The original data is：x:4194.06 3466.45 2070.08 874.98 corresponding to y：91540.07 109460.36 120338.64 102182.19
As shown in the first flow, the first result expression is obtained by using the polynomial regression operator.
<?xml version="1.0" encoding="UTF-8"?><process version="9.6.000">
<context>
<input/>
<output/>
<macros/>
</context>
<operator activated="true" class="process" compatibility="9.6.000" expanded="true" name="Process">
<parameter key="logverbosity" value="init"/>
<parameter key="random_seed" value="2001"/>
<parameter key="send_mail" value="never"/>
<parameter key="notification_email" value=""/>
<parameter key="process_duration_for_mail" value="30"/>
<parameter key="encoding" value="SYSTEM"/>
<process expanded="true">
<operator activated="true" class="read_excel" compatibility="9.6.000" expanded="true" height="68" name="Read Excel" width="90" x="45" y="85">
<parameter key="excel_file" value="C:\Users\1\Desktop\question data.xlsx"/>
<parameter key="sheet_selection" value="sheet number"/>
<parameter key="sheet_number" value="1"/>
<parameter key="imported_cell_range" value="A1"/>
<parameter key="encoding" value="SYSTEM"/>
<parameter key="first_row_as_names" value="true"/>
<list key="annotations"/>
<parameter key="date_format" value=""/>
<parameter key="time_zone" value="SYSTEM"/>
<parameter key="locale" value="English (United States)"/>
<parameter key="read_all_values_as_polynominal" value="false"/>
<list key="data_set_meta_data_information">
<parameter key="0" value="x.true.real.attribute"/>
<parameter key="1" value="y.true.real.attribute"/>
</list>
<parameter key="read_not_matching_values_as_missings" value="false"/>
<parameter key="datamanagement" value="double_array"/>
<parameter key="data_management" value="auto"/>
</operator>
<operator activated="true" class="set_role" compatibility="9.6.000" expanded="true" height="82" name="Set Role" width="90" x="179" y="85">
<parameter key="attribute_name" value="y"/>
<parameter key="target_role" value="label"/>
<list key="set_additional_roles">
<parameter key="x" value="regular"/>
</list>
</operator>
<operator activated="true" class="polynomial_regression" compatibility="9.6.000" expanded="true" height="82" name="Polynomial Regression" width="90" x="313" y="85">
<parameter key="max_iterations" value="5000"/>
<parameter key="replication_factor" value="2"/>
<parameter key="max_degree" value="2"/>
<parameter key="min_coefficient" value="-100.0"/>
<parameter key="max_coefficient" value="100.0"/>
<parameter key="use_local_random_seed" value="false"/>
<parameter key="local_random_seed" value="1992"/>
</operator>
<connect from_op="Read Excel" from_port="output" to_op="Set Role" to_port="example set input"/>
<connect from_op="Set Role" from_port="example set output" to_op="Polynomial Regression" to_port="training set"/>
<connect from_op="Polynomial Regression" from_port="model" to_port="result 1"/>
<portSpacing port="source_input 1" spacing="0"/>
<portSpacing port="sink_result 1" spacing="0"/>
<portSpacing port="sink_result 2" spacing="0"/>
</process>
</operator>
</process>
The second flow, based on the original data, creates a new list of attributes as x^2=z, and uses the linear regression operator to make the second result expression.
<?xml version="1.0" encoding="UTF-8"?><process version="9.6.000">
<context>
<input/>
<output/>
<macros/>
</context>
<operator activated="true" class="process" compatibility="9.6.000" expanded="true" name="Process">
<parameter key="logverbosity" value="init"/>
<parameter key="random_seed" value="2001"/>
<parameter key="send_mail" value="never"/>
<parameter key="notification_email" value=""/>
<parameter key="process_duration_for_mail" value="30"/>
<parameter key="encoding" value="SYSTEM"/>
<process expanded="true">
<operator activated="true" class="read_excel" compatibility="9.6.000" expanded="true" height="68" name="Read Excel" width="90" x="45" y="85">
<parameter key="excel_file" value="C:\Users\1\Desktop\question data.xlsx"/>
<parameter key="sheet_selection" value="sheet number"/>
<parameter key="sheet_number" value="1"/>
<parameter key="imported_cell_range" value="A1"/>
<parameter key="encoding" value="SYSTEM"/>
<parameter key="first_row_as_names" value="true"/>
<list key="annotations"/>
<parameter key="date_format" value=""/>
<parameter key="time_zone" value="SYSTEM"/>
<parameter key="locale" value="English (United States)"/>
<parameter key="read_all_values_as_polynominal" value="false"/>
<list key="data_set_meta_data_information">
<parameter key="0" value="x.true.real.attribute"/>
<parameter key="1" value="y.true.real.attribute"/>
</list>
<parameter key="read_not_matching_values_as_missings" value="false"/>
<parameter key="datamanagement" value="double_array"/>
<parameter key="data_management" value="auto"/>
</operator>
<operator activated="true" class="generate_attributes" compatibility="9.6.000" expanded="true" height="82" name="Generate Attributes" width="90" x="179" y="85">
<list key="function_descriptions">
<parameter key="z" value="x*x"/>
</list>
<parameter key="keep_all" value="true"/>
</operator>
<operator activated="false" class="rename" compatibility="9.6.000" expanded="true" height="82" name="Rename" width="90" x="246" y="238">
<parameter key="old_name" value="x"/>
<parameter key="new_name" value="x^2"/>
<list key="rename_additional_attributes"/>
</operator>
<operator activated="true" class="set_role" compatibility="9.6.000" expanded="true" height="82" name="Set Role" width="90" x="313" y="85">
<parameter key="attribute_name" value="y"/>
<parameter key="target_role" value="label"/>
<list key="set_additional_roles">
<parameter key="x" value="regular"/>
</list>
</operator>
<operator activated="true" class="linear_regression" compatibility="9.6.000" expanded="true" height="103" name="Linear Regression" width="90" x="514" y="85">
<parameter key="feature_selection" value="none"/>
<parameter key="alpha" value="0.05"/>
<parameter key="max_iterations" value="10"/>
<parameter key="forward_alpha" value="0.05"/>
<parameter key="backward_alpha" value="0.05"/>
<parameter key="eliminate_colinear_features" value="false"/>
<parameter key="min_tolerance" value="0.05"/>
<parameter key="use_bias" value="true"/>
<parameter key="ridge" value="1.0E-8"/>
</operator>
<operator activated="false" class="polynomial_regression" compatibility="9.6.000" expanded="true" height="82" name="Polynomial Regression" width="90" x="581" y="238">
<parameter key="max_iterations" value="5000"/>
<parameter key="replication_factor" value="2"/>
<parameter key="max_degree" value="2"/>
<parameter key="min_coefficient" value="-100.0"/>
<parameter key="max_coefficient" value="100.0"/>
<parameter key="use_local_random_seed" value="false"/>
<parameter key="local_random_seed" value="1992"/>
</operator>
<connect from_op="Read Excel" from_port="output" to_op="Generate Attributes" to_port="example set input"/>
<connect from_op="Generate Attributes" from_port="example set output" to_op="Set Role" to_port="example set input"/>
<connect from_op="Set Role" from_port="example set output" to_op="Linear Regression" to_port="training set"/>
<connect from_op="Linear Regression" from_port="model" to_port="result 1"/>
<portSpacing port="source_input 1" spacing="0"/>
<portSpacing port="sink_result 1" spacing="0"/>
<portSpacing port="sink_result 2" spacing="0"/>
</process>
</operator>
</process>
I want to ask why the results of the two processes are not the same, the original data presents a quadratic nonlinear relationship, and why the quadratic expression cannot be made by polynomial regression.
Thanks you very much!
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. According to your description, I am as the data is too little, and not standardized, to lead to the results out? But these four samples are real data , need the four data to construct a yuan quadratic polynomial, Because nonlinear equations can be converted to linear equations , so I use z instead of x2, I have the linear regression equation. But why do with polynomial regression is not to come out, how do you explain that please？Polynomial regression is there any limit to this operator ？Sorry in advance, I don't know how to use the function of this forum.That's why it took so long to reply
First of all, thank you for your answer
. According to your description, I am as the data is too little, and not standardized, to lead to the results out? But these four samples are real data , need the four data to construct a yuan quadratic polynomial, Because nonlinear equations can be converted to linear equations , so I use z instead of x2, I have the linear regression equation. But why do with polynomial regression is not to come out, how do you explain that please？Polynomial regression is there any limit to this operator ？
Thanks for sharing the data and process.
If we have got four (4) example and train a polynomial regression, we may fail for the model. So I filled up the gap with interpolation to add more data here. Also this Polynomial regression will not perform well without the normalization...
Process attached here for your reference.
<?xml version="1.0" encoding="UTF-8"?><process version="9.6.000"> <operator activated="false" class="read_excel" compatibility="9.6.000" expanded="true" height="68" name="Read Excel" width="90" x="45" y="136"> <parameter key="excel_file" value="C:\Users\1\Desktop\question data.xlsx"/> <parameter key="sheet_selection" value="sheet number"/> <parameter key="sheet_number" value="1"/> <parameter key="imported_cell_range" value="A1"/> <parameter key="encoding" value="SYSTEM"/> <parameter key="first_row_as_names" value="true"/> <list key="annotations"/> <parameter key="date_format" value=""/> <parameter key="time_zone" value="SYSTEM"/> <parameter key="locale" value="English (United States)"/> <parameter key="read_all_values_as_polynominal" value="false"/> <list key="data_set_meta_data_information"> <parameter key="0" value="x.true.real.attribute"/> <parameter key="1" value="y.true.real.attribute"/> </list> <parameter key="read_not_matching_values_as_missings" value="false"/> <parameter key="datamanagement" value="double_array"/> <parameter key="data_management" value="auto"/> </operator> </process> <?xml version="1.0" encoding="UTF-8"?><process version="9.6.000"> <operator activated="true" class="utility:create_exampleset" compatibility="9.6.000" expanded="true" height="68" name="Create ExampleSet" width="90" x="45" y="34"> <parameter key="generator_type" value="comma separated text"/> <parameter key="number_of_examples" value="100"/> <parameter key="use_stepsize" value="false"/> <list key="function_descriptions"/> <parameter key="add_id_attribute" value="false"/> <list key="numeric_series_configuration"/> <list key="date_series_configuration"/> <list key="date_series_configuration (interval)"/> <parameter key="date_format" value="yyyy-MM-dd HH:mm:ss"/> <parameter key="time_zone" value="SYSTEM"/> <parameter key="input_csv_text" value="x,y 4194.06, 91540.07 3466.45, 109460.36 2070.08, 120338.64 874.98, 102182.19 "/> <parameter key="column_separator" value=","/> <parameter key="parse_all_as_nominal" value="false"/> <parameter key="decimal_point_character" value="."/> <parameter key="trim_attribute_names" value="true"/> </operator> </process> <?xml version="1.0" encoding="UTF-8"?><process version="9.6.000"> <operator activated="true" class="parse_numbers" compatibility="9.6.000" expanded="true" height="82" name="Parse Numbers" width="90" x="179" y="34"> <parameter key="attribute_filter_type" value="all"/> <parameter key="attribute" value=""/> <parameter key="attributes" value=""/> <parameter key="use_except_expression" value="false"/> <parameter key="value_type" value="nominal"/> <parameter key="use_value_type_exception" value="false"/> <parameter key="except_value_type" value="file_path"/> <parameter key="block_type" value="single_value"/> <parameter key="use_block_type_exception" value="false"/> <parameter key="except_block_type" value="single_value"/> <parameter key="invert_selection" value="false"/> <parameter key="include_special_attributes" value="false"/> <parameter key="decimal_character" value="."/> <parameter key="grouped_digits" value="false"/> <parameter key="grouping_character" value=","/> <parameter key="infinity_representation" value=""/> <parameter key="unparsable_value_handling" value="fail"/> </operator> </process> <?xml version="1.0" encoding="UTF-8"?><process version="9.6.000"> <operator activated="true" class="set_role" compatibility="9.6.000" expanded="true" height="82" name="Set Role" width="90" x="313" y="34"> <parameter key="attribute_name" value="y"/> <parameter key="target_role" value="label"/> <list key="set_additional_roles"> <parameter key="x" value="regular"/> </list> </operator> </process> <?xml version="1.0" encoding="UTF-8"?><process version="9.6.000"> <operator activated="true" class="normalize" compatibility="9.6.000" expanded="true" height="103" name="Normalize" width="90" x="447" y="34"> <parameter key="return_preprocessing_model" value="false"/> <parameter key="create_view" value="false"/> <parameter key="attribute_filter_type" value="all"/> <parameter key="attribute" value=""/> <parameter key="attributes" value=""/> <parameter key="use_except_expression" value="false"/> <parameter key="value_type" value="numeric"/> <parameter key="use_value_type_exception" value="false"/> <parameter key="except_value_type" value="real"/> <parameter key="block_type" value="value_series"/> <parameter key="use_block_type_exception" value="false"/> <parameter key="except_block_type" value="value_series_end"/> <parameter key="invert_selection" value="false"/> <parameter key="include_special_attributes" value="true"/> <parameter key="method" value="Z-transformation"/> <parameter key="min" value="0.0"/> <parameter key="max" value="1.0"/> <parameter key="allow_negative_values" value="false"/> <description align="center" color="transparent" colored="false" width="126">rescale the range</description> </operator> </process> <?xml version="1.0" encoding="UTF-8"?><process version="9.6.000"> <operator activated="true" class="subprocess" compatibility="9.6.000" expanded="true" height="82" name="Subprocess" width="90" x="581" y="34"> <process expanded="true"> <operator activated="true" class="sort" compatibility="9.6.000" expanded="true" height="82" name="Sort" width="90" x="112" y="34"> <parameter key="attribute_name" value="x"/> <parameter key="sorting_direction" value="increasing"/> </operator> <operator activated="true" class="generate_id" compatibility="9.6.000" expanded="true" height="82" name="Generate ID" width="90" x="246" y="34"> <parameter key="create_nominal_ids" value="false"/> <parameter key="offset" value="0"/> </operator> <operator activated="true" class="generate_attributes" compatibility="9.6.000" expanded="true" height="82" name="Generate Attributes" width="90" x="380" y="34"> <list key="function_descriptions"> <parameter key="INDEX" value="50*(id-1)+1"/> </list> <parameter key="keep_all" value="true"/> </operator> <operator activated="true" class="time_series:equalize_numerical_indices" compatibility="9.6.000" expanded="true" height="82" name="Equalize Numerical Indices" width="90" x="514" y="34"> <parameter key="indices_attribute" value="INDEX"/> <parameter key="equalize_method" value="number of examples and range(start,stop)"/> <parameter key="number_of_examples" value="custom"/> <parameter key="custom_number_of_examples" value="151"/> <parameter key="start_value" value="same as original data"/> <parameter key="custom_start_value" value="0.0"/> <parameter key="stop_value" value="same as original data"/> <parameter key="custom_stop_value" value="100.0"/> <parameter key="step_size_(numerical)" value="1.0"/> <parameter key="replace_type_numerical" value="linear interpolation"/> <parameter key="replace_type_nominal" value="previous value"/> <parameter key="replace_type_date_time" value="previous value"/> <parameter key="replace_value_numerical" value="0.0"/> <parameter key="replace_value_nominal" value="unknown"/> <parameter key="skip_other_missings" value="true"/> <parameter key="replace_infinity" value="true"/> <parameter key="replace_empty_strings" value="true"/> <parameter key="ensure_finite_values" value="true"/> </operator> <operator activated="true" class="select_attributes" compatibility="9.6.000" expanded="true" height="82" name="Select Attributes" width="90" x="715" y="34"> <parameter key="attribute_filter_type" value="subset"/> <parameter key="attribute" value=""/> <parameter key="attributes" value="x|y"/> <parameter key="use_except_expression" value="false"/> <parameter key="value_type" value="attribute_value"/> <parameter key="use_value_type_exception" value="false"/> <parameter key="except_value_type" value="time"/> <parameter key="block_type" value="attribute_block"/> <parameter key="use_block_type_exception" value="false"/> <parameter key="except_block_type" value="value_matrix_row_start"/> <parameter key="invert_selection" value="false"/> <parameter key="include_special_attributes" value="false"/> </operator> <connect from_port="in 1" to_op="Sort" to_port="example set input"/> <connect from_op="Sort" from_port="example set output" to_op="Generate ID" to_port="example set input"/> <connect from_op="Generate ID" from_port="example set output" to_op="Generate Attributes" to_port="example set input"/> <connect from_op="Generate Attributes" from_port="example set output" to_op="Equalize Numerical Indices" to_port="example set"/> <connect from_op="Equalize Numerical Indices" from_port="equalized example set" to_op="Select Attributes" to_port="example set input"/> <connect from_op="Select Attributes" from_port="example set output" to_port="out 1"/> <portSpacing port="source_in 1" spacing="0"/> <portSpacing port="source_in 2" spacing="0"/> <portSpacing port="sink_out 1" spacing="0"/> <portSpacing port="sink_out 2" spacing="0"/> </process> <description align="center" color="transparent" colored="false" width="126">add more points to the training set</description> </operator> </process> <?xml version="1.0" encoding="UTF-8"?><process version="9.6.000"> <operator activated="true" class="multiply" compatibility="9.6.000" expanded="true" height="103" name="Multiply" width="90" x="715" y="34"/> </process> <?xml version="1.0" encoding="UTF-8"?><process version="9.6.000"> <operator activated="true" class="polynomial_regression" compatibility="9.6.000" expanded="true" height="82" name="Polynomial Regression (2)" width="90" x="849" y="238"> <parameter key="max_iterations" value="280"/> <parameter key="replication_factor" value="2"/> <parameter key="max_degree" value="2"/> <parameter key="min_coefficient" value="-10.0"/> <parameter key="max_coefficient" value="10.0"/> <parameter key="use_local_random_seed" value="false"/> <parameter key="local_random_seed" value="23"/> </operator> </process> <?xml version="1.0" encoding="UTF-8"?><process version="9.6.000"> <operator activated="true" class="generate_attributes" compatibility="9.6.000" expanded="true" height="82" name="Generate Attributes (2)" width="90" x="849" y="34"> <list key="function_descriptions"> <parameter key="z" value="x^2"/> </list> <parameter key="keep_all" value="true"/> <description align="center" color="transparent" colored="false" width="126">get quadratic term x^2</description> </operator> </process> <?xml version="1.0" encoding="UTF-8"?><process version="9.6.000"> <operator activated="false" class="concurrency:optimize_parameters_grid" compatibility="9.6.000" expanded="true" height="145" name="Optimize Parameters (Grid)" width="90" x="648" y="289"> <list key="parameters"> <parameter key="Polynomial Regression.max_iterations" value="[1.0;300;30;linear]"/> <parameter key="Polynomial Regression.max_degree" value="[1.0;2;3;linear]"/> <parameter key="Polynomial Regression.replication_factor" value="[1.0;2;3;linear]"/> </list> <parameter key="error_handling" value="fail on error"/> <parameter key="log_performance" value="true"/> <parameter key="log_all_criteria" value="false"/> <parameter key="synchronize" value="false"/> <parameter key="enable_parallel_execution" value="true"/> <process expanded="true"> <operator activated="true" class="concurrency:cross_validation" compatibility="9.6.000" expanded="true" height="145" name="Cross Validation" width="90" x="246" y="34"> <parameter key="split_on_batch_attribute" value="false"/> <parameter key="leave_one_out" value="false"/> <parameter key="number_of_folds" value="5"/> <parameter key="sampling_type" value="automatic"/> <parameter key="use_local_random_seed" value="false"/> <parameter key="local_random_seed" value="1992"/> <parameter key="enable_parallel_execution" value="true"/> <process expanded="true"> <operator activated="true" class="polynomial_regression" compatibility="9.6.000" expanded="true" height="82" name="Polynomial Regression" width="90" x="112" y="34"> <parameter key="max_iterations" value="50"/> <parameter key="replication_factor" value="5"/> <parameter key="max_degree" value="5"/> <parameter key="min_coefficient" value="-10.0"/> <parameter key="max_coefficient" value="10.0"/> <parameter key="use_local_random_seed" value="false"/> <parameter key="local_random_seed" value="23"/> </operator> <connect from_port="training set" to_op="Polynomial Regression" to_port="training set"/> <connect from_op="Polynomial Regression" from_port="model" to_port="model"/> <portSpacing port="source_training set" spacing="0"/> <portSpacing port="sink_model" spacing="0"/> <portSpacing port="sink_through 1" spacing="0"/> </process> <process expanded="true"> <operator activated="true" class="apply_model" compatibility="9.6.000" expanded="true" height="82" name="Apply Model" width="90" x="45" y="34"> <list key="application_parameters"/> <parameter key="create_view" value="false"/> </operator> <operator activated="true" class="performance_regression" compatibility="9.6.000" expanded="true" height="82" name="Performance" width="90" x="179" y="34"> <parameter key="main_criterion" value="first"/> <parameter key="root_mean_squared_error" value="true"/> <parameter key="absolute_error" value="false"/> <parameter key="relative_error" value="false"/> <parameter key="relative_error_lenient" value="false"/> <parameter key="relative_error_strict" value="false"/> <parameter key="normalized_absolute_error" value="false"/> <parameter key="root_relative_squared_error" value="false"/> <parameter key="squared_error" value="false"/> <parameter key="correlation" value="false"/> <parameter key="squared_correlation" value="false"/> <parameter key="prediction_average" value="false"/> <parameter key="spearman_rho" value="false"/> <parameter key="kendall_tau" value="false"/> <parameter key="skip_undefined_labels" value="true"/> <parameter key="use_example_weights" value="true"/> </operator> <connect from_port="model" to_op="Apply Model" to_port="model"/> <connect from_port="test set" to_op="Apply Model" to_port="unlabelled data"/> <connect from_op="Apply Model" from_port="labelled data" to_op="Performance" to_port="labelled data"/> <connect from_op="Performance" from_port="performance" to_port="performance 1"/> <portSpacing port="source_model" spacing="0"/> <portSpacing port="source_test set" spacing="0"/> <portSpacing port="source_through 1" spacing="0"/> <portSpacing port="sink_test set results" spacing="0"/> <portSpacing port="sink_performance 1" spacing="0"/> <portSpacing port="sink_performance 2" spacing="0"/> </process> </operator> <connect from_port="input 1" to_op="Cross Validation" to_port="example set"/> <connect from_op="Cross Validation" from_port="model" to_port="model"/> <connect from_op="Cross Validation" from_port="example set" to_port="output 1"/> <connect from_op="Cross Validation" from_port="performance 1" to_port="performance"/> <portSpacing port="source_input 1" spacing="0"/> <portSpacing port="source_input 2" spacing="0"/> <portSpacing port="sink_performance" spacing="0"/> <portSpacing port="sink_model" spacing="0"/> <portSpacing port="sink_output 1" spacing="0"/> <portSpacing port="sink_output 2" spacing="0"/> </process> </operator> </process> <?xml version="1.0" encoding="UTF-8"?><process version="9.6.000"> <operator activated="true" class="h2o:generalized_linear_model" compatibility="9.3.001" expanded="true" height="124" name="Generalized Linear Model" width="90" x="983" y="34"> <parameter key="family" value="AUTO"/> <parameter key="link" value="family_default"/> <parameter key="solver" value="AUTO"/> <parameter key="reproducible" value="false"/> <parameter key="maximum_number_of_threads" value="4"/> <parameter key="use_regularization" value="false"/> <parameter key="lambda_search" value="false"/> <parameter key="number_of_lambdas" value="0"/> <parameter key="lambda_min_ratio" value="0.0"/> <parameter key="early_stopping" value="true"/> <parameter key="stopping_rounds" value="3"/> <parameter key="stopping_tolerance" value="0.001"/> <parameter key="standardize" value="false"/> <parameter key="non-negative_coefficients" value="false"/> <parameter key="add_intercept" value="true"/> <parameter key="compute_p-values" value="false"/> <parameter key="remove_collinear_columns" value="false"/> <parameter key="missing_values_handling" value="MeanImputation"/> <parameter key="max_iterations" value="0"/> <parameter key="specify_beta_constraints" value="false"/> <list key="beta_constraints"/> <parameter key="max_runtime_seconds" value="0"/> <list key="expert_parameters"/> </operator> </process>These two models are close but I can not guarantee the polynomial will output similar coefficient without normalization
I would strongly suggest to use GLM with new attribute manually created or attributes from Auto Feature Engineer.
Happy Rapid-Mining and Stay Healthy!
YY